From 964e2ee8a53f2e7c8fbe9b2c7c1fa506bb2d6214 Mon Sep 17 00:00:00 2001
From: 0000OOOO0000 <63518686+0000OOOO0000@users.noreply.github.com>
Date: Thu, 16 Jun 2022 01:01:03 +0300
Subject: [PATCH] =?UTF-8?q?XHG.=E2=A0=80=E2=A0=80=E2=A0=80=E2=A0=80?=
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...��ᗴ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀⠀⠀⠀.GHX | 29186 ++++++++++++++++
1 file changed, 29186 insertions(+)
create mode 100644 ◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯ⵙ◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯/◯✤ᴥᗩ◯ⵙ◯ᗩᴥ✤◯/◯ᗱᗴᴥᗩᗯ✤⏀Ⓞᔓᔕ◯ⵙ◯ᔓᔕⓄ⏀✤ᗯᗩᴥᗱᗴ◯/◯ᗝⵈ◯ⵙ◯ⵈᗝ◯/◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯ⵙ◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯/◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯ⵙ◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯/XHG.⠀⠀⠀⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀✤⠀ⵙ⠀ᗩ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀◯⠀ⵙ⠀ᗝ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙏ⠀ⵙ⠀◯⠀ⵙ⠀ᗩ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ꖴ⠀ⵙ⠀✤⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀✤⠀ⵙ⠀ꖴ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᗩ⠀ⵙ⠀◯⠀ⵙ⠀ᙏ⠀ⵙ⠀ᗩ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᗝ⠀ⵙ⠀◯⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᗩ⠀ⵙ⠀✤⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀⠀⠀⠀.GHX
diff --git a/◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯ⵙ◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯/◯✤ᴥᗩ◯ⵙ◯ᗩᴥ✤◯/◯ᗱᗴᴥᗩᗯ✤⏀Ⓞᔓᔕ◯ⵙ◯ᔓᔕⓄ⏀✤ᗯᗩᴥᗱᗴ◯/◯ᗝⵈ◯ⵙ◯ⵈᗝ◯/◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯ⵙ◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯/◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯ⵙ◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯/XHG.⠀⠀⠀⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀✤⠀ⵙ⠀ᗩ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀◯⠀ⵙ⠀ᗝ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙏ⠀ⵙ⠀◯⠀ⵙ⠀ᗩ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ꖴ⠀ⵙ⠀✤⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀✤⠀ⵙ⠀ꖴ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᗩ⠀ⵙ⠀◯⠀ⵙ⠀ᙏ⠀ⵙ⠀ᗩ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᗝ⠀ⵙ⠀◯⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᗩ⠀ⵙ⠀✤⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀⠀⠀⠀.GHX b/◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯ⵙ◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯/◯✤ᴥᗩ◯ⵙ◯ᗩᴥ✤◯/◯ᗱᗴᴥᗩᗯ✤⏀Ⓞᔓᔕ◯ⵙ◯ᔓᔕⓄ⏀✤ᗯᗩᴥᗱᗴ◯/◯ᗝⵈ◯ⵙ◯ⵈᗝ◯/◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯ⵙ◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯/◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯ⵙ◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯/XHG.⠀⠀⠀⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀✤⠀ⵙ⠀ᗩ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀◯⠀ⵙ⠀ᗝ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙏ⠀ⵙ⠀◯⠀ⵙ⠀ᗩ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ꖴ⠀ⵙ⠀✤⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀✤⠀ⵙ⠀ꖴ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᗩ⠀ⵙ⠀◯⠀ⵙ⠀ᙏ⠀ⵙ⠀ᗩ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᗝ⠀ⵙ⠀◯⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᗩ⠀ⵙ⠀✤⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀⠀⠀⠀.GHX
new file mode 100644
index 00000000..39ba3b2b
--- /dev/null
+++ b/◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯ⵙ◯ᗩIᗝI⚭◯⚪◯⚭IᗝIᗩ◯/◯✤ᴥᗩ◯ⵙ◯ᗩᴥ✤◯/◯ᗱᗴᴥᗩᗯ✤⏀Ⓞᔓᔕ◯ⵙ◯ᔓᔕⓄ⏀✤ᗯᗩᴥᗱᗴ◯/◯ᗝⵈ◯ⵙ◯ⵈᗝ◯/◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯ⵙ◯ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ◯⚪◯ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ◯/◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯ⵙ◯ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ◯⚪◯ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ◯/XHG.⠀⠀⠀⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀✤⠀ⵙ⠀ᗩ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀◯⠀ⵙ⠀ᗝ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙏ⠀ⵙ⠀◯⠀ⵙ⠀ᗩ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ꖴ⠀ⵙ⠀✤⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀⠀⠀⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᙁ⠀ⵙ⠀ᗩ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀✤⠀ⵙ⠀ꖴ⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᗩ⠀ⵙ⠀◯⠀ⵙ⠀ᙏ⠀ⵙ⠀ᗩ⠀ⵙ⠀ߦ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᗝ⠀ⵙ⠀◯⠀ⵙ⠀ᑐᑕ⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗯ⠀ⵙ⠀ᗩ⠀ⵙ⠀✤⠀ⵙ⠀ᑎ⠀ⵙ⠀ᴥ⠀ⵙ⠀ᗱᗴ⠀ⵙ⠀ᔓᔕ⠀ⵙ⠀⠀⠀⠀.GHX
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+ <item name="Description" type_name="gh_string" type_code="10">The points plotted on the X Axis which represent the input values</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
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+ <item name="Description" type_name="gh_string" type_code="10">The lines from the graph curves to the Y Axis graph mapped values</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">63bb4bb9-da44-4f8e-8284-9321d002f230</item>
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+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <item name="Description" type_name="gh_string" type_code="10">The points mapped on the Y Axis which represent the graph mapped values</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
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+ </chunks>
+ </chunk>
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+ <item name="Description" type_name="gh_string" type_code="10">The graph boundary background as a surface</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">8a39292d-bf27-45fa-b641-9e61af3087fd</item>
+ <item name="Name" type_name="gh_string" type_code="10">Boundary</item>
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+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">The graph labels as curve outlines</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">94f4b70f-994c-4e81-89e0-4e8c57818b8f</item>
+ <item name="Name" type_name="gh_string" type_code="10">Labels</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Labels</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ </items>
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+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">True for input values outside of the X Axis domain bounds
+False for input values inside of the X Axis domain bounds</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">29d03712-a8e1-44a1-ad57-33a6bec0f5b3</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">Out Of Bounds</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <X>1927</X>
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+ </items>
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+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">True for input values on the X Axis which intersect a graph curve
+False for input values on the X Axis which do not intersect a graph curve</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">2a7a89c4-4910-4ecb-bf2f-4ca1a695fbb5</item>
+ <item name="Name" type_name="gh_string" type_code="10">Intersected</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Intersected</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
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+ <X>1891</X>
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+ <item name="Name" type_name="gh_string" type_code="10">Group</item>
+ </items>
+ <chunks count="1">
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+ <item name="Border" type_name="gh_int32" type_code="3">1</item>
+ <item name="Colour" type_name="gh_drawing_color" type_code="36">
+ <ARGB>150;170;135;255</ARGB>
+ </item>
+ <item name="Description" type_name="gh_string" type_code="10">A group of Grasshopper objects</item>
+ <item name="ID" index="0" type_name="gh_guid" type_code="9">be482996-5742-45ed-b0db-b31948b25ecc</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">0e793369-6e78-49fb-90ed-b51263f573d0</item>
+ <item name="Name" type_name="gh_string" type_code="10">Group</item>
+ <item name="NickName" type_name="gh_string" type_code="10"></item>
+ </items>
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+ <chunk name="Attributes" />
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+ <item name="GUID" type_name="gh_guid" type_code="9">079bd9bd-54a0-41d4-98af-db999015f63d</item>
+ <item name="Name" type_name="gh_string" type_code="10">VB Script</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="10">
+ <item name="AdditionalSource" type_name="gh_string" type_code="10"> Private Function IsSet(ByVal param As String) As Boolean ' Check if an input parameter has data
+ Dim i As Integer = Component.Params.IndexOfInputParam(param)
+ If i > -1 Then
+ Return Component.Params.Input.ElementAt(i).DataType > 1 ' input parameter DataType of 1 means it's not receiving input (internal or external)
+ Else
+ Msg("error", "Input parameter '" & param & "' not found")
+ Return False
+ End If
+ End Function
+
+ Private Sub Msg(ByVal type As String, ByVal msg As String) ' Output an error, warning, or informational message
+ Select Case type
+ Case "error"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Error, msg)
+ Print("Error: " & msg)
+ Case "warning"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Warning, msg)
+ Print("Warning: " & msg)
+ Case "info"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Remark, msg)
+ Print(msg)
+ End Select
+ End Sub
+
+ ' Solve for the m parameter from length and width (reference {1} equation (34), except b = width and K(k) and E(k) should be K(m) and E(m))
+ Private Function SolveMFromLenWid(ByVal L As Double, ByVal w As Double) As Double
+ If w = 0 Then
+ Return Defined.M_ZERO_W ' for the boundry condition width = 0, bypass the function and return the known m value
+ End If
+
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim m As Double
+ Dim cwl As Double
+
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ cwl = 2 * EllipticE(m) / EllipticK(m) - 1 ' calculate w/L with the test value of m
+ If cwl < w / L Then ' compares the calculated w/L with the actual w/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ Return m
+ End Function
+
+ ' Solve for the m parameter from length and height (reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m))
+ ' Note that it's actually possible to find 2 valid values for m (hence 2 width values) at certain height values
+ Private Function SolveMFromLenHt(ByVal L As Double, ByVal h As Double) As List(Of Double)
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim twoWidths As Boolean = h / L >= Defined.DOUBLE_W_HL_RATIO And h / L < Defined.MAX_HL_RATIO ' check to see if h/L is within the range where 2 solutions for the width are possible
+ Dim m As Double
+ Dim mult_m As New List(Of Double)
+ Dim chl As Double
+
+ If twoWidths Then
+ ' find the first of two possible solutions for m with the following limits:
+ lower = Defined.M_DOUBLE_W ' see constants at bottom of script
+ upper = Defined.M_MAXHEIGHT ' see constants at bottom of script
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl > h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ mult_m.Add(m)
+
+ ' then find the second of two possible solutions for m with the following limits:
+ lower = Defined.M_MAXHEIGHT ' see constants at bottom of script
+ upper = 1
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl < h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+
+ If m <= Defined.M_MAX Then ' return this m parameter only if it falls within the maximum useful value (above which the curve breaks down)
+ mult_m.Add(m)
+ End If
+
+ Else
+ ' find the one possible solution for the m parameter
+ upper = Defined.M_DOUBLE_W ' limit the upper end of the search to the maximum value of m for which only one solution exists
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl > h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ mult_m.Add(m)
+ End If
+
+ Return mult_m
+ End Function
+
+ ' Solve for the m parameter from width and height (derived from reference {1} equations (33) and (34) with same notes as above)
+ Private Function SolveMFromWidHt(ByVal w As Double, ByVal h As Double) As Double
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim m As Double
+ Dim cwh As Double
+
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ cwh = (2 * EllipticE(m) - EllipticK(m)) / Math.Sqrt(m) ' calculate w/h with the test value of m
+ If cwh < w / h Then ' compares the calculated w/h with the actual w/h then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+
+ Return m
+ End Function
+
+ ' Calculate length based on height and an m parameter, derived from reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m)
+ Private Function Cal_L(ByVal h As Double, ByVal m As Double) As Double
+ Return h * EllipticK(m) / Math.Sqrt(m)
+ End Function
+
+ ' Calculate width based on length and an m parameter, derived from reference {1} equation (34), except b = width and K(k) and E(k) should be K(m) and E(m)
+ Private Function Cal_W(ByVal L As Double, ByVal m As Double) As Double
+ Return L * (2 * EllipticE(m) / EllipticK(m) - 1)
+ End Function
+
+ ' Calculate height based on length and an m parameter, from reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m)
+ Private Function Cal_H(ByVal L As Double, ByVal m As Double) As Double
+ Return L * Math.Sqrt(m) / EllipticK(m)
+ End Function
+
+ ' Calculate the unique m parameter based on a start tangent angle, from reference {2}, just above equation (9a), that states k = Sin(angle / 2 + Pi / 4),
+ ' but as m = k^2 and due to this script's need for an angle rotated 90° versus the one in reference {1}, the following formula is the result
+ ' New note: verified by reference {4}, pg. 78 at the bottom
+ Private Function Cal_M(ByVal a As Double) As Double
+ Return (1 - Math.Cos(a)) / 2 ' equal to Sin^2(a/2) too
+ End Function
+
+ ' Calculate start tangent angle based on an m parameter, derived from above formula
+ Private Function Cal_A(ByVal m As Double) As Double
+ Return Math.Acos(1 - 2 * m)
+ End Function
+
+ ' This is the heart of this script, taking the found (or specified) length, width, and angle values along with the found m parameter to create
+ ' a list of points that approximate the shape or form of the elastica. It works by finding the x and y coordinates (which are reversed versus
+ ' the original equations (12a) and (12b) from reference {2} due to the 90° difference in orientation) based on the tangent angle along the curve.
+ ' See reference {2} for more details on how they derived it. Note that to simplify things, the algorithm only calculates the points for half of the
+ ' curve, then mirrors those points along the y-axis.
+ Private Function FindBendForm(ByVal L As Double, ByVal w As Double, ByVal m As Double, ByVal ang As Double, ByVal refPln As Plane) As List(Of Point3d)
+ L = L / 2 ' because the below algorithm is based on the formulas in reference {2} for only half of the curve
+ w = w / 2 ' same
+
+ If ang = 0 Then ' if angle (and height) = 0, then simply return the start and end points of the straight line
+ Dim out As New List(Of Point3d)
+ out.Add(refPln.PointAt(w, 0, 0))
+ out.Add(refPln.PointAt(-w, 0, 0))
+ Return out
+ End If
+
+ Dim x As Double
+ Dim y As Double
+ Dim halfCurvePts As New List(Of Point3d)
+ Dim fullCurvePts As New List(Of Point3d)
+ Dim translatedPts As New List(Of Point3d)
+
+ ang -= Math.PI / 2 ' a hack to allow this algorithm to work, since the original curve in paper {2} was rotated 90°
+ Dim angB As Double = ang + (-Math.PI / 2 - ang) / Defined.CURVEDIVS ' angB is the 'lowercase theta' which should be in formula {2}(12b) as the interval
+ ' start [a typo...see equation(3)]. It's necessary to start angB at ang + [interval] instead of just ang due to integration failing at angB = ang
+ halfCurvePts.Add(New Point3d(w, 0, 0)) ' start with this known initial point, as integration will fail when angB = ang
+
+ ' each point {x, y} is calculated from the tangent angle, angB, that occurs at each point (which is why this iterates from ~ang to -pi/2, the known end condition)
+ Do While Math.Round(angB, Defined.ROUNDTO) >= Math.Round(-Math.PI / 2, Defined.ROUNDTO)
+ y = (Math.Sqrt(2) * Math.Sqrt(Math.Sin(ang) - Math.Sin(angB)) * (w + L)) / (2 * EllipticE(m)) ' note that x and y are swapped vs. (12a) and (12b)
+ x = (L / (Math.Sqrt(2) * EllipticK(m))) * Simpson(angB, -Math.PI / 2, 500, ang) ' calculate the Simpson approximation of the integral (function f below)
+ ' over the interval angB ('lowercase theta') to -pi/2. side note: is 500 too few iterations for the Simson algorithm?
+
+ If Math.Round(x, Defined.ROUNDTO) = 0 Then x = 0
+ halfCurvePts.Add(New Point3d(x, y, 0))
+
+ angB += (-Math.PI / 2 - ang) / Defined.CURVEDIVS ' onto the next tangent angle
+ Loop
+
+ ' After finding the x and y values for half of the curve, add the {-x, y} values for the rest of the curve
+ For Each point As Point3d In halfCurvePts
+ If Math.Round(point.X, Defined.ROUNDTO) = 0 Then
+ If Math.Round(point.Y, Defined.ROUNDTO) = 0 Then
+ fullCurvePts.Add(New Point3d(0, 0, 0)) ' special case when width = 0: when x = 0, only duplicate the point when y = 0 too
+ End If
+ Else
+ fullCurvePts.Add(New Point3d(-point.X, point.Y, 0))
+ End If
+ Next
+ halfCurvePts.Reverse
+ fullCurvePts.AddRange(halfCurvePts)
+
+ For Each p As Point3d In fullCurvePts
+ translatedPts.Add(refPln.PointAt(p.X, p.Y, p.Z)) ' translate the points from the reference plane to the world plane
+ Next
+
+ Return translatedPts
+ End Function
+
+ ' Interpolates the points from FindBendForm to create the Elastica curve. Uses start & end tangents for greater accuracy.
+ Private Function MakeCurve(ByVal pts As List(Of Point3d), ByVal ang As Double, ByVal refPln As Plane) As Curve
+ If ang <> 0 Then
+ Dim ts, te As New Vector3d(refPln.XAxis)
+ ts.Rotate(ang, refPln.ZAxis)
+ te.Rotate(-ang, refPln.ZAxis)
+ Return Curve.CreateInterpolatedCurve(pts, 3, CurveKnotStyle.Chord, ts, te) ' 3rd degree curve with 'Chord' Knot Style
+ Else
+ Return Curve.CreateInterpolatedCurve(pts, 3) ' if angle (and height) = 0, then simply interpolate the straight line (no start/end tangents)
+ End If
+ End Function
+
+ ' Implements the Simpson approximation for an integral of function f below
+ Public Function Simpson(a As Double, b As Double, n As Integer, theta As Double) As Double 'n should be an even number
+ Dim j As Integer, s1 As Double, s2 As Double, h As Double
+ h = (b - a) / n
+ s1 = 0
+ s2 = 0
+ For j = 1 To n - 1 Step 2
+ s1 = s1 + fn(a + j * h, theta)
+ Next j
+ For j = 2 To n - 2 Step 2
+ s2 = s2 + fn(a + j * h, theta)
+ Next j
+ Simpson = h / 3 * (fn(a, theta) + 4 * s1 + 2 * s2 + fn(b, theta))
+ End Function
+
+ ' Specific calculation for the above integration
+ Public Function fn(x As Double, theta As Double) As Double
+ fn = Math.Sin(x) / (Math.Sqrt(Math.Sin(theta) - Math.Sin(x))) ' from reference {2} formula (12b)
+ End Function
+
+
+ ' Return the Complete Elliptic integral of the 1st kind
+ ' Abramowitz and Stegun p.591, formula 17.3.11
+ ' Code from http://www.codeproject.com/Articles/566614/Elliptic-integrals
+ Public Function EllipticK(ByVal m As Double) As Double
+ Dim sum, term, above, below As Double
+ sum = 1
+ term = 1
+ above = 1
+ below = 2
+
+ For i As Integer = 1 To 100
+ term *= above / below
+ sum += Math.Pow(m, i) * Math.Pow(term, 2)
+ above += 2
+ below += 2
+ Next
+ sum *= 0.5 * Math.PI
+ Return sum
+ End Function
+
+
+ ' Return the Complete Elliptic integral of the 2nd kind
+ ' Abramowitz and Stegun p.591, formula 17.3.12
+ ' Code from http://www.codeproject.com/Articles/566614/Elliptic-integrals
+ Public Function EllipticE(ByVal m As Double) As Double
+ Dim sum, term, above, below As Double
+ sum = 1
+ term = 1
+ above = 1
+ below = 2
+
+ For i As Integer = 1 To 100
+ term *= above / below
+ sum -= Math.Pow(m, i) * Math.Pow(term, 2) / above
+ above += 2
+ below += 2
+ Next
+ sum *= 0.5 * Math.PI
+ Return sum
+ End Function
+
+ Friend Partial NotInheritable Class Defined
+ Private Sub New()
+ End Sub
+
+ ' Note: most of these values for m and h/L ratio were found with Wolfram Alpha and either specific intercepts (x=0) or local minima/maxima. They should be constant.
+ Public Const M_SKETCHY As Double = 0.95 ' value of the m parameter where the curvature near the ends of the curve gets wonky
+ Public Const M_MAX As Double = 0.993 ' maximum useful value of the m parameter, above which this algorithm for the form of the curve breaks down
+ Public Const M_ZERO_W As Double = 0.826114765984970336 ' value of the m parameter when width = 0
+ Public Const M_MAXHEIGHT As Double = 0.701327460663101223 ' value of the m parameter at maximum possible height of the bent rod/wire
+ Public Const M_DOUBLE_W As Double = 0.180254422335013983 ' minimum value of the m parameter when two width values are possible for a given height and length
+ Public Const DOUBLE_W_HL_RATIO As Double = 0.257342117984635757 ' value of the height/length ratio above which there are two possible width values
+ Public Const MAX_HL_RATIO As Double = 0.403140189705650243 ' maximum possible value of the height/length ratio
+
+ Public Const MAXERR As Double = 0.0000000001 ' error tolerance
+ Public Const MAXIT As Integer = 100 ' maximum number of iterations
+ Public Const ROUNDTO As Integer = 10 ' number of decimal places to round off to
+ Public Const CURVEDIVS As Integer = 50 ' number of sample points for building the curve (or half-curve as it were)
+ End Class</item>
+ <item name="Description" type_name="gh_string" type_code="10">A VB.NET scriptable component</item>
+ <item name="EditorPosition" type_name="gh_drawing_point" type_code="30">
+ <X>98</X>
+ <Y>86</Y>
+ </item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">be482996-5742-45ed-b0db-b31948b25ecc</item>
+ <item name="Name" type_name="gh_string" type_code="10">VB Script</item>
+ <item name="NickName" type_name="gh_string" type_code="10">VB</item>
+ <item name="OutParameter" type_name="gh_bool" type_code="1">true</item>
+ <item name="ReferenceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="ScriptSource" type_name="gh_string" type_code="10"> ' -----------------------------------------------------------------
+ ' Elastic Bending Script by Will McElwain
+ ' Created February 2014
+ '
+ ' DESCRIPTION:
+ ' This beast creates the so-called 'elastica curve', the shape a long, thin rod or wire makes when it is bent elastically (i.e. not permanently). In this case, force
+ ' is assumed to only be applied horizontally (which would be in line with the rod at rest) and both ends are assumed to be pinned or hinged meaning they are free
+ ' to rotate (as opposed to clamped, when the end tangent angle is fixed, usually horizontally). An interesting finding is that it doesn't matter what the material or
+ ' cross-sectional area is, as long as they're uniform along the entire length. Everything makes the same shape when bent as long as it doesn't cross the threshold
+ ' from elastic to plastic (permanent) deformation (I don't bother to find that limit here, but can be found if the yield stress for a material is known).
+ '
+ ' Key to the formulas used in this script are elliptic integrals, specifically K(m), the complete elliptic integral of the first kind, and E(m), the complete elliptic
+ ' integral of the second kind. There was a lot of confusion over the 'm' and 'k' parameters for these functions, as some people use them interchangeably, but they are
+ ' not the same. m = k^2 (thus k = Sqrt(m)). I try to use the 'm' parameter exclusively to avoid this confusion. Note that there is a unique 'm' parameter for every
+ ' configuration/shape of the elastica curve.
+ '
+ ' This script tries to find that unique 'm' parameter based on the inputs. The algorithm starts with a test version of m, evaluates an expression, say 2*E(m)/K(m)-1,
+ ' then compares the result to what it should be (in this case, a known width/length ratio). Iterate until the correct m is found. Once we have m, we can then calculate
+ ' all of the other unknowns, then find points that lie on that curve, then interpolate those points for the actual curve. You can also use Wolfram|Alpha as I did to
+ ' find the m parameter based on the equations in this script (example here: http://tiny.cc/t4tpbx for when say width=45.2 and length=67.1).
+ '
+ ' Other notes:
+ ' * This script works with negative values for width, which will creat a self-intersecting curve (as it should). The curvature of the elastica starts to break down around
+ ' m=0.95 (~154°), but this script will continue to work until M_MAX, m=0.993 (~169°). If you wish to ignore self-intersecting curves, set ignoreSelfIntersecting to True
+ ' * When the only known values are length and height, it is actually possible for certain ratios of height to length to have two valid m values (thus 2 possible widths
+ ' and angles). This script will return them both.
+ ' * Only the first two valid parameters (of the required ones) will be used, meaning if all four are connected (length, width or a PtB, height, and angle), this script will
+ ' only use length and width (or a PtB).
+ ' * Depending on the magnitude of your inputs (say if they're really small, like if length < 10), you might have to increase the constant ROUNDTO at the bottom
+ '
+ ' REFERENCES:
+ ' {1} "The elastic rod" by M.E. Pacheco Q. & E. Pina, http://www.scielo.org.mx/pdf/rmfe/v53n2/v53n2a8.pdf
+ ' {2} "An experiment in nonlinear beam theory" by A. Valiente, http://www.deepdyve.com/lp/doc/I3lwnxdfGz , also here: http://tiny.cc/Valiente_AEiNBT
+ ' {3} "Snap buckling, writhing and Loop formation In twisted rods" by V.G.A. GOSS, http://myweb.lsbu.ac.uk/~gossga/thesisFinal.pdf
+ ' {4} "Theory of Elastic Stability" by Stephen Timoshenko, http://www.scribd.com/doc/50402462/Timoshenko-Theory-of-Elastic-Stability (start on p. 76)
+ '
+ ' INPUT:
+ ' PtA - First anchor point (required)
+ ' PtB - Second anchor point (optional, though 2 out of the 4--length, width, height, angle--need to be specified)
+ ' [note that PtB can be the same as PtA (meaning width would be zero)]
+ ' [also note that if a different width is additionally specified that's not equal to the distance between PtA and PtB, then the end point will not equal PtB anymore]
+ ' Pln - Plane of the bent rod/wire, which bends up in the +y direction. The line between PtA and PtB (if specified) must be parallel to the x-axis of this plane
+ '
+ ' ** 2 of the following 4 need to be specified **
+ ' Len - Length of the rod/wire, which needs to be > 0
+ ' Wid - Width between the endpoints of the curve [note: if PtB is specified in addition, and distance between PtA and PtB <> width, the end point will be relocated
+ ' Ht - Height of the bent rod/wire (when negative, curve will bend downward, relative to the input plane, instead)
+ ' Ang - Inner departure angle or tangent angle (in radians) at the ends of the bent rod/wire. Set up so as width approaches length (thus height approaches zero), angle approaches zero
+ '
+ ' * Following variables only needed for optional calculating of bending force, not for shape of curve.
+ ' E - Young's modulus (modulus of elasticity) in GPa (=N/m^2) (material-specific. for example, 7075 aluminum is roughly 71.7 GPa)
+ ' I - Second moment of area (or area moment of inertia) in m^4 (cross-section-specific. for example, a hollow rod
+ ' would have I = pi * (outer_diameter^4 - inner_diameter^4) / 32
+ ' Note: E*I is also known as flexural rigidity or bending stiffness
+ '
+ ' OUTPUT:
+ ' out - only for debugging messages
+ ' Pts - the list of points that approximate the shape of the elastica
+ ' Crv - the 3rd-degree curve interpolated from those points (with accurate start & end tangents)
+ ' L - the length of the rod/wire
+ ' W - the distance (width) between the endpoints of the rod/wire
+ ' H - the height of the bent rod/wire
+ ' A - the tangent angle at the (start) end of the rod/wire
+ ' F - the force needed to hold the rod/wire in a specific shape (based on the material properties & cross-section) **be sure your units for 'I' match your units for the
+ ' rest of your inputs (length, width, etc.). Also note that the critical buckling load (force) that makes the rod/wire start to bend can be found at height=0
+ '
+ ' THANKS TO:
+ ' Mårten Nettelbladt (thegeometryofbending.blogspot.com)
+ ' Daniel Piker (Kangaroo plugin)
+ ' David Rutten (Grasshopper guru)
+ ' Euler & Bernoulli (the O.G.'s)
+ '
+ ' -----------------------------------------------------------------
+
+ Dim ignoreSelfIntersecting As Boolean = False ' set to True if you don't want to output curves where width < 0, which creates a self-intersecting curve
+
+ Dim inCt As Integer = 0 ' count the number of required parameters that are receiving data
+ Dim length As Double
+ Dim width As System.Object = Nothing ' need to set as Nothing so we can check if it has been assigned a value later
+ Dim height As Double
+ Dim angle As Double
+ Dim m As Double
+ Dim multiple_m As New List(Of Double)
+ Dim AtoB As Line
+ Dim flip_H As Boolean = False ' if height is negative, this flag will be set
+ Dim flip_A As Boolean = False ' if angle is negative, this flag will be set
+
+ If Not IsSet("Pln") Then
+ Msg("error", "Base plane is not set")
+ Return
+ End If
+
+ If Not IsSet("PtA") Then
+ Msg("error", "Point A is not set")
+ Return
+ End If
+
+ If Math.Round(Pln.DistanceTo(PtA), Defined.ROUNDTO) <> 0 Then
+ Msg("error", "Point A is not on the base plane")
+ Return
+ End If
+
+ Dim refPlane As Plane = Pln ' create a reference plane = input plane and set the origin of it to PtA in case PtA isn't the origin already
+ refPlane.Origin = PtA
+
+ If IsSet("PtB") Then
+ If Math.Round(Pln.DistanceTo(PtB), Defined.ROUNDTO) <> 0 Then
+ Msg("error", "Point B is not on the base plane")
+ Return
+ End If
+
+ AtoB = New Line(PtA, PtB)
+ If AtoB.Length <> 0 And Not AtoB.Direction.IsPerpendicularTo(Pln.YAxis) Then
+ Msg("error", "The line between PtA and PtB is not perpendicular to the Y-axis of the specified plane")
+ Return
+ End If
+
+ inCt += 1
+ If IsSet("Wid") Then Msg("info", "Wid will override the distance between PtA and PtB. If you do not want this to happen, disconnect PtB or Wid.")
+
+ width = PtA.DistanceTo(PtB) ' get the width (distance) between PtA and PtB
+
+ Dim refPtB As Point3d
+ refPlane.RemapToPlaneSpace(PtB, refPtB)
+ If refPtB.X < 0 Then width = -width ' check if PtB is to the left of PtA...if so, width is negative
+ End If
+
+ If IsSet("Len") Then inCt += 1
+ If IsSet("Wid") Then inCt += 1
+ If IsSet("Ht") Then inCt += 1
+ If IsSet("Ang") Then inCt += 1
+ If inCt > 2 Then Msg("info", "More parameters set than are required (out of length, width, height, angle). Only using the first two valid ones.")
+
+ ' check for connected/specified inputs. note: only the first two that it comes across will be used
+ If IsSet("Len") Then ' if length is specified then...
+ If Len <= 0 Then
+ Msg("error", "Length cannot be negative or zero")
+ Return
+ End If
+ If IsSet("Wid") Then ' find height & angle based on length and specified width
+ If Wid > Len Then
+ Msg("error", "Width is greater than length")
+ Return
+ End If
+ If Wid = Len Then ' skip the solver and set the known values
+ height = 0
+ m = 0
+ angle = 0
+ width = Wid
+ Else
+ m = SolveMFromLenWid(Len, Wid)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ width = Wid
+ End If
+
+ Else If width IsNot Nothing Then ' find height & angle based on length and calculated width (distance between PtA and PtB)
+ If width > Len Then
+ Msg("error", "Width is greater than length")
+ Return
+ End If
+ If width = Len Then ' skip the solver and set the known values
+ height = 0
+ m = 0
+ angle = 0
+ Else
+ m = SolveMFromLenWid(Len, width)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+
+ Else If IsSet("Ht") Then ' find width & angle based on length and height ** possible to return 2 results **
+ If Math.Abs(Ht / Len) > Defined.MAX_HL_RATIO Then
+ Msg("error", "Height not possible with given length")
+ Return
+ End If
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ width = Len
+ angle = 0
+ Else
+ multiple_m = SolveMFromLenHt(Len, Ht) ' note that it's possible for two values of m to be found if height is close to max height
+ If multiple_m.Count = 1 Then ' if there's only one m value returned, calculate the width & angle here. we'll deal with multiple m values later
+ m = multiple_m.Item(0)
+ width = Cal_W(Len, m) ' L * (2 * E(m) / K(m) - 1)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find width & height based on length and angle
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ width = Len
+ height = 0
+ Else
+ width = Cal_W(Len, m) ' L * (2 * E(m) / K(m) - 1)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to length")
+ Return
+ End If
+ length = Len
+
+ Else If IsSet("Wid") Then ' if width is specified then...
+ If IsSet("Ht") Then ' find length & angle based on specified width and height
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ length = Wid
+ angle = 0
+ Else
+ m = SolveMFromWidHt(Wid, Ht)
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find length & height based on specified width and angle
+ If Wid = 0 Then
+ Msg("error", "Curve not possible with width = 0 and an angle as inputs")
+ Return
+ End If
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ length = Wid
+ height = 0
+ Else
+ length = Wid / (2 * EllipticE(m) / EllipticK(m) - 1)
+ If length < 0 Then
+ Msg("error", "Curve not possible at specified width and angle (calculated length is negative)")
+ Return
+ End If
+ height = Cal_H(length, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to width (Wid)")
+ Return
+ End If
+ width = Wid
+
+ Else If width IsNot Nothing Then ' if width is determined by PtA and PtB then...
+ If IsSet("Ht") Then ' find length & angle based on calculated width and height
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ length = width
+ angle = 0
+ Else
+ m = SolveMFromWidHt(width, Ht)
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find length & height based on calculated width and angle
+ If width = 0 Then
+ Msg("error", "Curve not possible with width = 0 and an angle as inputs")
+ Return
+ End If
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ length = width
+ height = 0
+ Else
+ length = width / (2 * EllipticE(m) / EllipticK(m) - 1)
+ If length < 0 Then
+ Msg("error", "Curve not possible at specified width and angle (calculated length is negative)")
+ Return
+ End If
+ height = Cal_H(length, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to PtA and PtB")
+ Return
+ End If
+
+ Else If IsSet("Ht") Then ' if height is specified then...
+ If IsSet("Ang") Then ' find length & width based on height and angle
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_H = True
+ flip_A = True
+ End If
+ If Ht = 0 Then
+ Msg("error", "Height can't = 0 if only height and angle are specified")
+ Return
+ Else
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = Not flip_A
+ flip_H = Not flip_H
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then
+ Msg("error", "Angle can't = 0 if only height and angle are specified")
+ Return
+ Else
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ width = Cal_W(length, m) ' L * (2 * E(m) / K(m) - 1)
+ End If
+ angle = Ang
+ End If
+ height = Ht
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to height")
+ Return
+ End If
+
+ Else If IsSet("Ang") Then
+ Msg("error", "Need to specify one more parameter in addition to angle")
+ Return
+ Else
+ Msg("error", "Need to specify two of the four parameters: length, width (or PtB), height, and angle")
+ Return
+ End If
+
+ If m > Defined.M_MAX Then
+ Msg("error", "Form of curve not solvable with current algorithm and given inputs")
+ Return
+ End If
+
+ refPlane.Origin = refPlane.PointAt(width / 2, 0, 0) ' adjust the origin of the reference plane so that the curve is centered about the y-axis (start of the curve is at x = -width/2)
+
+ If multiple_m.Count > 1 Then ' if there is more than one m value returned, calculate the width, angle, and curve for each
+ Dim multi_pts As New DataTree(Of Point3d)
+ Dim multi_crv As New List(Of Curve)
+ Dim tmp_pts As New List(Of Point3d)
+ Dim multi_W, multi_A, multi_F As New List(Of Double)
+ Dim j As Integer = 0 ' used for creating a new branch (GH_Path) for storing pts which is itself a list of points
+
+ For Each m_val As Double In multiple_m
+ width = Cal_W(length, m_val) 'length * (2 * EllipticE(m_val) / EllipticK(m_val) - 1)
+
+ If width < 0 And ignoreSelfIntersecting Then
+ Msg("warning", "One curve is self-intersecting. To enable these, set ignoreSelfIntersecting to False")
+ Continue For
+ End If
+
+ If m_val >= Defined.M_SKETCHY Then Msg("info", "Accuracy of the curve whose width = " & Math.Round(width, 4) & " is not guaranteed")
+
+ angle = Cal_A(m_val) 'Math.Asin(2 * m_val - 1)
+ refPlane.Origin = refPlane.PointAt(width / 2, 0, 0) ' adjust the origin of the reference plane so that the curve is centered about the y-axis (start of the curve is at x = -width/2)
+
+ tmp_pts = FindBendForm(length, width, m_val, angle, refPlane)
+ multi_pts.AddRange(tmp_pts, New GH_Path(j))
+ multi_crv.Add(MakeCurve(tmp_pts, angle, refPlane))
+
+ multi_W.Add(width)
+ If flip_A Then angle = -angle
+ multi_A.Add(angle)
+
+ E = E * 10 ^ 9 ' Young's modulus input E is in GPa, so we convert to Pa here (= N/m^2)
+ multi_F.Add(EllipticK(m_val) ^ 2 * E * I / length ^ 2) ' from reference {4} pg. 79
+
+ j += 1
+ refPlane.Origin = PtA ' reset the reference plane origin to PtA for the next m_val
+ 'Print("length=" & length & ", width=" & width & ", height=" & height & ", angle=" & angle & ", m=" & m_val & ", k=" & Math.Sqrt(m_val) & ", w/L=" & width / length & ", h/L=" & height / length & ", w/h=" & width / height)
+ Next
+
+ ' assign the outputs
+ Pts = multi_pts
+ Crv = multi_crv
+ L = length
+ W = multi_W
+ If flip_H Then height = -height
+ H = height
+ A = multi_A
+ F = multi_F
+
+ Else ' only deal with the single m value
+ If m >= Defined.M_SKETCHY Then Msg("info", "Accuracy of the curve at these parameters is not guaranteed")
+
+ If width < 0 And ignoreSelfIntersecting Then
+ Msg("error", "Curve is self-intersecting. To enable these, set ignoreSelfIntersecting to False")
+ Return
+ End If
+
+ Pts = FindBendForm(length, width, m, angle, refPlane)
+ Crv = MakeCurve(pts, angle, refPlane)
+ L = length
+ W = width
+ If flip_H Then height = -height
+ H = height
+ If flip_A Then angle = -angle
+ A = angle
+
+ E = E * 10 ^ 9 ' Young's modulus input E is in GPa, so we convert to Pa here (= N/m^2)
+ F = EllipticK(m) ^ 2 * E * I / length ^ 2 ' from reference {4} pg. 79. Note: the critical buckling (that makes the rod/wire start to bend) can be found at height=0 (width=length)
+
+ 'height = Math.Sqrt(((2 * Len / 5) ^ 2 - ((Wid - Len / 5) / 2) ^ 2) ' quick approximation discovered by Mårten of 'Geometry of Bending' fame ( http://tiny.cc/it2pbx )
+ 'width = (Len +/- 2 * Math.Sqrt(4 * Len ^ 2 - 25 * Ht ^ 2)) / 5 ' derived from above
+ 'length = (2 * Math.Sqrt(15 * Ht ^ 2 + 4 * Wid ^ 2) - Wid) / 3 ' derived from above
+
+ 'Print("length=" & length & ", width=" & width & ", height=" & height & ", angle=" & angle & ", m=" & m & ", k=" & Math.Sqrt(m) & ", w/L=" & width / length & ", h/L=" & height / length & ", w/h=" & width / height)
+ End If
+</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>471</X>
+ <Y>731</Y>
+ <W>69</W>
+ <H>184</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>507</X>
+ <Y>823</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="ParameterData">
+ <items count="19">
+ <item name="InputCount" type_name="gh_int32" type_code="3">9</item>
+ <item name="InputId" index="0" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="1" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="2" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="3" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="4" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="5" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="6" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="7" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="8" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="OutputCount" type_name="gh_int32" type_code="3">8</item>
+ <item name="OutputId" index="0" type_name="gh_guid" type_code="9">3ede854e-c753-40eb-84cb-b48008f14fd4</item>
+ <item name="OutputId" index="1" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="2" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="3" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="4" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="5" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="6" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="7" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ </items>
+ <chunks count="17">
+ <chunk name="InputParam" index="0">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable PtA</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">59449ef9-05ed-4dc9-8226-c71140ebee0e</item>
+ <item name="Name" type_name="gh_string" type_code="10">PtA</item>
+ <item name="NickName" type_name="gh_string" type_code="10">PtA</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">185356cd-7c2c-43be-929c-08664fead7b6</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">e1937b56-b1da-4c12-8bd8-e34ee81746ef</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>733</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>743</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="1">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable PtB</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">dcfecc5a-a797-4dd5-8113-7ff42a34b690</item>
+ <item name="Name" type_name="gh_string" type_code="10">PtB</item>
+ <item name="NickName" type_name="gh_string" type_code="10">PtB</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">3650af54-be61-49e3-84ef-0d855566cb94</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">e1937b56-b1da-4c12-8bd8-e34ee81746ef</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>753</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>763</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="2">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Pln</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">e5baa4bf-8832-464d-b509-5e5a63a6c1f7</item>
+ <item name="Name" type_name="gh_string" type_code="10">Pln</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Pln</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">553f31ec-0f72-481e-ab04-97626f07c43a</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">3897522d-58e9-4d60-b38c-978ddacfedd8</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>773</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
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+ <X>484</X>
+ <Y>783</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="3">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Len</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">109dbfe4-0341-4971-89fa-f5d18de07927</item>
+ <item name="Name" type_name="gh_string" type_code="10">Len</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Len</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>793</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>803</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="4">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Wid</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">9f556d24-607a-43ea-9776-93ac44530b2d</item>
+ <item name="Name" type_name="gh_string" type_code="10">Wid</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Wid</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>813</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>823</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="5">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Ht</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">35c2e17b-323c-4f1c-bf60-0e6dfbd26156</item>
+ <item name="Name" type_name="gh_string" type_code="10">Ht</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Ht</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>833</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
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+ <X>484</X>
+ <Y>843</Y>
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+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="6">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Ang</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">40ffc963-a05b-46d6-8714-34be65128aff</item>
+ <item name="Name" type_name="gh_string" type_code="10">Ang</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Ang</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">f8e31412-714a-4cc1-bfef-678fe31bf9eb</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>853</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>863</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="7">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable E</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">d6304781-6e12-4d73-a7f3-998a65ee405e</item>
+ <item name="Name" type_name="gh_string" type_code="10">E</item>
+ <item name="NickName" type_name="gh_string" type_code="10">E</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
+ <Y>873</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>883</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="8">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable I</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">bd4895e2-5742-4cbf-83da-9c7d2e49c01e</item>
+ <item name="Name" type_name="gh_string" type_code="10">I</item>
+ <item name="NickName" type_name="gh_string" type_code="10">I</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
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+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>473</X>
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+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>484</X>
+ <Y>903</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="0">
+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">Print, Reflect and Error streams</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f28f837e-8c12-4625-8cb7-328675d707f4</item>
+ <item name="Name" type_name="gh_string" type_code="10">out</item>
+ <item name="NickName" type_name="gh_string" type_code="10">out</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>519</X>
+ <Y>733</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>528.5</X>
+ <Y>744.25</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="1">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Pts</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">e9b2febf-f54f-4469-a015-c2bac110b4a3</item>
+ <item name="Name" type_name="gh_string" type_code="10">Pts</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Pts</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>519</X>
+ <Y>755</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>528.5</X>
+ <Y>766.75</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="2">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Crv</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a20a05cc-1099-41a9-86c6-1cb13c534ffc</item>
+ <item name="Name" type_name="gh_string" type_code="10">Crv</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Crv</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
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+ <item name="Name" type_name="gh_string" type_code="10">L</item>
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+ <item name="Name" type_name="gh_string" type_code="10">W</item>
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+ <item name="Name" type_name="gh_string" type_code="10">F</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Number Slider</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Number Slider</item>
+ <item name="NickName" type_name="gh_string" type_code="10">width</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Radians</item>
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+ <item name="Name" type_name="gh_string" type_code="10">X coordinate</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Y coordinate</item>
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+ <item name="Description" type_name="gh_string" type_code="10">Numeric domain between {A} and {B}</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">196cbbe7-089b-4b6f-8268-5a1a27de1f26</item>
+ <item name="Name" type_name="gh_string" type_code="10">Domain</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Domain</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>851</X>
+ <Y>1213</Y>
+ <W>38</W>
+ <H>40</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>870</X>
+ <Y>1233</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
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+ <item name="GUID" type_name="gh_guid" type_code="9">33bcf975-a0b2-4b54-99fd-585c893b9e88</item>
+ <item name="Name" type_name="gh_string" type_code="10">Digit Scroller</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Numeric scroller for single numbers</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">af3fb1cd-4a6d-4dc8-92ce-9498185187cf</item>
+ <item name="Name" type_name="gh_string" type_code="10">Digit Scroller</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Digit Scroller</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Scroller">
+ <items count="5">
+ <item name="Digits" type_name="gh_int32" type_code="3">12</item>
+ <item name="Prefix" type_name="gh_string" type_code="10">Digit Scroller</item>
+ <item name="Radix" type_name="gh_int32" type_code="3">3</item>
+ <item name="Suffix" type_name="gh_string" type_code="10"></item>
+ <item name="Value" type_name="gh_decimal" type_code="7">85.300000000</item>
+ </items>
+ </chunk>
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1047</X>
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+ <H>20</H>
+ </item>
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+ </chunk>
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+ <item name="GUID" type_name="gh_guid" type_code="9">7376fe41-74ec-497e-b367-1ffe5072608b</item>
+ <item name="Name" type_name="gh_string" type_code="10">Curvature Graph</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="5">
+ <item name="Description" type_name="gh_string" type_code="10">Draws Rhino Curvature Graphs.</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">b044fc47-2218-43a9-a3b0-2df6397c7b5f</item>
+ <item name="Name" type_name="gh_string" type_code="10">Curvature Graph</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Curvature Graph</item>
+ </items>
+ <chunks count="4">
+ <chunk name="Attributes">
+ <items count="2">
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+ <W>65</W>
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+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ </items>
+ </chunk>
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+ <items count="8">
+ <item name="Description" type_name="gh_string" type_code="10">Curve for Curvature graph display</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">46611437-aad9-4467-8439-44ec9ae87f7f</item>
+ <item name="Name" type_name="gh_string" type_code="10">Curve</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Curve</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
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+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1390.5</X>
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+ </items>
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+ </chunk>
+ <chunk name="param_input" index="1">
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+ <item name="Description" type_name="gh_string" type_code="10">Sampling density of the Graph</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">101641d2-b0bd-4e14-8cf1-608b5c0f42ed</item>
+ <item name="Name" type_name="gh_string" type_code="10">Density</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Density</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
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+ <item name="Path" type_name="gh_string" type_code="10">{0}</item>
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+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">Scale of graph</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">1e907d78-b6c0-4b9e-bf28-59e5523809cc</item>
+ <item name="Name" type_name="gh_string" type_code="10">Scale</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Scale</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">af3fb1cd-4a6d-4dc8-92ce-9498185187cf</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ </items>
+ <chunks count="2">
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+ </items>
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+ <item name="number" type_name="gh_int32" type_code="3">105</item>
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+ <item name="GUID" type_name="gh_guid" type_code="9">fb6aba99-fead-4e42-b5d8-c6de5ff90ea6</item>
+ <item name="Name" type_name="gh_string" type_code="10">DotNET VB Script (LEGACY)</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">A VB.NET scriptable component</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">adb123dc-4c8b-4d8e-b8af-465911caa3a4</item>
+ <item name="Name" type_name="gh_string" type_code="10">DotNET VB Script (LEGACY)</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Turtle</item>
+ <item name="ReferenceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="ScriptSource" type_name="gh_string" type_code="10"> Dim i As Integer
+ Dim dir As New On3dVector(1, 0, 0)
+ Dim pos As New On3dVector(0, 0, 0)
+ Dim axis As New On3dVector(0, 0, 1)
+ Dim pnts As New List(Of On3dVector)
+
+ pnts.Add(pos)
+
+ For i = 0 To Forward.Count() - 1
+ Dim P As New On3dVector
+ dir.Rotate(Left(i), axis)
+ P = dir * Forward(i) + pnts(i)
+ pnts.Add(P)
+ Next
+
+ Points = pnts</item>
+ </items>
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+ <item name="Optional" index="0" type_name="gh_bool" type_code="1">true</item>
+ <item name="Optional" index="1" type_name="gh_bool" type_code="1">true</item>
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+ <item name="Description" index="0" type_name="gh_string" type_code="10">Print, Reflect and Error streams</item>
+ <item name="Description" index="1" type_name="gh_string" type_code="10">Output parameter Points</item>
+ <item name="ID" index="0" type_name="gh_guid" type_code="9">3ede854e-c753-40eb-84cb-b48008f14fd4</item>
+ <item name="ID" index="1" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
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+ <item name="Mutable" index="1" type_name="gh_bool" type_code="1">true</item>
+ <item name="Name" index="0" type_name="gh_string" type_code="10">Output</item>
+ <item name="Name" index="1" type_name="gh_string" type_code="10">Points</item>
+ <item name="Optional" index="0" type_name="gh_bool" type_code="1">false</item>
+ <item name="Optional" index="1" type_name="gh_bool" type_code="1">false</item>
+ </items>
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+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">false</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Forward</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">64ea07bd-2ad8-4674-abc3-2e5035e25438</item>
+ <item name="Name" type_name="gh_string" type_code="10">Forward</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Forward</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">1</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
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+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
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+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">false</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f3a9ae4c-2ef8-4f61-a3d6-a8cc805154cb</item>
+ <item name="Name" type_name="gh_string" type_code="10">Left</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">out</item>
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+ </chunks>
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+ <chunk name="param_output" index="1">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Points</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">8c6309b7-19ef-4990-a24c-6a9cd29aedde</item>
+ <item name="Name" type_name="gh_string" type_code="10">Points</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Points</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">e64c5fb1-845c-4ab1-8911-5f338516ba67</item>
+ <item name="Name" type_name="gh_string" type_code="10">Series</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="5">
+ <item name="Description" type_name="gh_string" type_code="10">Create a series of numbers.</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">0cb9ecff-ea56-4e17-b511-9bbc9d37213d</item>
+ <item name="Name" type_name="gh_string" type_code="10">Series</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Series</item>
+ </items>
+ <chunks count="5">
+ <chunk name="Attributes">
+ <items count="2">
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+ <Y>114</Y>
+ <W>49</W>
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+ </item>
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+ </item>
+ </items>
+ </chunk>
+ <chunk name="param_input" index="0">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">First number in the series</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">cd21e6f4-b907-4df3-b15f-9636506736c4</item>
+ <item name="Name" type_name="gh_string" type_code="10">Start</item>
+ <item name="NickName" type_name="gh_string" type_code="10">S</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>461</X>
+ <Y>116</Y>
+ <W>11</W>
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+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>466.5</X>
+ <Y>126</Y>
+ </item>
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+ <item name="Name" type_name="gh_string" type_code="10">Parameter</item>
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+ <items count="12">
+ <item name="AdditionalSource" type_name="gh_string" type_code="10"> Private Function IsSet(ByVal param As String) As Boolean ' Check if an input parameter has data
+ Dim i As Integer = Component.Params.IndexOfInputParam(param)
+ If i > -1 Then
+ Return Component.Params.Input.ElementAt(i).DataType > 1 ' input parameter DataType of 1 means it's not receiving input (internal or external)
+ Else
+ Msg("error", "Input parameter '" & param & "' not found")
+ Return False
+ End If
+ End Function
+
+ Private Sub Msg(ByVal type As String, ByVal msg As String) ' Output an error, warning, or informational message
+ Select Case type
+ Case "error"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Error, msg)
+ Print("Error: " & msg)
+ Case "warning"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Warning, msg)
+ Print("Warning: " & msg)
+ Case "info"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Remark, msg)
+ Print(msg)
+ End Select
+ End Sub
+
+ ' Solve for the m parameter from length and width (reference {1} equation (34), except b = width and K(k) and E(k) should be K(m) and E(m))
+ Private Function SolveMFromLenWid(ByVal L As Double, ByVal w As Double) As Double
+ If w = 0 Then
+ Return Defined.M_ZERO_W ' for the boundry condition width = 0, bypass the function and return the known m value
+ End If
+
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim m As Double
+ Dim cwl As Double
+
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ cwl = 2 * EllipticE(m) / EllipticK(m) - 1 ' calculate w/L with the test value of m
+ If cwl < w / L Then ' compares the calculated w/L with the actual w/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ Return m
+ End Function
+
+ ' Solve for the m parameter from length and height (reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m))
+ ' Note that it's actually possible to find 2 valid values for m (hence 2 width values) at certain height values
+ Private Function SolveMFromLenHt(ByVal L As Double, ByVal h As Double) As List(Of Double)
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim twoWidths As Boolean = h / L >= Defined.DOUBLE_W_HL_RATIO And h / L < Defined.MAX_HL_RATIO ' check to see if h/L is within the range where 2 solutions for the width are possible
+ Dim m As Double
+ Dim mult_m As New List(Of Double)
+ Dim chl As Double
+
+ If twoWidths Then
+ ' find the first of two possible solutions for m with the following limits:
+ lower = Defined.M_DOUBLE_W ' see constants at bottom of script
+ upper = Defined.M_MAXHEIGHT ' see constants at bottom of script
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl > h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ mult_m.Add(m)
+
+ ' then find the second of two possible solutions for m with the following limits:
+ lower = Defined.M_MAXHEIGHT ' see constants at bottom of script
+ upper = 1
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl < h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+
+ If m <= Defined.M_MAX Then ' return this m parameter only if it falls within the maximum useful value (above which the curve breaks down)
+ mult_m.Add(m)
+ End If
+
+ Else
+ ' find the one possible solution for the m parameter
+ upper = Defined.M_DOUBLE_W ' limit the upper end of the search to the maximum value of m for which only one solution exists
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl > h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ mult_m.Add(m)
+ End If
+
+ Return mult_m
+ End Function
+
+ ' Solve for the m parameter from width and height (derived from reference {1} equations (33) and (34) with same notes as above)
+ Private Function SolveMFromWidHt(ByVal w As Double, ByVal h As Double) As Double
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim m As Double
+ Dim cwh As Double
+
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ cwh = (2 * EllipticE(m) - EllipticK(m)) / Math.Sqrt(m) ' calculate w/h with the test value of m
+ If cwh < w / h Then ' compares the calculated w/h with the actual w/h then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+
+ Return m
+ End Function
+
+ ' Calculate length based on height and an m parameter, derived from reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m)
+ Private Function Cal_L(ByVal h As Double, ByVal m As Double) As Double
+ Return h * EllipticK(m) / Math.Sqrt(m)
+ End Function
+
+ ' Calculate width based on length and an m parameter, derived from reference {1} equation (34), except b = width and K(k) and E(k) should be K(m) and E(m)
+ Private Function Cal_W(ByVal L As Double, ByVal m As Double) As Double
+ Return L * (2 * EllipticE(m) / EllipticK(m) - 1)
+ End Function
+
+ ' Calculate height based on length and an m parameter, from reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m)
+ Private Function Cal_H(ByVal L As Double, ByVal m As Double) As Double
+ Return L * Math.Sqrt(m) / EllipticK(m)
+ End Function
+
+ ' Calculate the unique m parameter based on a start tangent angle, from reference {2}, just above equation (9a), that states k = Sin(angle / 2 + Pi / 4),
+ ' but as m = k^2 and due to this script's need for an angle rotated 90° versus the one in reference {1}, the following formula is the result
+ ' New note: verified by reference {4}, pg. 78 at the bottom
+ Private Function Cal_M(ByVal a As Double) As Double
+ Return (1 - Math.Cos(a)) / 2 ' equal to Sin^2(a/2) too
+ End Function
+
+ ' Calculate start tangent angle based on an m parameter, derived from above formula
+ Private Function Cal_A(ByVal m As Double) As Double
+ Return Math.Acos(1 - 2 * m)
+ End Function
+
+ ' This is the heart of this script, taking the found (or specified) length, width, and angle values along with the found m parameter to create
+ ' a list of points that approximate the shape or form of the elastica. It works by finding the x and y coordinates (which are reversed versus
+ ' the original equations (12a) and (12b) from reference {2} due to the 90° difference in orientation) based on the tangent angle along the curve.
+ ' See reference {2} for more details on how they derived it. Note that to simplify things, the algorithm only calculates the points for half of the
+ ' curve, then mirrors those points along the y-axis.
+ Private Function FindBendForm(ByVal L As Double, ByVal w As Double, ByVal m As Double, ByVal ang As Double, ByVal refPln As Plane) As List(Of Point3d)
+ L = L / 2 ' because the below algorithm is based on the formulas in reference {2} for only half of the curve
+ w = w / 2 ' same
+
+ If ang = 0 Then ' if angle (and height) = 0, then simply return the start and end points of the straight line
+ Dim out As New List(Of Point3d)
+ out.Add(refPln.PointAt(w, 0, 0))
+ out.Add(refPln.PointAt(-w, 0, 0))
+ Return out
+ End If
+
+ Dim x As Double
+ Dim y As Double
+ Dim halfCurvePts As New List(Of Point3d)
+ Dim fullCurvePts As New List(Of Point3d)
+ Dim translatedPts As New List(Of Point3d)
+
+ ang -= Math.PI / 2 ' a hack to allow this algorithm to work, since the original curve in paper {2} was rotated 90°
+ Dim angB As Double = ang + (-Math.PI / 2 - ang) / Defined.CURVEDIVS ' angB is the 'lowercase theta' which should be in formula {2}(12b) as the interval
+ ' start [a typo...see equation(3)]. It's necessary to start angB at ang + [interval] instead of just ang due to integration failing at angB = ang
+ halfCurvePts.Add(New Point3d(w, 0, 0)) ' start with this known initial point, as integration will fail when angB = ang
+
+ ' each point {x, y} is calculated from the tangent angle, angB, that occurs at each point (which is why this iterates from ~ang to -pi/2, the known end condition)
+ Do While Math.Round(angB, Defined.ROUNDTO) >= Math.Round(-Math.PI / 2, Defined.ROUNDTO)
+ y = (Math.Sqrt(2) * Math.Sqrt(Math.Sin(ang) - Math.Sin(angB)) * (w + L)) / (2 * EllipticE(m)) ' note that x and y are swapped vs. (12a) and (12b)
+ x = (L / (Math.Sqrt(2) * EllipticK(m))) * Simpson(angB, -Math.PI / 2, 500, ang) ' calculate the Simpson approximation of the integral (function f below)
+ ' over the interval angB ('lowercase theta') to -pi/2. side note: is 500 too few iterations for the Simson algorithm?
+
+ If Math.Round(x, Defined.ROUNDTO) = 0 Then x = 0
+ halfCurvePts.Add(New Point3d(x, y, 0))
+
+ angB += (-Math.PI / 2 - ang) / Defined.CURVEDIVS ' onto the next tangent angle
+ Loop
+
+ ' After finding the x and y values for half of the curve, add the {-x, y} values for the rest of the curve
+ For Each point As Point3d In halfCurvePts
+ If Math.Round(point.X, Defined.ROUNDTO) = 0 Then
+ If Math.Round(point.Y, Defined.ROUNDTO) = 0 Then
+ fullCurvePts.Add(New Point3d(0, 0, 0)) ' special case when width = 0: when x = 0, only duplicate the point when y = 0 too
+ End If
+ Else
+ fullCurvePts.Add(New Point3d(-point.X, point.Y, 0))
+ End If
+ Next
+ halfCurvePts.Reverse
+ fullCurvePts.AddRange(halfCurvePts)
+
+ For Each p As Point3d In fullCurvePts
+ translatedPts.Add(refPln.PointAt(p.X, p.Y, p.Z)) ' translate the points from the reference plane to the world plane
+ Next
+
+ Return translatedPts
+ End Function
+
+ ' Interpolates the points from FindBendForm to create the Elastica curve. Uses start & end tangents for greater accuracy.
+ Private Function MakeCurve(ByVal pts As List(Of Point3d), ByVal ang As Double, ByVal refPln As Plane) As Curve
+ If ang <> 0 Then
+ Dim ts, te As New Vector3d(refPln.XAxis)
+ ts.Rotate(ang, refPln.ZAxis)
+ te.Rotate(-ang, refPln.ZAxis)
+ Return Curve.CreateInterpolatedCurve(pts, 3, CurveKnotStyle.Chord, ts, te) ' 3rd degree curve with 'Chord' Knot Style
+ Else
+ Return Curve.CreateInterpolatedCurve(pts, 3) ' if angle (and height) = 0, then simply interpolate the straight line (no start/end tangents)
+ End If
+ End Function
+
+ ' Implements the Simpson approximation for an integral of function f below
+ Public Function Simpson(a As Double, b As Double, n As Integer, theta As Double) As Double 'n should be an even number
+ Dim j As Integer, s1 As Double, s2 As Double, h As Double
+ h = (b - a) / n
+ s1 = 0
+ s2 = 0
+ For j = 1 To n - 1 Step 2
+ s1 = s1 + fn(a + j * h, theta)
+ Next j
+ For j = 2 To n - 2 Step 2
+ s2 = s2 + fn(a + j * h, theta)
+ Next j
+ Simpson = h / 3 * (fn(a, theta) + 4 * s1 + 2 * s2 + fn(b, theta))
+ End Function
+
+ ' Specific calculation for the above integration
+ Public Function fn(x As Double, theta As Double) As Double
+ fn = Math.Sin(x) / (Math.Sqrt(Math.Sin(theta) - Math.Sin(x))) ' from reference {2} formula (12b)
+ End Function
+
+
+ ' Return the Complete Elliptic integral of the 1st kind
+ ' Abramowitz and Stegun p.591, formula 17.3.11
+ ' Code from http://www.codeproject.com/Articles/566614/Elliptic-integrals
+ Public Function EllipticK(ByVal m As Double) As Double
+ Dim sum, term, above, below As Double
+ sum = 1
+ term = 1
+ above = 1
+ below = 2
+
+ For i As Integer = 1 To 100
+ term *= above / below
+ sum += Math.Pow(m, i) * Math.Pow(term, 2)
+ above += 2
+ below += 2
+ Next
+ sum *= 0.5 * Math.PI
+ Return sum
+ End Function
+
+
+ ' Return the Complete Elliptic integral of the 2nd kind
+ ' Abramowitz and Stegun p.591, formula 17.3.12
+ ' Code from http://www.codeproject.com/Articles/566614/Elliptic-integrals
+ Public Function EllipticE(ByVal m As Double) As Double
+ Dim sum, term, above, below As Double
+ sum = 1
+ term = 1
+ above = 1
+ below = 2
+
+ For i As Integer = 1 To 100
+ term *= above / below
+ sum -= Math.Pow(m, i) * Math.Pow(term, 2) / above
+ above += 2
+ below += 2
+ Next
+ sum *= 0.5 * Math.PI
+ Return sum
+ End Function
+
+ Friend Partial NotInheritable Class Defined
+ Private Sub New()
+ End Sub
+
+ ' Note: most of these values for m and h/L ratio were found with Wolfram Alpha and either specific intercepts (x=0) or local minima/maxima. They should be constant.
+ Public Const M_SKETCHY As Double = 0.95 ' value of the m parameter where the curvature near the ends of the curve gets wonky
+ Public Const M_MAX As Double = 0.993 ' maximum useful value of the m parameter, above which this algorithm for the form of the curve breaks down
+ Public Const M_ZERO_W As Double = 0.826114765984970336 ' value of the m parameter when width = 0
+ Public Const M_MAXHEIGHT As Double = 0.701327460663101223 ' value of the m parameter at maximum possible height of the bent rod/wire
+ Public Const M_DOUBLE_W As Double = 0.180254422335013983 ' minimum value of the m parameter when two width values are possible for a given height and length
+ Public Const DOUBLE_W_HL_RATIO As Double = 0.257342117984635757 ' value of the height/length ratio above which there are two possible width values
+ Public Const MAX_HL_RATIO As Double = 0.403140189705650243 ' maximum possible value of the height/length ratio
+
+ Public Const MAXERR As Double = 0.0000000001 ' error tolerance
+ Public Const MAXIT As Integer = 100 ' maximum number of iterations
+ Public Const ROUNDTO As Integer = 10 ' number of decimal places to round off to
+ Public Const CURVEDIVS As Integer = 50 ' number of sample points for building the curve (or half-curve as it were)
+ End Class</item>
+ <item name="CustomUsing" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">A VB.NET scriptable component</item>
+ <item name="EditorPosition" type_name="gh_drawing_point" type_code="30">
+ <X>98</X>
+ <Y>86</Y>
+ </item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">26fe933d-1698-4d29-8acd-71f478537911</item>
+ <item name="Name" type_name="gh_string" type_code="10">VB Script</item>
+ <item name="NickName" type_name="gh_string" type_code="10">VB</item>
+ <item name="OutParameter" type_name="gh_bool" type_code="1">true</item>
+ <item name="ReferenceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="ScriptSource" type_name="gh_string" type_code="10"> ' -----------------------------------------------------------------
+ ' Elastic Bending Script by Will McElwain
+ ' Created February 2014
+ '
+ ' DESCRIPTION:
+ ' This beast creates the so-called 'elastica curve', the shape a long, thin rod or wire makes when it is bent elastically (i.e. not permanently). In this case, force
+ ' is assumed to only be applied horizontally (which would be in line with the rod at rest) and both ends are assumed to be pinned or hinged meaning they are free
+ ' to rotate (as opposed to clamped, when the end tangent angle is fixed, usually horizontally). An interesting finding is that it doesn't matter what the material or
+ ' cross-sectional area is, as long as they're uniform along the entire length. Everything makes the same shape when bent as long as it doesn't cross the threshold
+ ' from elastic to plastic (permanent) deformation (I don't bother to find that limit here, but can be found if the yield stress for a material is known).
+ '
+ ' Key to the formulas used in this script are elliptic integrals, specifically K(m), the complete elliptic integral of the first kind, and E(m), the complete elliptic
+ ' integral of the second kind. There was a lot of confusion over the 'm' and 'k' parameters for these functions, as some people use them interchangeably, but they are
+ ' not the same. m = k^2 (thus k = Sqrt(m)). I try to use the 'm' parameter exclusively to avoid this confusion. Note that there is a unique 'm' parameter for every
+ ' configuration/shape of the elastica curve.
+ '
+ ' This script tries to find that unique 'm' parameter based on the inputs. The algorithm starts with a test version of m, evaluates an expression, say 2*E(m)/K(m)-1,
+ ' then compares the result to what it should be (in this case, a known width/length ratio). Iterate until the correct m is found. Once we have m, we can then calculate
+ ' all of the other unknowns, then find points that lie on that curve, then interpolate those points for the actual curve. You can also use Wolfram|Alpha as I did to
+ ' find the m parameter based on the equations in this script (example here: http://tiny.cc/t4tpbx for when say width=45.2 and length=67.1).
+ '
+ ' Other notes:
+ ' * This script works with negative values for width, which will creat a self-intersecting curve (as it should). The curvature of the elastica starts to break down around
+ ' m=0.95 (~154°), but this script will continue to work until M_MAX, m=0.993 (~169°). If you wish to ignore self-intersecting curves, set ignoreSelfIntersecting to True
+ ' * When the only known values are length and height, it is actually possible for certain ratios of height to length to have two valid m values (thus 2 possible widths
+ ' and angles). This script will return them both.
+ ' * Only the first two valid parameters (of the required ones) will be used, meaning if all four are connected (length, width or a PtB, height, and angle), this script will
+ ' only use length and width (or a PtB).
+ ' * Depending on the magnitude of your inputs (say if they're really small, like if length < 10), you might have to increase the constant ROUNDTO at the bottom
+ '
+ ' REFERENCES:
+ ' {1} "The elastic rod" by M.E. Pacheco Q. & E. Pina, http://www.scielo.org.mx/pdf/rmfe/v53n2/v53n2a8.pdf
+ ' {2} "An experiment in nonlinear beam theory" by A. Valiente, http://www.deepdyve.com/lp/doc/I3lwnxdfGz , also here: http://tiny.cc/Valiente_AEiNBT
+ ' {3} "Snap buckling, writhing and Loop formation In twisted rods" by V.G.A. GOSS, http://myweb.lsbu.ac.uk/~gossga/thesisFinal.pdf
+ ' {4} "Theory of Elastic Stability" by Stephen Timoshenko, http://www.scribd.com/doc/50402462/Timoshenko-Theory-of-Elastic-Stability (start on p. 76)
+ '
+ ' INPUT:
+ ' PtA - First anchor point (required)
+ ' PtB - Second anchor point (optional, though 2 out of the 4--length, width, height, angle--need to be specified)
+ ' [note that PtB can be the same as PtA (meaning width would be zero)]
+ ' [also note that if a different width is additionally specified that's not equal to the distance between PtA and PtB, then the end point will not equal PtB anymore]
+ ' Pln - Plane of the bent rod/wire, which bends up in the +y direction. The line between PtA and PtB (if specified) must be parallel to the x-axis of this plane
+ '
+ ' ** 2 of the following 4 need to be specified **
+ ' Len - Length of the rod/wire, which needs to be > 0
+ ' Wid - Width between the endpoints of the curve [note: if PtB is specified in addition, and distance between PtA and PtB <> width, the end point will be relocated
+ ' Ht - Height of the bent rod/wire (when negative, curve will bend downward, relative to the input plane, instead)
+ ' Ang - Inner departure angle or tangent angle (in radians) at the ends of the bent rod/wire. Set up so as width approaches length (thus height approaches zero), angle approaches zero
+ '
+ ' * Following variables only needed for optional calculating of bending force, not for shape of curve.
+ ' E - Young's modulus (modulus of elasticity) in GPa (=N/m^2) (material-specific. for example, 7075 aluminum is roughly 71.7 GPa)
+ ' I - Second moment of area (or area moment of inertia) in m^4 (cross-section-specific. for example, a hollow rod
+ ' would have I = pi * (outer_diameter^4 - inner_diameter^4) / 32
+ ' Note: E*I is also known as flexural rigidity or bending stiffness
+ '
+ ' OUTPUT:
+ ' out - only for debugging messages
+ ' Pts - the list of points that approximate the shape of the elastica
+ ' Crv - the 3rd-degree curve interpolated from those points (with accurate start & end tangents)
+ ' L - the length of the rod/wire
+ ' W - the distance (width) between the endpoints of the rod/wire
+ ' H - the height of the bent rod/wire
+ ' A - the tangent angle at the (start) end of the rod/wire
+ ' F - the force needed to hold the rod/wire in a specific shape (based on the material properties & cross-section) **be sure your units for 'I' match your units for the
+ ' rest of your inputs (length, width, etc.). Also note that the critical buckling load (force) that makes the rod/wire start to bend can be found at height=0
+ '
+ ' THANKS TO:
+ ' Mårten Nettelbladt (thegeometryofbending.blogspot.com)
+ ' Daniel Piker (Kangaroo plugin)
+ ' David Rutten (Grasshopper guru)
+ ' Euler & Bernoulli (the O.G.'s)
+ '
+ ' -----------------------------------------------------------------
+
+ Dim ignoreSelfIntersecting As Boolean = False ' set to True if you don't want to output curves where width < 0, which creates a self-intersecting curve
+
+ Dim inCt As Integer = 0 ' count the number of required parameters that are receiving data
+ Dim length As Double
+ Dim width As System.Object = Nothing ' need to set as Nothing so we can check if it has been assigned a value later
+ Dim height As Double
+ Dim angle As Double
+ Dim m As Double
+ Dim multiple_m As New List(Of Double)
+ Dim AtoB As Line
+ Dim flip_H As Boolean = False ' if height is negative, this flag will be set
+ Dim flip_A As Boolean = False ' if angle is negative, this flag will be set
+
+ If Not IsSet("Pln") Then
+ Msg("error", "Base plane is not set")
+ Return
+ End If
+
+ If Not IsSet("PtA") Then
+ Msg("error", "Point A is not set")
+ Return
+ End If
+
+ If Math.Round(Pln.DistanceTo(PtA), Defined.ROUNDTO) <> 0 Then
+ Msg("error", "Point A is not on the base plane")
+ Return
+ End If
+
+ Dim refPlane As Plane = Pln ' create a reference plane = input plane and set the origin of it to PtA in case PtA isn't the origin already
+ refPlane.Origin = PtA
+
+ If IsSet("PtB") Then
+ If Math.Round(Pln.DistanceTo(PtB), Defined.ROUNDTO) <> 0 Then
+ Msg("error", "Point B is not on the base plane")
+ Return
+ End If
+
+ AtoB = New Line(PtA, PtB)
+ If AtoB.Length <> 0 And Not AtoB.Direction.IsPerpendicularTo(Pln.YAxis) Then
+ Msg("error", "The line between PtA and PtB is not perpendicular to the Y-axis of the specified plane")
+ Return
+ End If
+
+ inCt += 1
+ If IsSet("Wid") Then Msg("info", "Wid will override the distance between PtA and PtB. If you do not want this to happen, disconnect PtB or Wid.")
+
+ width = PtA.DistanceTo(PtB) ' get the width (distance) between PtA and PtB
+
+ Dim refPtB As Point3d
+ refPlane.RemapToPlaneSpace(PtB, refPtB)
+ If refPtB.X < 0 Then width = -width ' check if PtB is to the left of PtA...if so, width is negative
+ End If
+
+ If IsSet("Len") Then inCt += 1
+ If IsSet("Wid") Then inCt += 1
+ If IsSet("Ht") Then inCt += 1
+ If IsSet("Ang") Then inCt += 1
+ If inCt > 2 Then Msg("info", "More parameters set than are required (out of length, width, height, angle). Only using the first two valid ones.")
+
+ ' check for connected/specified inputs. note: only the first two that it comes across will be used
+ If IsSet("Len") Then ' if length is specified then...
+ If Len <= 0 Then
+ Msg("error", "Length cannot be negative or zero")
+ Return
+ End If
+ If IsSet("Wid") Then ' find height & angle based on length and specified width
+ If Wid > Len Then
+ Msg("error", "Width is greater than length")
+ Return
+ End If
+ If Wid = Len Then ' skip the solver and set the known values
+ height = 0
+ m = 0
+ angle = 0
+ width = Wid
+ Else
+ m = SolveMFromLenWid(Len, Wid)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ width = Wid
+ End If
+
+ Else If width IsNot Nothing Then ' find height & angle based on length and calculated width (distance between PtA and PtB)
+ If width > Len Then
+ Msg("error", "Width is greater than length")
+ Return
+ End If
+ If width = Len Then ' skip the solver and set the known values
+ height = 0
+ m = 0
+ angle = 0
+ Else
+ m = SolveMFromLenWid(Len, width)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+
+ Else If IsSet("Ht") Then ' find width & angle based on length and height ** possible to return 2 results **
+ If Math.Abs(Ht / Len) > Defined.MAX_HL_RATIO Then
+ Msg("error", "Height not possible with given length")
+ Return
+ End If
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ width = Len
+ angle = 0
+ Else
+ multiple_m = SolveMFromLenHt(Len, Ht) ' note that it's possible for two values of m to be found if height is close to max height
+ If multiple_m.Count = 1 Then ' if there's only one m value returned, calculate the width & angle here. we'll deal with multiple m values later
+ m = multiple_m.Item(0)
+ width = Cal_W(Len, m) ' L * (2 * E(m) / K(m) - 1)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find width & height based on length and angle
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ width = Len
+ height = 0
+ Else
+ width = Cal_W(Len, m) ' L * (2 * E(m) / K(m) - 1)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to length")
+ Return
+ End If
+ length = Len
+
+ Else If IsSet("Wid") Then ' if width is specified then...
+ If IsSet("Ht") Then ' find length & angle based on specified width and height
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ length = Wid
+ angle = 0
+ Else
+ m = SolveMFromWidHt(Wid, Ht)
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find length & height based on specified width and angle
+ If Wid = 0 Then
+ Msg("error", "Curve not possible with width = 0 and an angle as inputs")
+ Return
+ End If
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ length = Wid
+ height = 0
+ Else
+ length = Wid / (2 * EllipticE(m) / EllipticK(m) - 1)
+ If length < 0 Then
+ Msg("error", "Curve not possible at specified width and angle (calculated length is negative)")
+ Return
+ End If
+ height = Cal_H(length, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to width (Wid)")
+ Return
+ End If
+ width = Wid
+
+ Else If width IsNot Nothing Then ' if width is determined by PtA and PtB then...
+ If IsSet("Ht") Then ' find length & angle based on calculated width and height
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ length = width
+ angle = 0
+ Else
+ m = SolveMFromWidHt(width, Ht)
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find length & height based on calculated width and angle
+ If width = 0 Then
+ Msg("error", "Curve not possible with width = 0 and an angle as inputs")
+ Return
+ End If
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ length = width
+ height = 0
+ Else
+ length = width / (2 * EllipticE(m) / EllipticK(m) - 1)
+ If length < 0 Then
+ Msg("error", "Curve not possible at specified width and angle (calculated length is negative)")
+ Return
+ End If
+ height = Cal_H(length, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to PtA and PtB")
+ Return
+ End If
+
+ Else If IsSet("Ht") Then ' if height is specified then...
+ If IsSet("Ang") Then ' find length & width based on height and angle
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_H = True
+ flip_A = True
+ End If
+ If Ht = 0 Then
+ Msg("error", "Height can't = 0 if only height and angle are specified")
+ Return
+ Else
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = Not flip_A
+ flip_H = Not flip_H
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then
+ Msg("error", "Angle can't = 0 if only height and angle are specified")
+ Return
+ Else
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ width = Cal_W(length, m) ' L * (2 * E(m) / K(m) - 1)
+ End If
+ angle = Ang
+ End If
+ height = Ht
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to height")
+ Return
+ End If
+
+ Else If IsSet("Ang") Then
+ Msg("error", "Need to specify one more parameter in addition to angle")
+ Return
+ Else
+ Msg("error", "Need to specify two of the four parameters: length, width (or PtB), height, and angle")
+ Return
+ End If
+
+ If m > Defined.M_MAX Then
+ Msg("error", "Form of curve not solvable with current algorithm and given inputs")
+ Return
+ End If
+
+ refPlane.Origin = refPlane.PointAt(width / 2, 0, 0) ' adjust the origin of the reference plane so that the curve is centered about the y-axis (start of the curve is at x = -width/2)
+
+ If multiple_m.Count > 1 Then ' if there is more than one m value returned, calculate the width, angle, and curve for each
+ Dim multi_pts As New DataTree(Of Point3d)
+ Dim multi_crv As New List(Of Curve)
+ Dim tmp_pts As New List(Of Point3d)
+ Dim multi_W, multi_A, multi_F As New List(Of Double)
+ Dim j As Integer = 0 ' used for creating a new branch (GH_Path) for storing pts which is itself a list of points
+
+ For Each m_val As Double In multiple_m
+ width = Cal_W(length, m_val) 'length * (2 * EllipticE(m_val) / EllipticK(m_val) - 1)
+
+ If width < 0 And ignoreSelfIntersecting Then
+ Msg("warning", "One curve is self-intersecting. To enable these, set ignoreSelfIntersecting to False")
+ Continue For
+ End If
+
+ If m_val >= Defined.M_SKETCHY Then Msg("info", "Accuracy of the curve whose width = " & Math.Round(width, 4) & " is not guaranteed")
+
+ angle = Cal_A(m_val) 'Math.Asin(2 * m_val - 1)
+ refPlane.Origin = refPlane.PointAt(width / 2, 0, 0) ' adjust the origin of the reference plane so that the curve is centered about the y-axis (start of the curve is at x = -width/2)
+
+ tmp_pts = FindBendForm(length, width, m_val, angle, refPlane)
+ multi_pts.AddRange(tmp_pts, New GH_Path(j))
+ multi_crv.Add(MakeCurve(tmp_pts, angle, refPlane))
+
+ multi_W.Add(width)
+ If flip_A Then angle = -angle
+ multi_A.Add(angle)
+
+ E = E * 10 ^ 9 ' Young's modulus input E is in GPa, so we convert to Pa here (= N/m^2)
+ multi_F.Add(EllipticK(m_val) ^ 2 * E * I / length ^ 2) ' from reference {4} pg. 79
+
+ j += 1
+ refPlane.Origin = PtA ' reset the reference plane origin to PtA for the next m_val
+ 'Print("length=" & length & ", width=" & width & ", height=" & height & ", angle=" & angle & ", m=" & m_val & ", k=" & Math.Sqrt(m_val) & ", w/L=" & width / length & ", h/L=" & height / length & ", w/h=" & width / height)
+ Next
+
+ ' assign the outputs
+ Pts = multi_pts
+ Crv = multi_crv
+ L = length
+ W = multi_W
+ If flip_H Then height = -height
+ H = height
+ A = multi_A
+ F = multi_F
+
+ Else ' only deal with the single m value
+ If m >= Defined.M_SKETCHY Then Msg("info", "Accuracy of the curve at these parameters is not guaranteed")
+
+ If width < 0 And ignoreSelfIntersecting Then
+ Msg("error", "Curve is self-intersecting. To enable these, set ignoreSelfIntersecting to False")
+ Return
+ End If
+
+ Pts = FindBendForm(length, width, m, angle, refPlane)
+ Crv = MakeCurve(pts, angle, refPlane)
+ L = length
+ W = width
+ If flip_H Then height = -height
+ H = height
+ If flip_A Then angle = -angle
+ A = angle
+
+ E = E * 10 ^ 9 ' Young's modulus input E is in GPa, so we convert to Pa here (= N/m^2)
+ F = EllipticK(m) ^ 2 * E * I / length ^ 2 ' from reference {4} pg. 79. Note: the critical buckling (that makes the rod/wire start to bend) can be found at height=0 (width=length)
+
+ 'height = Math.Sqrt(((2 * Len / 5) ^ 2 - ((Wid - Len / 5) / 2) ^ 2) ' quick approximation discovered by Mårten of 'Geometry of Bending' fame ( http://tiny.cc/it2pbx )
+ 'width = (Len +/- 2 * Math.Sqrt(4 * Len ^ 2 - 25 * Ht ^ 2)) / 5 ' derived from above
+ 'length = (2 * Math.Sqrt(15 * Ht ^ 2 + 4 * Wid ^ 2) - Wid) / 3 ' derived from above
+
+ 'Print("length=" & length & ", width=" & width & ", height=" & height & ", angle=" & angle & ", m=" & m & ", k=" & Math.Sqrt(m) & ", w/L=" & width / length & ", h/L=" & height / length & ", w/h=" & width / height)
+ End If
+</item>
+ <item name="UsingSource" type_name="gh_string" type_code="10">Imports System.IO
+Imports System.Linq
+Imports System.Data
+Imports System.Drawing
+Imports System.Reflection
+Imports System.Windows.Forms
+Imports System.Xml
+Imports System.Xml.Linq
+Imports Microsoft.VisualBasic
+Imports System.Runtime.InteropServices
+
+Imports Rhino.DocObjects
+Imports Rhino.Collections
+Imports GH_IO
+Imports GH_IO.Serialization</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1273</X>
+ <Y>273</Y>
+ <W>69</W>
+ <H>184</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1309</X>
+ <Y>365</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="ParameterData">
+ <items count="19">
+ <item name="InputCount" type_name="gh_int32" type_code="3">9</item>
+ <item name="InputId" index="0" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="1" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="2" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="3" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="4" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="5" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="6" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="7" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="InputId" index="8" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="OutputCount" type_name="gh_int32" type_code="3">8</item>
+ <item name="OutputId" index="0" type_name="gh_guid" type_code="9">3ede854e-c753-40eb-84cb-b48008f14fd4</item>
+ <item name="OutputId" index="1" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="2" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="3" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="4" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="5" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="6" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ <item name="OutputId" index="7" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
+ </items>
+ <chunks count="17">
+ <chunk name="InputParam" index="0">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable PtA</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">379a664a-9630-476f-8c20-256ddf3e943d</item>
+ <item name="Name" type_name="gh_string" type_code="10">PtA</item>
+ <item name="NickName" type_name="gh_string" type_code="10">PtA</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
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+ <item name="Source" index="0" type_name="gh_guid" type_code="9">5de5b792-8962-4638-be4a-86c646282e68</item>
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+ </chunk>
+ <chunk name="InputParam" index="1">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable PtB</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">b01c7d92-c595-4d7a-99a3-957cf497c826</item>
+ <item name="Name" type_name="gh_string" type_code="10">PtB</item>
+ <item name="NickName" type_name="gh_string" type_code="10">PtB</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">16fb0b71-416e-432e-a77f-b9e8590e307f</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">e1937b56-b1da-4c12-8bd8-e34ee81746ef</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
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+ <X>1275</X>
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+ <W>22</W>
+ <H>20</H>
+ </item>
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+ <X>1286</X>
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+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="2">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Pln</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">2e167bf2-eb59-4ca7-9464-7bde7df029f3</item>
+ <item name="Name" type_name="gh_string" type_code="10">Pln</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Pln</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">3d941ab3-84a6-460a-ac4c-e5c4efca8e47</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">3897522d-58e9-4d60-b38c-978ddacfedd8</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>315</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>325</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="3">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Len</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">61596bb3-a4f5-40b6-92e6-92d9ae8bc194</item>
+ <item name="Name" type_name="gh_string" type_code="10">Len</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Len</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>335</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>345</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="4">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Wid</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">d1851653-5fa8-44b5-a695-13eabdf10a15</item>
+ <item name="Name" type_name="gh_string" type_code="10">Wid</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Wid</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>355</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>365</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="5">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Ht</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">64fd744a-673e-41f1-988e-91bebdb8a308</item>
+ <item name="Name" type_name="gh_string" type_code="10">Ht</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Ht</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>375</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>385</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="6">
+ <items count="11">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Ang</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">8dfb957f-e4c5-4592-9f98-049164a4e9a7</item>
+ <item name="Name" type_name="gh_string" type_code="10">Ang</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Ang</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">3d353983-c48d-4967-baae-8b74c2abee7e</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>395</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>405</Y>
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+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="7">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable E</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f831c67e-99d4-413a-8d4a-c8cde2dd88f6</item>
+ <item name="Name" type_name="gh_string" type_code="10">E</item>
+ <item name="NickName" type_name="gh_string" type_code="10">E</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>415</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>425</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="8">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable I</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">b198e951-41a9-4c89-a1c4-5edcc7b4b0de</item>
+ <item name="Name" type_name="gh_string" type_code="10">I</item>
+ <item name="NickName" type_name="gh_string" type_code="10">I</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1275</X>
+ <Y>435</Y>
+ <W>22</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1286</X>
+ <Y>445</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="0">
+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">Print, Reflect and Error streams</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">d7c128dd-a6ec-4944-8ea9-c4460afa58f8</item>
+ <item name="Name" type_name="gh_string" type_code="10">out</item>
+ <item name="NickName" type_name="gh_string" type_code="10">out</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>275</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1330.5</X>
+ <Y>286.25</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="1">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Pts</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">b23dc398-765b-468f-907e-9b7e6781486a</item>
+ <item name="Name" type_name="gh_string" type_code="10">Pts</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Pts</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>297</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1330.5</X>
+ <Y>308.75</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="2">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Crv</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">7ef4522e-b915-4f20-98c0-46077f0157f6</item>
+ <item name="Name" type_name="gh_string" type_code="10">Crv</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Crv</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>320</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1330.5</X>
+ <Y>331.25</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="3">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter L</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">7090fadb-2ca9-4c0c-be28-893ad204d749</item>
+ <item name="Name" type_name="gh_string" type_code="10">L</item>
+ <item name="NickName" type_name="gh_string" type_code="10">L</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>342</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1330.5</X>
+ <Y>353.75</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="4">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter W</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">5b43b5d2-f91d-4aff-ae44-e894e1bb5cd2</item>
+ <item name="Name" type_name="gh_string" type_code="10">W</item>
+ <item name="NickName" type_name="gh_string" type_code="10">W</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>365</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1330.5</X>
+ <Y>376.25</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="5">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter H</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">e490d0a3-dbd6-438f-924f-befb23b428f3</item>
+ <item name="Name" type_name="gh_string" type_code="10">H</item>
+ <item name="NickName" type_name="gh_string" type_code="10">H</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>387</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1330.5</X>
+ <Y>398.75</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="OutputParam" index="6">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter A</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">1d23bbf4-3a2b-4814-839c-52ef5c2fafa3</item>
+ <item name="Name" type_name="gh_string" type_code="10">A</item>
+ <item name="NickName" type_name="gh_string" type_code="10">A</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1321</X>
+ <Y>410</Y>
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+ <item name="Name" type_name="gh_string" type_code="10">F</item>
+ <item name="NickName" type_name="gh_string" type_code="10">F</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Origin</item>
+ <item name="NickName" type_name="gh_string" type_code="10">O</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <chunk name="Attributes">
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+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
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+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ <Y>377</Y>
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+ <chunks count="1">
+ <chunk name="Branch" index="0">
+ <items count="2">
+ <item name="Count" type_name="gh_int32" type_code="3">1</item>
+ <item name="Path" type_name="gh_string" type_code="10">{0}</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Item" index="0">
+ <!--GH_Point only stores data which exists, test the existence of data fields prior to reading.-->
+ <items count="1">
+ <item name="Coordinate" type_name="gh_point3d" type_code="51">
+ <X>0</X>
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+ <item name="Name" type_name="gh_string" type_code="10">Plane</item>
+ <item name="NickName" type_name="gh_string" type_code="10">P</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
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+ <W>10</W>
+ <H>24</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ <chunks count="5">
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+ <item name="Description" type_name="gh_string" type_code="10">Input point</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Point</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Point</item>
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+ <H>60</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ <chunk name="param_output" index="0">
+ <items count="6">
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+ <chunk name="param_output" index="1">
+ <items count="6">
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">798aeadd-978c-45e4-8c94-72f0051b4754</item>
+ <item name="Name" type_name="gh_string" type_code="10">Y component</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Y component</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Z component</item>
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+ <item name="Description" type_name="gh_string" type_code="10">Construct a point from {xyz} coordinates.</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a7788758-befc-49c7-99aa-854487086770</item>
+ <item name="Name" type_name="gh_string" type_code="10">Construct Point</item>
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+ <chunks count="5">
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+ <item name="Name" type_name="gh_string" type_code="10">X coordinate</item>
+ <item name="NickName" type_name="gh_string" type_code="10">X coordinate</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">Y coordinate</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Z coordinate</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Z coordinate</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Point</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Point</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ </items>
+ <chunks count="5">
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+ <item name="Name" type_name="gh_string" type_code="10">X coordinate</item>
+ <item name="NickName" type_name="gh_string" type_code="10">X coordinate</item>
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+ <item name="Source" index="0" type_name="gh_guid" type_code="9">2fcdaa53-203a-4fe5-861d-d5a592274133</item>
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+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="10">
+ <item name="AdditionalSource" type_name="gh_string" type_code="10"> Private Function IsSet(ByVal param As String) As Boolean ' Check if an input parameter has data
+ Dim i As Integer = Component.Params.IndexOfInputParam(param)
+ If i > -1 Then
+ Return Component.Params.Input.ElementAt(i).DataType > 1 ' input parameter DataType of 1 means it's not receiving input (internal or external)
+ Else
+ Msg("error", "Input parameter '" & param & "' not found")
+ Return False
+ End If
+ End Function
+
+ Private Sub Msg(ByVal type As String, ByVal msg As String) ' Output an error, warning, or informational message
+ Select Case type
+ Case "error"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Error, msg)
+ Print("Error: " & msg)
+ Case "warning"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Warning, msg)
+ Print("Warning: " & msg)
+ Case "info"
+ Component.AddRuntimeMessage(GH_RuntimeMessageLevel.Remark, msg)
+ Print(msg)
+ End Select
+ End Sub
+
+ ' Solve for the m parameter from length and width (reference {1} equation (34), except b = width and K(k) and E(k) should be K(m) and E(m))
+ Private Function SolveMFromLenWid(ByVal L As Double, ByVal w As Double) As Double
+ If w = 0 Then
+ Return Defined.M_ZERO_W ' for the boundry condition width = 0, bypass the function and return the known m value
+ End If
+
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim m As Double
+ Dim cwl As Double
+
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ cwl = 2 * EllipticE(m) / EllipticK(m) - 1 ' calculate w/L with the test value of m
+ If cwl < w / L Then ' compares the calculated w/L with the actual w/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ Return m
+ End Function
+
+ ' Solve for the m parameter from length and height (reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m))
+ ' Note that it's actually possible to find 2 valid values for m (hence 2 width values) at certain height values
+ Private Function SolveMFromLenHt(ByVal L As Double, ByVal h As Double) As List(Of Double)
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim twoWidths As Boolean = h / L >= Defined.DOUBLE_W_HL_RATIO And h / L < Defined.MAX_HL_RATIO ' check to see if h/L is within the range where 2 solutions for the width are possible
+ Dim m As Double
+ Dim mult_m As New List(Of Double)
+ Dim chl As Double
+
+ If twoWidths Then
+ ' find the first of two possible solutions for m with the following limits:
+ lower = Defined.M_DOUBLE_W ' see constants at bottom of script
+ upper = Defined.M_MAXHEIGHT ' see constants at bottom of script
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl > h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ mult_m.Add(m)
+
+ ' then find the second of two possible solutions for m with the following limits:
+ lower = Defined.M_MAXHEIGHT ' see constants at bottom of script
+ upper = 1
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl < h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+
+ If m <= Defined.M_MAX Then ' return this m parameter only if it falls within the maximum useful value (above which the curve breaks down)
+ mult_m.Add(m)
+ End If
+
+ Else
+ ' find the one possible solution for the m parameter
+ upper = Defined.M_DOUBLE_W ' limit the upper end of the search to the maximum value of m for which only one solution exists
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ chl = Math.Sqrt(m) / EllipticK(m) ' calculate h/L with the test value of m
+ If chl > h / L Then ' compares the calculated h/L with the actual h/L then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+ mult_m.Add(m)
+ End If
+
+ Return mult_m
+ End Function
+
+ ' Solve for the m parameter from width and height (derived from reference {1} equations (33) and (34) with same notes as above)
+ Private Function SolveMFromWidHt(ByVal w As Double, ByVal h As Double) As Double
+ Dim n As Integer = 1 ' Iteration counter (quit if >MAXIT)
+ Dim lower As Double = 0 ' m must be within this range
+ Dim upper As Double = 1
+ Dim m As Double
+ Dim cwh As Double
+
+ Do While (upper - lower) > Defined.MAXERR AndAlso (n) < Defined.MAXIT ' Repeat until range narrow enough or MAXIT
+ m = (upper + lower) / 2
+ cwh = (2 * EllipticE(m) - EllipticK(m)) / Math.Sqrt(m) ' calculate w/h with the test value of m
+ If cwh < w / h Then ' compares the calculated w/h with the actual w/h then narrows the range of possible m
+ upper = m
+ Else
+ lower = m
+ End If
+ n += 1
+ Loop
+
+ Return m
+ End Function
+
+ ' Calculate length based on height and an m parameter, derived from reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m)
+ Private Function Cal_L(ByVal h As Double, ByVal m As Double) As Double
+ Return h * EllipticK(m) / Math.Sqrt(m)
+ End Function
+
+ ' Calculate width based on length and an m parameter, derived from reference {1} equation (34), except b = width and K(k) and E(k) should be K(m) and E(m)
+ Private Function Cal_W(ByVal L As Double, ByVal m As Double) As Double
+ Return L * (2 * EllipticE(m) / EllipticK(m) - 1)
+ End Function
+
+ ' Calculate height based on length and an m parameter, from reference {1} equation (33), except K(k) should be K(m) and k = sqrt(m)
+ Private Function Cal_H(ByVal L As Double, ByVal m As Double) As Double
+ Return L * Math.Sqrt(m) / EllipticK(m)
+ End Function
+
+ ' Calculate the unique m parameter based on a start tangent angle, from reference {2}, just above equation (9a), that states k = Sin(angle / 2 + Pi / 4),
+ ' but as m = k^2 and due to this script's need for an angle rotated 90° versus the one in reference {1}, the following formula is the result
+ ' New note: verified by reference {4}, pg. 78 at the bottom
+ Private Function Cal_M(ByVal a As Double) As Double
+ Return (1 - Math.Cos(a)) / 2 ' equal to Sin^2(a/2) too
+ End Function
+
+ ' Calculate start tangent angle based on an m parameter, derived from above formula
+ Private Function Cal_A(ByVal m As Double) As Double
+ Return Math.Acos(1 - 2 * m)
+ End Function
+
+ ' This is the heart of this script, taking the found (or specified) length, width, and angle values along with the found m parameter to create
+ ' a list of points that approximate the shape or form of the elastica. It works by finding the x and y coordinates (which are reversed versus
+ ' the original equations (12a) and (12b) from reference {2} due to the 90° difference in orientation) based on the tangent angle along the curve.
+ ' See reference {2} for more details on how they derived it. Note that to simplify things, the algorithm only calculates the points for half of the
+ ' curve, then mirrors those points along the y-axis.
+ Private Function FindBendForm(ByVal L As Double, ByVal w As Double, ByVal m As Double, ByVal ang As Double, ByVal refPln As Plane) As List(Of Point3d)
+ L = L / 2 ' because the below algorithm is based on the formulas in reference {2} for only half of the curve
+ w = w / 2 ' same
+
+ If ang = 0 Then ' if angle (and height) = 0, then simply return the start and end points of the straight line
+ Dim out As New List(Of Point3d)
+ out.Add(refPln.PointAt(w, 0, 0))
+ out.Add(refPln.PointAt(-w, 0, 0))
+ Return out
+ End If
+
+ Dim x As Double
+ Dim y As Double
+ Dim halfCurvePts As New List(Of Point3d)
+ Dim fullCurvePts As New List(Of Point3d)
+ Dim translatedPts As New List(Of Point3d)
+
+ ang -= Math.PI / 2 ' a hack to allow this algorithm to work, since the original curve in paper {2} was rotated 90°
+ Dim angB As Double = ang + (-Math.PI / 2 - ang) / Defined.CURVEDIVS ' angB is the 'lowercase theta' which should be in formula {2}(12b) as the interval
+ ' start [a typo...see equation(3)]. It's necessary to start angB at ang + [interval] instead of just ang due to integration failing at angB = ang
+ halfCurvePts.Add(New Point3d(w, 0, 0)) ' start with this known initial point, as integration will fail when angB = ang
+
+ ' each point {x, y} is calculated from the tangent angle, angB, that occurs at each point (which is why this iterates from ~ang to -pi/2, the known end condition)
+ Do While Math.Round(angB, Defined.ROUNDTO) >= Math.Round(-Math.PI / 2, Defined.ROUNDTO)
+ y = (Math.Sqrt(2) * Math.Sqrt(Math.Sin(ang) - Math.Sin(angB)) * (w + L)) / (2 * EllipticE(m)) ' note that x and y are swapped vs. (12a) and (12b)
+ x = (L / (Math.Sqrt(2) * EllipticK(m))) * Simpson(angB, -Math.PI / 2, 500, ang) ' calculate the Simpson approximation of the integral (function f below)
+ ' over the interval angB ('lowercase theta') to -pi/2. side note: is 500 too few iterations for the Simson algorithm?
+
+ If Math.Round(x, Defined.ROUNDTO) = 0 Then x = 0
+ halfCurvePts.Add(New Point3d(x, y, 0))
+
+ angB += (-Math.PI / 2 - ang) / Defined.CURVEDIVS ' onto the next tangent angle
+ Loop
+
+ ' After finding the x and y values for half of the curve, add the {-x, y} values for the rest of the curve
+ For Each point As Point3d In halfCurvePts
+ If Math.Round(point.X, Defined.ROUNDTO) = 0 Then
+ If Math.Round(point.Y, Defined.ROUNDTO) = 0 Then
+ fullCurvePts.Add(New Point3d(0, 0, 0)) ' special case when width = 0: when x = 0, only duplicate the point when y = 0 too
+ End If
+ Else
+ fullCurvePts.Add(New Point3d(-point.X, point.Y, 0))
+ End If
+ Next
+ halfCurvePts.Reverse
+ fullCurvePts.AddRange(halfCurvePts)
+
+ For Each p As Point3d In fullCurvePts
+ translatedPts.Add(refPln.PointAt(p.X, p.Y, p.Z)) ' translate the points from the reference plane to the world plane
+ Next
+
+ Return translatedPts
+ End Function
+
+ ' Interpolates the points from FindBendForm to create the Elastica curve. Uses start & end tangents for greater accuracy.
+ Private Function MakeCurve(ByVal pts As List(Of Point3d), ByVal ang As Double, ByVal refPln As Plane) As Curve
+ If ang <> 0 Then
+ Dim ts, te As New Vector3d(refPln.XAxis)
+ ts.Rotate(ang, refPln.ZAxis)
+ te.Rotate(-ang, refPln.ZAxis)
+ Return Curve.CreateInterpolatedCurve(pts, 3, CurveKnotStyle.Chord, ts, te) ' 3rd degree curve with 'Chord' Knot Style
+ Else
+ Return Curve.CreateInterpolatedCurve(pts, 3) ' if angle (and height) = 0, then simply interpolate the straight line (no start/end tangents)
+ End If
+ End Function
+
+ ' Implements the Simpson approximation for an integral of function f below
+ Public Function Simpson(a As Double, b As Double, n As Integer, theta As Double) As Double 'n should be an even number
+ Dim j As Integer, s1 As Double, s2 As Double, h As Double
+ h = (b - a) / n
+ s1 = 0
+ s2 = 0
+ For j = 1 To n - 1 Step 2
+ s1 = s1 + fn(a + j * h, theta)
+ Next j
+ For j = 2 To n - 2 Step 2
+ s2 = s2 + fn(a + j * h, theta)
+ Next j
+ Simpson = h / 3 * (fn(a, theta) + 4 * s1 + 2 * s2 + fn(b, theta))
+ End Function
+
+ ' Specific calculation for the above integration
+ Public Function fn(x As Double, theta As Double) As Double
+ fn = Math.Sin(x) / (Math.Sqrt(Math.Sin(theta) - Math.Sin(x))) ' from reference {2} formula (12b)
+ End Function
+
+
+ ' Return the Complete Elliptic integral of the 1st kind
+ ' Abramowitz and Stegun p.591, formula 17.3.11
+ ' Code from http://www.codeproject.com/Articles/566614/Elliptic-integrals
+ Public Function EllipticK(ByVal m As Double) As Double
+ Dim sum, term, above, below As Double
+ sum = 1
+ term = 1
+ above = 1
+ below = 2
+
+ For i As Integer = 1 To 100
+ term *= above / below
+ sum += Math.Pow(m, i) * Math.Pow(term, 2)
+ above += 2
+ below += 2
+ Next
+ sum *= 0.5 * Math.PI
+ Return sum
+ End Function
+
+
+ ' Return the Complete Elliptic integral of the 2nd kind
+ ' Abramowitz and Stegun p.591, formula 17.3.12
+ ' Code from http://www.codeproject.com/Articles/566614/Elliptic-integrals
+ Public Function EllipticE(ByVal m As Double) As Double
+ Dim sum, term, above, below As Double
+ sum = 1
+ term = 1
+ above = 1
+ below = 2
+
+ For i As Integer = 1 To 100
+ term *= above / below
+ sum -= Math.Pow(m, i) * Math.Pow(term, 2) / above
+ above += 2
+ below += 2
+ Next
+ sum *= 0.5 * Math.PI
+ Return sum
+ End Function
+
+ Friend Partial NotInheritable Class Defined
+ Private Sub New()
+ End Sub
+
+ ' Note: most of these values for m and h/L ratio were found with Wolfram Alpha and either specific intercepts (x=0) or local minima/maxima. They should be constant.
+ Public Const M_SKETCHY As Double = 0.95 ' value of the m parameter where the curvature near the ends of the curve gets wonky
+ Public Const M_MAX As Double = 0.993 ' maximum useful value of the m parameter, above which this algorithm for the form of the curve breaks down
+ Public Const M_ZERO_W As Double = 0.826114765984970336 ' value of the m parameter when width = 0
+ Public Const M_MAXHEIGHT As Double = 0.701327460663101223 ' value of the m parameter at maximum possible height of the bent rod/wire
+ Public Const M_DOUBLE_W As Double = 0.180254422335013983 ' minimum value of the m parameter when two width values are possible for a given height and length
+ Public Const DOUBLE_W_HL_RATIO As Double = 0.257342117984635757 ' value of the height/length ratio above which there are two possible width values
+ Public Const MAX_HL_RATIO As Double = 0.403140189705650243 ' maximum possible value of the height/length ratio
+
+ Public Const MAXERR As Double = 0.0000000001 ' error tolerance
+ Public Const MAXIT As Integer = 100 ' maximum number of iterations
+ Public Const ROUNDTO As Integer = 10 ' number of decimal places to round off to
+ Public Const CURVEDIVS As Integer = 50 ' number of sample points for building the curve (or half-curve as it were)
+ End Class</item>
+ <item name="Description" type_name="gh_string" type_code="10">A VB.NET scriptable component</item>
+ <item name="EditorPosition" type_name="gh_drawing_point" type_code="30">
+ <X>98</X>
+ <Y>86</Y>
+ </item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">b1551a80-522e-48bd-909f-f47901a99aa7</item>
+ <item name="Name" type_name="gh_string" type_code="10">VB Script</item>
+ <item name="NickName" type_name="gh_string" type_code="10">VB</item>
+ <item name="OutParameter" type_name="gh_bool" type_code="1">true</item>
+ <item name="ReferenceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="ScriptSource" type_name="gh_string" type_code="10"> ' -----------------------------------------------------------------
+ ' Elastic Bending Script by Will McElwain
+ ' Created February 2014
+ '
+ ' DESCRIPTION:
+ ' This beast creates the so-called 'elastica curve', the shape a long, thin rod or wire makes when it is bent elastically (i.e. not permanently). In this case, force
+ ' is assumed to only be applied horizontally (which would be in line with the rod at rest) and both ends are assumed to be pinned or hinged meaning they are free
+ ' to rotate (as opposed to clamped, when the end tangent angle is fixed, usually horizontally). An interesting finding is that it doesn't matter what the material or
+ ' cross-sectional area is, as long as they're uniform along the entire length. Everything makes the same shape when bent as long as it doesn't cross the threshold
+ ' from elastic to plastic (permanent) deformation (I don't bother to find that limit here, but can be found if the yield stress for a material is known).
+ '
+ ' Key to the formulas used in this script are elliptic integrals, specifically K(m), the complete elliptic integral of the first kind, and E(m), the complete elliptic
+ ' integral of the second kind. There was a lot of confusion over the 'm' and 'k' parameters for these functions, as some people use them interchangeably, but they are
+ ' not the same. m = k^2 (thus k = Sqrt(m)). I try to use the 'm' parameter exclusively to avoid this confusion. Note that there is a unique 'm' parameter for every
+ ' configuration/shape of the elastica curve.
+ '
+ ' This script tries to find that unique 'm' parameter based on the inputs. The algorithm starts with a test version of m, evaluates an expression, say 2*E(m)/K(m)-1,
+ ' then compares the result to what it should be (in this case, a known width/length ratio). Iterate until the correct m is found. Once we have m, we can then calculate
+ ' all of the other unknowns, then find points that lie on that curve, then interpolate those points for the actual curve. You can also use Wolfram|Alpha as I did to
+ ' find the m parameter based on the equations in this script (example here: http://tiny.cc/t4tpbx for when say width=45.2 and length=67.1).
+ '
+ ' Other notes:
+ ' * This script works with negative values for width, which will creat a self-intersecting curve (as it should). The curvature of the elastica starts to break down around
+ ' m=0.95 (~154°), but this script will continue to work until M_MAX, m=0.993 (~169°). If you wish to ignore self-intersecting curves, set ignoreSelfIntersecting to True
+ ' * When the only known values are length and height, it is actually possible for certain ratios of height to length to have two valid m values (thus 2 possible widths
+ ' and angles). This script will return them both.
+ ' * Only the first two valid parameters (of the required ones) will be used, meaning if all four are connected (length, width or a PtB, height, and angle), this script will
+ ' only use length and width (or a PtB).
+ ' * Depending on the magnitude of your inputs (say if they're really small, like if length < 10), you might have to increase the constant ROUNDTO at the bottom
+ '
+ ' REFERENCES:
+ ' {1} "The elastic rod" by M.E. Pacheco Q. & E. Pina, http://www.scielo.org.mx/pdf/rmfe/v53n2/v53n2a8.pdf
+ ' {2} "An experiment in nonlinear beam theory" by A. Valiente, http://www.deepdyve.com/lp/doc/I3lwnxdfGz , also here: http://tiny.cc/Valiente_AEiNBT
+ ' {3} "Snap buckling, writhing and Loop formation In twisted rods" by V.G.A. GOSS, http://myweb.lsbu.ac.uk/~gossga/thesisFinal.pdf
+ ' {4} "Theory of Elastic Stability" by Stephen Timoshenko, http://www.scribd.com/doc/50402462/Timoshenko-Theory-of-Elastic-Stability (start on p. 76)
+ '
+ ' INPUT:
+ ' PtA - First anchor point (required)
+ ' PtB - Second anchor point (optional, though 2 out of the 4--length, width, height, angle--need to be specified)
+ ' [note that PtB can be the same as PtA (meaning width would be zero)]
+ ' [also note that if a different width is additionally specified that's not equal to the distance between PtA and PtB, then the end point will not equal PtB anymore]
+ ' Pln - Plane of the bent rod/wire, which bends up in the +y direction. The line between PtA and PtB (if specified) must be parallel to the x-axis of this plane
+ '
+ ' ** 2 of the following 4 need to be specified **
+ ' Len - Length of the rod/wire, which needs to be > 0
+ ' Wid - Width between the endpoints of the curve [note: if PtB is specified in addition, and distance between PtA and PtB <> width, the end point will be relocated
+ ' Ht - Height of the bent rod/wire (when negative, curve will bend downward, relative to the input plane, instead)
+ ' Ang - Inner departure angle or tangent angle (in radians) at the ends of the bent rod/wire. Set up so as width approaches length (thus height approaches zero), angle approaches zero
+ '
+ ' * Following variables only needed for optional calculating of bending force, not for shape of curve.
+ ' E - Young's modulus (modulus of elasticity) in GPa (=N/m^2) (material-specific. for example, 7075 aluminum is roughly 71.7 GPa)
+ ' I - Second moment of area (or area moment of inertia) in m^4 (cross-section-specific. for example, a hollow rod
+ ' would have I = pi * (outer_diameter^4 - inner_diameter^4) / 32
+ ' Note: E*I is also known as flexural rigidity or bending stiffness
+ '
+ ' OUTPUT:
+ ' out - only for debugging messages
+ ' Pts - the list of points that approximate the shape of the elastica
+ ' Crv - the 3rd-degree curve interpolated from those points (with accurate start & end tangents)
+ ' L - the length of the rod/wire
+ ' W - the distance (width) between the endpoints of the rod/wire
+ ' H - the height of the bent rod/wire
+ ' A - the tangent angle at the (start) end of the rod/wire
+ ' F - the force needed to hold the rod/wire in a specific shape (based on the material properties & cross-section) **be sure your units for 'I' match your units for the
+ ' rest of your inputs (length, width, etc.). Also note that the critical buckling load (force) that makes the rod/wire start to bend can be found at height=0
+ '
+ ' THANKS TO:
+ ' Mårten Nettelbladt (thegeometryofbending.blogspot.com)
+ ' Daniel Piker (Kangaroo plugin)
+ ' David Rutten (Grasshopper guru)
+ ' Euler & Bernoulli (the O.G.'s)
+ '
+ ' -----------------------------------------------------------------
+
+ Dim ignoreSelfIntersecting As Boolean = False ' set to True if you don't want to output curves where width < 0, which creates a self-intersecting curve
+
+ Dim inCt As Integer = 0 ' count the number of required parameters that are receiving data
+ Dim length As Double
+ Dim width As System.Object = Nothing ' need to set as Nothing so we can check if it has been assigned a value later
+ Dim height As Double
+ Dim angle As Double
+ Dim m As Double
+ Dim multiple_m As New List(Of Double)
+ Dim AtoB As Line
+ Dim flip_H As Boolean = False ' if height is negative, this flag will be set
+ Dim flip_A As Boolean = False ' if angle is negative, this flag will be set
+
+ If Not IsSet("Pln") Then
+ Msg("error", "Base plane is not set")
+ Return
+ End If
+
+ If Not IsSet("PtA") Then
+ Msg("error", "Point A is not set")
+ Return
+ End If
+
+ If Math.Round(Pln.DistanceTo(PtA), Defined.ROUNDTO) <> 0 Then
+ Msg("error", "Point A is not on the base plane")
+ Return
+ End If
+
+ Dim refPlane As Plane = Pln ' create a reference plane = input plane and set the origin of it to PtA in case PtA isn't the origin already
+ refPlane.Origin = PtA
+
+ If IsSet("PtB") Then
+ If Math.Round(Pln.DistanceTo(PtB), Defined.ROUNDTO) <> 0 Then
+ Msg("error", "Point B is not on the base plane")
+ Return
+ End If
+
+ AtoB = New Line(PtA, PtB)
+ If AtoB.Length <> 0 And Not AtoB.Direction.IsPerpendicularTo(Pln.YAxis) Then
+ Msg("error", "The line between PtA and PtB is not perpendicular to the Y-axis of the specified plane")
+ Return
+ End If
+
+ inCt += 1
+ If IsSet("Wid") Then Msg("info", "Wid will override the distance between PtA and PtB. If you do not want this to happen, disconnect PtB or Wid.")
+
+ width = PtA.DistanceTo(PtB) ' get the width (distance) between PtA and PtB
+
+ Dim refPtB As Point3d
+ refPlane.RemapToPlaneSpace(PtB, refPtB)
+ If refPtB.X < 0 Then width = -width ' check if PtB is to the left of PtA...if so, width is negative
+ End If
+
+ If IsSet("Len") Then inCt += 1
+ If IsSet("Wid") Then inCt += 1
+ If IsSet("Ht") Then inCt += 1
+ If IsSet("Ang") Then inCt += 1
+ If inCt > 2 Then Msg("info", "More parameters set than are required (out of length, width, height, angle). Only using the first two valid ones.")
+
+ ' check for connected/specified inputs. note: only the first two that it comes across will be used
+ If IsSet("Len") Then ' if length is specified then...
+ If Len <= 0 Then
+ Msg("error", "Length cannot be negative or zero")
+ Return
+ End If
+ If IsSet("Wid") Then ' find height & angle based on length and specified width
+ If Wid > Len Then
+ Msg("error", "Width is greater than length")
+ Return
+ End If
+ If Wid = Len Then ' skip the solver and set the known values
+ height = 0
+ m = 0
+ angle = 0
+ width = Wid
+ Else
+ m = SolveMFromLenWid(Len, Wid)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ width = Wid
+ End If
+
+ Else If width IsNot Nothing Then ' find height & angle based on length and calculated width (distance between PtA and PtB)
+ If width > Len Then
+ Msg("error", "Width is greater than length")
+ Return
+ End If
+ If width = Len Then ' skip the solver and set the known values
+ height = 0
+ m = 0
+ angle = 0
+ Else
+ m = SolveMFromLenWid(Len, width)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+
+ Else If IsSet("Ht") Then ' find width & angle based on length and height ** possible to return 2 results **
+ If Math.Abs(Ht / Len) > Defined.MAX_HL_RATIO Then
+ Msg("error", "Height not possible with given length")
+ Return
+ End If
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ width = Len
+ angle = 0
+ Else
+ multiple_m = SolveMFromLenHt(Len, Ht) ' note that it's possible for two values of m to be found if height is close to max height
+ If multiple_m.Count = 1 Then ' if there's only one m value returned, calculate the width & angle here. we'll deal with multiple m values later
+ m = multiple_m.Item(0)
+ width = Cal_W(Len, m) ' L * (2 * E(m) / K(m) - 1)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find width & height based on length and angle
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ width = Len
+ height = 0
+ Else
+ width = Cal_W(Len, m) ' L * (2 * E(m) / K(m) - 1)
+ height = Cal_H(Len, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to length")
+ Return
+ End If
+ length = Len
+
+ Else If IsSet("Wid") Then ' if width is specified then...
+ If IsSet("Ht") Then ' find length & angle based on specified width and height
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ length = Wid
+ angle = 0
+ Else
+ m = SolveMFromWidHt(Wid, Ht)
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find length & height based on specified width and angle
+ If Wid = 0 Then
+ Msg("error", "Curve not possible with width = 0 and an angle as inputs")
+ Return
+ End If
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ length = Wid
+ height = 0
+ Else
+ length = Wid / (2 * EllipticE(m) / EllipticK(m) - 1)
+ If length < 0 Then
+ Msg("error", "Curve not possible at specified width and angle (calculated length is negative)")
+ Return
+ End If
+ height = Cal_H(length, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to width (Wid)")
+ Return
+ End If
+ width = Wid
+
+ Else If width IsNot Nothing Then ' if width is determined by PtA and PtB then...
+ If IsSet("Ht") Then ' find length & angle based on calculated width and height
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ If Ht = 0 Then ' skip the solver and set the known values
+ length = width
+ angle = 0
+ Else
+ m = SolveMFromWidHt(width, Ht)
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ angle = Cal_A(m) ' Acos(1 - 2 * m)
+ End If
+ height = Ht
+
+ Else If IsSet("Ang") Then ' find length & height based on calculated width and angle
+ If width = 0 Then
+ Msg("error", "Curve not possible with width = 0 and an angle as inputs")
+ Return
+ End If
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = True
+ flip_H = True
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then ' skip the solver and set the known values
+ length = width
+ height = 0
+ Else
+ length = width / (2 * EllipticE(m) / EllipticK(m) - 1)
+ If length < 0 Then
+ Msg("error", "Curve not possible at specified width and angle (calculated length is negative)")
+ Return
+ End If
+ height = Cal_H(length, m) ' L * Sqrt(m) / K(m)
+ End If
+ angle = Ang
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to PtA and PtB")
+ Return
+ End If
+
+ Else If IsSet("Ht") Then ' if height is specified then...
+ If IsSet("Ang") Then ' find length & width based on height and angle
+ If Ht < 0 Then
+ Ht = -Ht ' if height is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_H = True
+ flip_A = True
+ End If
+ If Ht = 0 Then
+ Msg("error", "Height can't = 0 if only height and angle are specified")
+ Return
+ Else
+ If Ang < 0 Then
+ Ang = -Ang ' if angle is negative, set it to positive (for the calculations) but flip the reference plane about its x-axis
+ refPlane.Transform(Transform.Mirror(New Plane(refPlane.Origin, refPlane.XAxis, refPlane.ZAxis)))
+ flip_A = Not flip_A
+ flip_H = Not flip_H
+ End If
+ m = Cal_M(Ang) ' (1 - Cos(a)) / 2
+ If Ang = 0 Then
+ Msg("error", "Angle can't = 0 if only height and angle are specified")
+ Return
+ Else
+ length = Cal_L(Ht, m) ' h * K(m) / Sqrt(m)
+ width = Cal_W(length, m) ' L * (2 * E(m) / K(m) - 1)
+ End If
+ angle = Ang
+ End If
+ height = Ht
+
+ Else
+ Msg("error", "Need to specify one more parameter in addition to height")
+ Return
+ End If
+
+ Else If IsSet("Ang") Then
+ Msg("error", "Need to specify one more parameter in addition to angle")
+ Return
+ Else
+ Msg("error", "Need to specify two of the four parameters: length, width (or PtB), height, and angle")
+ Return
+ End If
+
+ If m > Defined.M_MAX Then
+ Msg("error", "Form of curve not solvable with current algorithm and given inputs")
+ Return
+ End If
+
+ refPlane.Origin = refPlane.PointAt(width / 2, 0, 0) ' adjust the origin of the reference plane so that the curve is centered about the y-axis (start of the curve is at x = -width/2)
+
+ If multiple_m.Count > 1 Then ' if there is more than one m value returned, calculate the width, angle, and curve for each
+ Dim multi_pts As New DataTree(Of Point3d)
+ Dim multi_crv As New List(Of Curve)
+ Dim tmp_pts As New List(Of Point3d)
+ Dim multi_W, multi_A, multi_F As New List(Of Double)
+ Dim j As Integer = 0 ' used for creating a new branch (GH_Path) for storing pts which is itself a list of points
+
+ For Each m_val As Double In multiple_m
+ width = Cal_W(length, m_val) 'length * (2 * EllipticE(m_val) / EllipticK(m_val) - 1)
+
+ If width < 0 And ignoreSelfIntersecting Then
+ Msg("warning", "One curve is self-intersecting. To enable these, set ignoreSelfIntersecting to False")
+ Continue For
+ End If
+
+ If m_val >= Defined.M_SKETCHY Then Msg("info", "Accuracy of the curve whose width = " & Math.Round(width, 4) & " is not guaranteed")
+
+ angle = Cal_A(m_val) 'Math.Asin(2 * m_val - 1)
+ refPlane.Origin = refPlane.PointAt(width / 2, 0, 0) ' adjust the origin of the reference plane so that the curve is centered about the y-axis (start of the curve is at x = -width/2)
+
+ tmp_pts = FindBendForm(length, width, m_val, angle, refPlane)
+ multi_pts.AddRange(tmp_pts, New GH_Path(j))
+ multi_crv.Add(MakeCurve(tmp_pts, angle, refPlane))
+
+ multi_W.Add(width)
+ If flip_A Then angle = -angle
+ multi_A.Add(angle)
+
+ E = E * 10 ^ 9 ' Young's modulus input E is in GPa, so we convert to Pa here (= N/m^2)
+ multi_F.Add(EllipticK(m_val) ^ 2 * E * I / length ^ 2) ' from reference {4} pg. 79
+
+ j += 1
+ refPlane.Origin = PtA ' reset the reference plane origin to PtA for the next m_val
+ 'Print("length=" & length & ", width=" & width & ", height=" & height & ", angle=" & angle & ", m=" & m_val & ", k=" & Math.Sqrt(m_val) & ", w/L=" & width / length & ", h/L=" & height / length & ", w/h=" & width / height)
+ Next
+
+ ' assign the outputs
+ Pts = multi_pts
+ Crv = multi_crv
+ L = length
+ W = multi_W
+ If flip_H Then height = -height
+ H = height
+ A = multi_A
+ F = multi_F
+
+ Else ' only deal with the single m value
+ If m >= Defined.M_SKETCHY Then Msg("info", "Accuracy of the curve at these parameters is not guaranteed")
+
+ If width < 0 And ignoreSelfIntersecting Then
+ Msg("error", "Curve is self-intersecting. To enable these, set ignoreSelfIntersecting to False")
+ Return
+ End If
+
+ Pts = FindBendForm(length, width, m, angle, refPlane)
+ Crv = MakeCurve(pts, angle, refPlane)
+ L = length
+ W = width
+ If flip_H Then height = -height
+ H = height
+ If flip_A Then angle = -angle
+ A = angle
+
+ E = E * 10 ^ 9 ' Young's modulus input E is in GPa, so we convert to Pa here (= N/m^2)
+ F = EllipticK(m) ^ 2 * E * I / length ^ 2 ' from reference {4} pg. 79. Note: the critical buckling (that makes the rod/wire start to bend) can be found at height=0 (width=length)
+
+ 'height = Math.Sqrt(((2 * Len / 5) ^ 2 - ((Wid - Len / 5) / 2) ^ 2) ' quick approximation discovered by Mårten of 'Geometry of Bending' fame ( http://tiny.cc/it2pbx )
+ 'width = (Len +/- 2 * Math.Sqrt(4 * Len ^ 2 - 25 * Ht ^ 2)) / 5 ' derived from above
+ 'length = (2 * Math.Sqrt(15 * Ht ^ 2 + 4 * Wid ^ 2) - Wid) / 3 ' derived from above
+
+ 'Print("length=" & length & ", width=" & width & ", height=" & height & ", angle=" & angle & ", m=" & m & ", k=" & Math.Sqrt(m) & ", w/L=" & width / length & ", h/L=" & height / length & ", w/h=" & width / height)
+ End If
+</item>
+ </items>
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+ <items count="2">
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+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Len</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">bbe98993-e009-4e52-8774-f139cc9ad344</item>
+ <item name="Name" type_name="gh_string" type_code="10">Len</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Len</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
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+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
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+ </item>
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+ <chunk name="InputParam" index="4">
+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Wid</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">318f6c25-142a-4cef-8d1b-56b349a56ae9</item>
+ <item name="Name" type_name="gh_string" type_code="10">Wid</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Wid</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
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+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
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+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Ht</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f065abd9-8c03-4b9a-ac26-8c0e09668b17</item>
+ <item name="Name" type_name="gh_string" type_code="10">Ht</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Ht</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
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+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
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+ </chunks>
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+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable Ang</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">5d5e434e-9221-484f-93a2-bdc1e197c273</item>
+ <item name="Name" type_name="gh_string" type_code="10">Ang</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Ang</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
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+ <chunks count="2">
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+ </items>
+ <chunks count="1">
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+ <items count="2">
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+ </items>
+ <chunks count="1">
+ <chunk name="Item" index="0">
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+ <item name="number" type_name="gh_double" type_code="6">-0.78539816339744828</item>
+ </items>
+ </chunk>
+ </chunks>
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+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable E</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">36d9b8b0-7c38-498f-8a97-0403b70adef6</item>
+ <item name="Name" type_name="gh_string" type_code="10">E</item>
+ <item name="NickName" type_name="gh_string" type_code="10">E</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
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+ <chunks count="1">
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+ </item>
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+ </item>
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+ <items count="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
+ <item name="Description" type_name="gh_string" type_code="10">Script Variable I</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a6b52055-8ebf-49f0-a429-b8b8185391ac</item>
+ <item name="Name" type_name="gh_string" type_code="10">I</item>
+ <item name="NickName" type_name="gh_string" type_code="10">I</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="ScriptParamAccess" type_name="gh_int32" type_code="3">0</item>
+ <item name="ShowTypeHints" type_name="gh_bool" type_code="1">true</item>
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+ <item name="TypeHintID" type_name="gh_guid" type_code="9">8e991e99-5fb8-41e1-928d-1bba8fb9f7d7</item>
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+ </item>
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+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">Print, Reflect and Error streams</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">562038bb-d4ef-4dda-8f24-19118cb2a92c</item>
+ <item name="Name" type_name="gh_string" type_code="10">out</item>
+ <item name="NickName" type_name="gh_string" type_code="10">out</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Pts</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f2abc1ef-f616-42de-9c3e-2fc55c013c47</item>
+ <item name="Name" type_name="gh_string" type_code="10">Pts</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Pts</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>432</X>
+ <Y>1592</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter Crv</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">d956c518-8143-4003-b468-0922d9b5d819</item>
+ <item name="Name" type_name="gh_string" type_code="10">Crv</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Crv</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
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+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>432</X>
+ <Y>1615</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter L</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">5f1ba0d6-87b3-4d7a-b620-493c780b9781</item>
+ <item name="Name" type_name="gh_string" type_code="10">L</item>
+ <item name="NickName" type_name="gh_string" type_code="10">L</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
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+ <items count="2">
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+ <X>432</X>
+ <Y>1637</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
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+ <X>441.5</X>
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter W</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a3aba44a-4ad7-4dc6-a6dd-95eb9c56bf10</item>
+ <item name="Name" type_name="gh_string" type_code="10">W</item>
+ <item name="NickName" type_name="gh_string" type_code="10">W</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>432</X>
+ <Y>1660</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>441.5</X>
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter H</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">fcbbe834-84c4-4680-ae56-76b50b45b590</item>
+ <item name="Name" type_name="gh_string" type_code="10">H</item>
+ <item name="NickName" type_name="gh_string" type_code="10">H</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
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+ <items count="2">
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+ <X>432</X>
+ <Y>1682</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>441.5</X>
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+ </chunk>
+ </chunks>
+ </chunk>
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter A</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">383ff64c-4b9f-4bdd-a03a-aabb8673ab4e</item>
+ <item name="Name" type_name="gh_string" type_code="10">A</item>
+ <item name="NickName" type_name="gh_string" type_code="10">A</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
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+ <Y>1705</Y>
+ <W>19</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ </chunks>
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+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Output parameter F</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">30690ce7-61b8-414e-9f41-260072b75cd7</item>
+ <item name="Name" type_name="gh_string" type_code="10">F</item>
+ <item name="NickName" type_name="gh_string" type_code="10">F</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>432</X>
+ <Y>1727</Y>
+ <W>19</W>
+ <H>23</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>441.5</X>
+ <Y>1738.75</Y>
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+ <item name="GUID" type_name="gh_guid" type_code="9">3581f42a-9592-4549-bd6b-1c0fc39d067b</item>
+ <item name="Name" type_name="gh_string" type_code="10">Construct Point</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="5">
+ <item name="Description" type_name="gh_string" type_code="10">Construct a point from {xyz} coordinates.</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">d4601b93-4450-4b6e-862a-bf2609a4735e</item>
+ <item name="Name" type_name="gh_string" type_code="10">Construct Point</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Pt</item>
+ </items>
+ <chunks count="5">
+ <chunk name="Attributes">
+ <items count="2">
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+ <Y>1580</Y>
+ <W>52</W>
+ <H>64</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>317</X>
+ <Y>1612</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="param_input" index="0">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">{x} coordinate</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">8c217294-5520-4b18-bff5-1088b16dcbd8</item>
+ <item name="Name" type_name="gh_string" type_code="10">X coordinate</item>
+ <item name="NickName" type_name="gh_string" type_code="10">X</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">284c1cc9-3635-4b27-8730-cabd5b035623</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>294</X>
+ <Y>1582</Y>
+ <W>11</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>299.5</X>
+ <Y>1592</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="PersistentData">
+ <items count="1">
+ <item name="Count" type_name="gh_int32" type_code="3">1</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Branch" index="0">
+ <items count="2">
+ <item name="Count" type_name="gh_int32" type_code="3">1</item>
+ <item name="Path" type_name="gh_string" type_code="10">{0}</item>
+ </items>
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+ <chunk name="Item" index="0">
+ <items count="1">
+ <item name="number" type_name="gh_double" type_code="6">-0.0625</item>
+ </items>
+ </chunk>
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+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="1">
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+ <item name="Name" type_name="gh_string" type_code="10">Text Size</item>
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+ <item name="Description" type_name="gh_string" type_code="10">Resulting graph mapped values, mapped on the Y Axis</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">71bc6904-175f-469f-b566-4dbe32d835bb</item>
+ <item name="Name" type_name="gh_string" type_code="10">Mapped</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a19be86e-3fe3-4691-8fd2-6cb3e162fb6a</item>
+ <item name="Name" type_name="gh_string" type_code="10">Graph Curves</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Graph Curves</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ </items>
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+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">The points on the graph curves where the X Axis input values intersected</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">642a1ea5-ea0c-4d1e-b21d-55bfa91afc3e</item>
+ <item name="Name" type_name="gh_string" type_code="10">Graph Points</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">c2cc14a6-bdbc-42c4-80ac-f04fc25244d7</item>
+ <item name="Name" type_name="gh_string" type_code="10">Value Lines</item>
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+ </items>
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+ </chunks>
+ </chunk>
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+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
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+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">6d4906b1-c07e-43fa-bab1-8b6651d8cf70</item>
+ <item name="Name" type_name="gh_string" type_code="10">Value Points</item>
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+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">The lines from the graph curves to the Y Axis graph mapped values</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f2e9fd13-480a-409c-9224-37b31d1b5e8a</item>
+ <item name="Name" type_name="gh_string" type_code="10">Mapped Lines</item>
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+ <chunk name="param_output" index="7">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">The graph boundary background as a surface</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">c77ce4ed-f82a-485e-861b-56e4af6cd670</item>
+ <item name="Name" type_name="gh_string" type_code="10">Boundary</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Boundary</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ </items>
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+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">The graph labels as curve outlines</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">1304912b-9e82-4215-9b9b-472899f3a3e0</item>
+ <item name="Name" type_name="gh_string" type_code="10">Labels</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Labels</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ </items>
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+ <items count="7">
+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">True for input values outside of the X Axis domain bounds
+False for input values inside of the X Axis domain bounds</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">0d520714-1f87-47f8-8e49-acc1bb50d032</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">Out Of Bounds</item>
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+ <item name="Access" type_name="gh_int32" type_code="3">1</item>
+ <item name="Description" type_name="gh_string" type_code="10">True for input values on the X Axis which intersect a graph curve
+False for input values on the X Axis which do not intersect a graph curve</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">dc75d0fb-7ad1-4ff6-be3f-405bd74925af</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">Intersected</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">b6236720-8d88-4289-93c3-ac4c99f9b97b</item>
+ <item name="Name" type_name="gh_string" type_code="10">Relay</item>
+ </items>
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+ <chunk name="Container">
+ <items count="8">
+ <item name="Access" type_name="gh_int32" type_code="3">2</item>
+ <item name="Description" type_name="gh_string" type_code="10">A wire relay object</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">fba4a0b5-d761-41e8-98e6-857040e4a72f</item>
+ <item name="Name" type_name="gh_string" type_code="10">Relay</item>
+ <item name="NickName" type_name="gh_string" type_code="10"></item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">71bc6904-175f-469f-b566-4dbe32d835bb</item>
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+ </items>
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+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2013</X>
+ <Y>1734</Y>
+ <W>40</W>
+ <H>16</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2033</X>
+ <Y>1742</Y>
+ </item>
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+ <chunk name="Object" index="186">
+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">fb6aba99-fead-4e42-b5d8-c6de5ff90ea6</item>
+ <item name="Name" type_name="gh_string" type_code="10">DotNET VB Script (LEGACY)</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">A VB.NET scriptable component</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">04f46bd6-5820-4e23-9fee-ec36f36a7db0</item>
+ <item name="Name" type_name="gh_string" type_code="10">DotNET VB Script (LEGACY)</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Turtle</item>
+ <item name="ReferenceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="ScriptSource" type_name="gh_string" type_code="10"> Dim i As Integer
+ Dim dir As New On3dVector(1, 0, 0)
+ Dim pos As New On3dVector(0, 0, 0)
+ Dim axis As New On3dVector(0, 0, 1)
+ Dim pnts As New List(Of On3dVector)
+
+ pnts.Add(pos)
+
+ For i = 0 To Forward.Count() - 1
+ Dim P As New On3dVector
+ dir.Rotate(Left(i), axis)
+ P = dir * Forward(i) + pnts(i)
+ pnts.Add(P)
+ Next
+
+ Points = pnts</item>
+ </items>
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+ <item name="ID" index="1" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item>
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</bitmap>
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+ </items>
+ </chunk>
+ </chunks>
+</Archive>
\ No newline at end of file