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.⠀⠀⠀⠀◯⠀ᗱᗴᴥᑎ✤ᗩᗯᴥᑎᑐᑕ⠀◯⠀ᗱᗴᗯꖴ✤ᗩᗯꖴᴥᗱᗴᗝ⠀◯⠀ᗝᗱᗴߦᗩᙏ⠀◯⠀옷ߦᗩᴥᕤᕦ⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀ᕤᕦᴥᗩߦ옷⠀◯⠀ᙏᗩߦᗱᗴᗝ⠀◯⠀ᗝᗱᗴᴥꖴᗯᗩ✤ꖴᗯᗱᗴ⠀◯⠀ᑐᑕᑎᴥᗯᗩ✤ᑎᴥᗱᗴ⠀◯⠀⠀⠀⠀.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.⠀⠀⠀⠀◯⠀ᗱᗴᴥᑎ✤ᗩᗯᴥᑎᑐᑕ⠀◯⠀ᗱᗴᗯꖴ✤ᗩᗯꖴᴥᗱᗴᗝ⠀◯⠀ᗝᗱᗴߦᗩᙏ⠀◯⠀옷ߦᗩᴥᕤᕦ⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀ᕤᕦᴥᗩߦ옷⠀◯⠀ᙏᗩߦᗱᗴᗝ⠀◯⠀ᗝᗱᗴᴥꖴᗯᗩ✤ꖴᗯᗱᗴ⠀◯⠀ᑐᑕᑎᴥᗯᗩ✤ᑎᴥᗱᗴ⠀◯⠀⠀⠀⠀.GHX
new file mode 100644
index 00000000..f75c103f
--- /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.⠀⠀⠀⠀◯⠀ᗱᗴᴥᑎ✤ᗩᗯᴥᑎᑐᑕ⠀◯⠀ᗱᗴᗯꖴ✤ᗩᗯꖴᴥᗱᗴᗝ⠀◯⠀ᗝᗱᗴߦᗩᙏ⠀◯⠀옷ߦᗩᴥᕤᕦ⠀◯⠀⠀⠀⠀ⵙ⠀⠀⠀⠀◯⠀ᕤᕦᴥᗩߦ옷⠀◯⠀ᙏᗩߦᗱᗴᗝ⠀◯⠀ᗝᗱᗴᴥꖴᗯᗩ✤ꖴᗯᗱᗴ⠀◯⠀ᑐᑕᑎᴥᗯᗩ✤ᑎᴥᗱᗴ⠀◯⠀⠀⠀⠀.GHX
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+ <item name="ID" index="3" type_name="gh_guid" type_code="9">db6d761f-a5ff-4557-88d7-7e388111c80b</item>
+ <item name="ID" index="4" type_name="gh_guid" type_code="9">05da3e76-3947-41c3-ba67-834e727e19e6</item>
+ <item name="ID" index="5" type_name="gh_guid" type_code="9">c724c2b6-0db7-40c2-8f7d-af88759b670e</item>
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+ <item name="ID_Count" type_name="gh_int32" type_code="3">8</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">399ae478-9faa-4113-878a-ecbeb9023e91</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>
+ <chunks count="1">
+ <chunk name="Attributes" />
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="3">
+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">c552a431-af5b-46a9-a8a4-0fcbc27ef596</item>
+ <item name="Name" type_name="gh_string" type_code="10">Group</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="14">
+ <item name="Border" type_name="gh_int32" type_code="3">3</item>
+ <item name="Colour" type_name="gh_drawing_color" type_code="36">
+ <ARGB>150;255;255;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">85b00841-044b-4e33-a4ec-9b92802b26a4</item>
+ <item name="ID" index="1" type_name="gh_guid" type_code="9">e0c48ccf-10ce-4e90-99aa-82531dc21fa4</item>
+ <item name="ID" index="2" type_name="gh_guid" type_code="9">52d7ea4f-a46f-446b-990e-bc0781dd5bfd</item>
+ <item name="ID" index="3" type_name="gh_guid" type_code="9">47c2637e-e747-48a1-8a92-8e349052dbe1</item>
+ <item name="ID" index="4" type_name="gh_guid" type_code="9">745c7cd8-626b-4ae3-af49-236a0540c9db</item>
+ <item name="ID" index="5" type_name="gh_guid" type_code="9">d2205dfc-8d4a-4036-b26c-f14bc5cca3f9</item>
+ <item name="ID" index="6" type_name="gh_guid" type_code="9">e5dbc17c-65a4-4ede-98e9-cc175d4ef477</item>
+ <item name="ID_Count" type_name="gh_int32" type_code="3">7</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">18e93f2f-ac8b-477a-9b1d-c3e107cc3c5b</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>
+ <chunks count="1">
+ <chunk name="Attributes" />
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="4">
+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">c552a431-af5b-46a9-a8a4-0fcbc27ef596</item>
+ <item name="Name" type_name="gh_string" type_code="10">Group</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="15">
+ <item name="Border" type_name="gh_int32" type_code="3">3</item>
+ <item name="Colour" type_name="gh_drawing_color" type_code="36">
+ <ARGB>150;255;255;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">3091dae8-d5dc-4fac-a891-c5a5c7118bd1</item>
+ <item name="ID" index="1" type_name="gh_guid" type_code="9">b15849e1-cdad-4c2e-becd-859af856d608</item>
+ <item name="ID" index="2" type_name="gh_guid" type_code="9">2187d492-e79a-43d1-9758-c683cee6a1a6</item>
+ <item name="ID" index="3" type_name="gh_guid" type_code="9">64a13dde-4d5b-4c3c-9590-dd2d98964c51</item>
+ <item name="ID" index="4" type_name="gh_guid" type_code="9">108b0aae-e403-4a36-b12b-8ef951a35c50</item>
+ <item name="ID" index="5" type_name="gh_guid" type_code="9">f33205f0-793a-41b8-b72a-e667cf426b4f</item>
+ <item name="ID" index="6" type_name="gh_guid" type_code="9">8d36667c-3eb9-462e-91a9-b77c202939ca</item>
+ <item name="ID" index="7" type_name="gh_guid" type_code="9">360c0603-8317-424e-a8c3-12ddeacddebd</item>
+ <item name="ID_Count" type_name="gh_int32" type_code="3">8</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">9c976e8a-0a2d-4fb1-a458-b40424176e99</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>
+ <chunks count="1">
+ <chunk name="Attributes" />
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="5">
+ <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="6">
+ <item name="Description" type_name="gh_string" type_code="10">A VB.NET scriptable component</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f8463a6a-537d-44ae-a102-2cbf6773c33a</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>
+ <chunks count="7">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>4298</X>
+ <Y>388</Y>
+ <W>119</W>
+ <H>44</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>4359</X>
+ <Y>410</Y>
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+ <items count="13">
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+ <item name="Count" type_name="gh_int32" type_code="3">2</item>
+ <item name="Description" index="0" type_name="gh_string" type_code="10">Script Variable Forward</item>
+ <item name="Description" index="1" type_name="gh_string" type_code="10">Script Variable Left</item>
+ <item name="ID" index="0" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="ID" index="1" type_name="gh_guid" type_code="9">84fa917c-1ed8-4db3-8be1-7bdc4a6495a2</item>
+ <item name="Mutable" index="0" type_name="gh_bool" type_code="1">true</item>
+ <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">Forward</item>
+ <item name="Name" index="1" type_name="gh_string" type_code="10">Left</item>
+ <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>
+ </items>
+ </chunk>
+ <chunk name="VariableOutput">
+ <items count="11">
+ <item name="Count" type_name="gh_int32" type_code="3">2</item>
+ <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>
+ <item name="Mutable" index="0" type_name="gh_bool" type_code="1">true</item>
+ <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>
+ </chunk>
+ <chunk name="param_input" index="0">
+ <items count="12">
+ <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">ce1f978e-a982-441e-8781-42beeed9349f</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>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">11d6ae9c-db85-41da-a72e-197fbac37970</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>4300</X>
+ <Y>390</Y>
+ <W>44</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>4323.5</X>
+ <Y>400</Y>
+ </item>
+ </items>
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+ </chunks>
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+ <items count="12">
+ <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 Left</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">57e2c9a0-b37d-4c4b-9e2b-b0e17a521d43</item>
+ <item name="Name" type_name="gh_string" type_code="10">Left</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Left</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>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">4ebc6662-8141-4321-80cb-843bf3aabe95</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>
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+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>4300</X>
+ <Y>410</Y>
+ <W>44</W>
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+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>4323.5</X>
+ <Y>420</Y>
+ </item>
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+ </chunks>
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+ <items count="6">
+ <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">33dd288d-3d90-4a29-8ab3-866accaf2be0</item>
+ <item name="Name" type_name="gh_string" type_code="10">Output</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Output</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>4374</X>
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+ <W>41</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>4394.5</X>
+ <Y>400</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <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">a7101779-445c-4899-9b31-ce0a4803f08d</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>
+ <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>4374</X>
+ <Y>410</Y>
+ <W>41</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>4394.5</X>
+ <Y>420</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="6">
+ <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="4">
+ <item name="Description" type_name="gh_string" type_code="10">Create a series of numbers.</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">3091dae8-d5dc-4fac-a891-c5a5c7118bd1</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">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>448</X>
+ <Y>502</Y>
+ <W>104</W>
+ <H>64</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>498</X>
+ <Y>534</Y>
+ </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">bfe8e6e2-eddc-4584-8ce4-005a112f16fc</item>
+ <item name="Name" type_name="gh_string" type_code="10">Start</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Start</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>450</X>
+ <Y>504</Y>
+ <W>33</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>468</X>
+ <Y>514</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>
+ <chunks count="1">
+ <chunk name="Item" index="0">
+ <items count="1">
+ <item name="number" type_name="gh_double" type_code="6">0</item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="1">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">Step size for each successive number</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">3ef6124c-d6dc-426b-a979-0ad9d65d59da</item>
+ <item name="Name" type_name="gh_string" type_code="10">Step</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Step</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">2b79d86a-c886-48ba-a41d-bd2a6298f66d</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>450</X>
+ <Y>524</Y>
+ <W>33</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>468</X>
+ <Y>534</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="PersistentData">
+ <items count="1">
+ <item name="Count" type_name="gh_int32" type_code="3">1</item>
+ </items>
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+ <chunk name="Branch" index="0">
+ <items count="2">
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+ <item name="Path" type_name="gh_string" type_code="10">{0}</item>
+ </items>
+ <chunks count="1">
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+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">Number of values in the series</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">41382c6d-efca-4f46-89a4-f4a83cdfe7f4</item>
+ <item name="Name" type_name="gh_string" type_code="10">Count</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Count</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">7f4503d3-711b-4865-8533-135f511f6962</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>450</X>
+ <Y>544</Y>
+ <W>33</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>468</X>
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+ <item name="Name" type_name="gh_string" type_code="10">Variable X</item>
+ <item name="NickName" type_name="gh_string" type_code="10">X</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">38133632-4c97-466b-b444-265770619668</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Variable O_EZIS_O_SIZE_O</item>
+ <item name="NickName" type_name="gh_string" type_code="10">O_EZIS_O_SIZE_O</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Variable O_REWOP_TOOR_O_ROOT_POWER_O</item>
+ <item name="NickName" type_name="gh_string" type_code="10">O_REWOP_TOOR_O_ROOT_POWER_O</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Variable O_REWOP_O_POWER_O</item>
+ <item name="NickName" type_name="gh_string" type_code="10">O_REWOP_O_POWER_O</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Result</item>
+ <item name="NickName" type_name="gh_string" type_code="10">R</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">Gate</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Gate</item>
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+ <Y>688</Y>
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+ <chunks count="1">
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">8b88afc8-fcb9-4c01-9028-fd394c23cf23</item>
+ <item name="Mutable" type_name="gh_bool" type_code="1">false</item>
+ <item name="Name" type_name="gh_string" type_code="10">Stream 0</item>
+ <item name="NickName" type_name="gh_string" type_code="10">0</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">f95124bc-63c1-434b-b826-b22df9438a92</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
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+ <Y>698</Y>
+ <W>28</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ <Y>708</Y>
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+ <item name="Description" type_name="gh_string" type_code="10">Input stream at index 1</item>
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+ <item name="Mutable" type_name="gh_bool" type_code="1">false</item>
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+ <item name="Source" index="0" type_name="gh_guid" type_code="9">d5068386-bfdb-4d84-9996-16eda0ccf7db</item>
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+ <Y>718</Y>
+ <W>28</W>
+ <H>20</H>
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+ <Y>728</Y>
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+ <item name="Description" type_name="gh_string" type_code="10">Input stream at index 2</item>
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+ <item name="Mutable" type_name="gh_bool" type_code="1">false</item>
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+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">f7b0f737-7ab2-4e8c-b330-bda8f73ff3ab</item>
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+ <item name="Mutable" type_name="gh_bool" type_code="1">false</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">3</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a39af198-a084-47e9-836d-0fc9ef465e43</item>
+ <item name="Mutable" type_name="gh_bool" type_code="1">false</item>
+ <item name="Name" type_name="gh_string" type_code="10">Stream 4</item>
+ <item name="NickName" type_name="gh_string" type_code="10">4</item>
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+ <item name="Mutable" type_name="gh_bool" type_code="1">false</item>
+ <item name="Name" type_name="gh_string" type_code="10">Stream</item>
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+ </items>
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+ <chunk name="Container">
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+ <item name="Description" type_name="gh_string" type_code="10">Numeric scroller for single numbers</item>
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+ <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>
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+ <item name="Radix" type_name="gh_int32" type_code="3">1</item>
+ <item name="Suffix" type_name="gh_string" type_code="10"></item>
+ <item name="Value" type_name="gh_decimal" type_code="7">0.00162145672</item>
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+ <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">84724672-afcf-4457-9ded-ef302f621c7f</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 Script</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>2239</X>
+ <Y>2912</Y>
+ <W>84</W>
+ <H>184</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2281</X>
+ <Y>3004</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="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 PtA</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">c384ac3f-df4d-453d-a7c5-387e93a60b13</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="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">e1937b56-b1da-4c12-8bd8-e34ee81746ef</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2241</X>
+ <Y>2914</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>2924</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>
+ <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="2">
+ <item name="Coordinate" type_name="gh_point3d" type_code="51">
+ <X>0</X>
+ <Y>0</Y>
+ <Z>0</Z>
+ </item>
+ <item name="TypeName" type_name="gh_string" type_code="10">Grasshopper.Kernel.Types.GH_Point</item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="1">
+ <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 PtB</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">8bddec7a-5cee-4c2d-a042-aa892fd83b36</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="SourceCount" type_name="gh_int32" type_code="3">0</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>2241</X>
+ <Y>2934</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>2944</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="2">
+ <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 Pln</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">b3259d85-c916-4d9a-99bf-7e895fca6eec</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="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">3897522d-58e9-4d60-b38c-978ddacfedd8</item>
+ </items>
+ <chunks count="2">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2241</X>
+ <Y>2954</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>2964</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>
+ <chunks count="1">
+ <chunk name="Item" index="0">
+ <items count="2">
+ <item name="TypeName" type_name="gh_string" type_code="10">Grasshopper.Kernel.Types.GH_Plane</item>
+ <item name="plane" type_name="gh_plane" type_code="72">
+ <Ox>0</Ox>
+ <Oy>0</Oy>
+ <Oz>0</Oz>
+ <Xx>1</Xx>
+ <Xy>0</Xy>
+ <Xz>0</Xz>
+ <Yx>0</Yx>
+ <Yy>1</Yy>
+ <Yz>0</Yz>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </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">fb43f351-f380-4f29-8e4f-9fb2010411db</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>2241</X>
+ <Y>2974</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>2984</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="4">
+ <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 Wid</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">93dbd769-ff0d-4cae-938b-75d6be10d33d</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="Source" index="0" type_name="gh_guid" type_code="9">5efa96ce-0a9b-4178-9dd5-b7e889d7e5f9</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>2241</X>
+ <Y>2994</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>3004</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">9ce1f865-89f1-4a5b-a1c9-65f77f658109</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>2241</X>
+ <Y>3014</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>3024</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">717409d3-a5de-4c70-987d-4ebacb963883</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">f67b69a9-68b4-4391-9b0b-36f79b377ace</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>2241</X>
+ <Y>3034</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>3044</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">e7404a32-6dcf-4dac-96ec-df9fcf003e19</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>2241</X>
+ <Y>3054</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>3064</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">3b61faa3-6a4f-4d43-96da-0fe1d52fda2b</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>2241</X>
+ <Y>3074</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2255</X>
+ <Y>3084</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">7de3b2dc-fe4e-43e1-a0a8-4bc81691250c</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>2296</X>
+ <Y>2914</Y>
+ <W>25</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2308.5</X>
+ <Y>2925.25</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">e309227c-8c84-4572-b1a0-62b15cb940a1</item>
+ <item name="Name" type_name="gh_string" type_code="10">Pts</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Crv</item>
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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">F</item>
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+ <item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
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+ </items>
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+ </items>
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+ <item name="Name" type_name="gh_string" type_code="10">Curve Middle</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Midpoint</item>
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+ </items>
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+You can Right click on the Heteromapper's icon and choose "AutoDomain" mode to define Output domain based on input domain interval; otherwise it'll be set to 0-1 in "Normalized" mode.</item>
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+ <item name="NickName" type_name="gh_string" type_code="10">Boundary</item>
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+ <item name="Description" type_name="gh_string" type_code="10">List of input numbers</item>
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+ <item name="Name" type_name="gh_string" type_code="10">Numbers</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Numbers</item>
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+ <item name="Count" type_name="gh_int32" type_code="3">9</item>
+ <item name="Path" type_name="gh_string" type_code="10">{0}</item>
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+ <item name="number" type_name="gh_double" type_code="6">0.5</item>
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+ <item name="number" type_name="gh_double" type_code="6">0.9</item>
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+ </chunk>
+ <chunk name="param_input" index="3">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">(Optional) Input Domain
+if omitted, it would be 0-1 in "Normalize" mode by default
+ or be the interval of the input list in case of selecting "AutoDomain" mode</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">5bcbd057-e761-453c-8d9b-0c136cd52c8a</item>
+ <item name="Name" type_name="gh_string" type_code="10">Input</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Input</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ </items>
+ <chunks count="1">
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+ <W>50</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1829.5</X>
+ <Y>2796</Y>
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+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="4">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">(Optional) Output Domain
+ if omitted, it would be 0-1 in "Normalize" mode by default
+ or be the interval of the input list in case of selecting "AutoDomain" mode</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">cb3c83b1-ea5d-4556-a2cd-947db2b85070</item>
+ <item name="Name" type_name="gh_string" type_code="10">Output</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Output</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</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>1803</X>
+ <Y>2806</Y>
+ <W>50</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1829.5</X>
+ <Y>2816</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_output" 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">Output Numbers</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">aa99eb53-f847-4761-874c-b2b7a794afd6</item>
+ <item name="Name" type_name="gh_string" type_code="10">Number</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Number</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>1883</X>
+ <Y>2726</Y>
+ <W>45</W>
+ <H>100</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1905.5</X>
+ <Y>2776</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="74">
+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">575660b1-8c79-4b8d-9222-7ab4a6ddb359</item>
+ <item name="Name" type_name="gh_string" type_code="10">Rectangle 2Pt</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="5">
+ <item name="Description" type_name="gh_string" type_code="10">Create a rectangle from a base plane and two points</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">854346d9-987e-4342-8d62-d29ccc1a4cd3</item>
+ <item name="Name" type_name="gh_string" type_code="10">Rectangle 2Pt</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Rectangle 2Pt</item>
+ </items>
+ <chunks count="7">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>1934</X>
+ <Y>2464</Y>
+ <W>129</W>
+ <H>84</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1992</X>
+ <Y>2506</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="param_input" index="0">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Rectangle base plane</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">c5fedded-f2bb-44cc-a6db-545b7f0215de</item>
+ <item name="Name" type_name="gh_string" type_code="10">Plane</item>
+ <item name="NickName" type_name="gh_string" type_code="10">RANGE</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>1936</X>
+ <Y>2466</Y>
+ <W>41</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1958</X>
+ <Y>2476</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>
+ <chunks count="1">
+ <chunk name="Item" index="0">
+ <items count="1">
+ <item name="plane" type_name="gh_plane" type_code="72">
+ <Ox>0</Ox>
+ <Oy>0</Oy>
+ <Oz>0</Oz>
+ <Xx>1</Xx>
+ <Xy>0</Xy>
+ <Xz>0</Xz>
+ <Yx>0</Yx>
+ <Yy>1</Yy>
+ <Yz>0</Yz>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="1">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">First corner point.</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">2c06c2ff-6848-4d61-8acd-ae78937cb293</item>
+ <item name="Name" type_name="gh_string" type_code="10">Point A</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Point A</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">52cef00d-db8e-4b87-8695-4352608b0e17</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>1936</X>
+ <Y>2486</Y>
+ <W>41</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1958</X>
+ <Y>2496</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>
+ <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>
+ <Y>0</Y>
+ <Z>0</Z>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="2">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">Second corner point.</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">114f8d8e-db76-4e96-86ba-7a143c7ced74</item>
+ <item name="Name" type_name="gh_string" type_code="10">Point B</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Point B</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">011b00fc-5add-41a0-9757-9d38ebdc9d11</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>1936</X>
+ <Y>2506</Y>
+ <W>41</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1958</X>
+ <Y>2516</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>
+ <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>1</X>
+ <Y>1</Y>
+ <Z>0</Z>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="3">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Rectangle corner fillet radius</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a236b107-43f0-4732-ab0f-101a758127ea</item>
+ <item name="Name" type_name="gh_string" type_code="10">Radius</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Radius</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>1936</X>
+ <Y>2526</Y>
+ <W>41</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>1958</X>
+ <Y>2536</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>
+ <chunks count="1">
+ <chunk name="Item" index="0">
+ <items count="1">
+ <item name="number" type_name="gh_double" type_code="6">0</item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_output" index="0">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Rectangle defined by P, A and B</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">d222d866-05d2-41e8-9567-8cca0e0544d2</item>
+ <item name="Name" type_name="gh_string" type_code="10">Rectangle</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Rectangle</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>2007</X>
+ <Y>2466</Y>
+ <W>54</W>
+ <H>40</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2034</X>
+ <Y>2486</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_output" index="1">
+ <items count="6">
+ <item name="Description" type_name="gh_string" type_code="10">Length of rectangle curve</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">830470ec-1feb-48e8-bbd9-ef386ee8c7cc</item>
+ <item name="Name" type_name="gh_string" type_code="10">Length</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Length</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>2007</X>
+ <Y>2506</Y>
+ <W>54</W>
+ <H>40</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2034</X>
+ <Y>2526</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="75">
+ <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>
+ <chunks count="1">
+ <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">bd4aaa1e-5c93-4d92-a13b-51513caaff31</item>
+ <item name="Name" type_name="gh_string" type_code="10">Relay</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Relay</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">8d0d12bd-da23-49cc-b34c-50a33768057a</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2819</X>
+ <Y>2867</Y>
+ <W>44</W>
+ <H>16</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2841</X>
+ <Y>2875</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="Object" index="76">
+ <items count="2">
+ <item name="GUID" type_name="gh_guid" type_code="9">e9eb1dcf-92f6-4d4d-84ae-96222d60f56b</item>
+ <item name="Name" type_name="gh_string" type_code="10">Move</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Container">
+ <items count="5">
+ <item name="Description" type_name="gh_string" type_code="10">Translate (move) an object along a vector.</item>
+ <item name="Hidden" type_name="gh_bool" type_code="1">true</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f678f333-3b39-4b6c-bd80-2b85058c90ac</item>
+ <item name="Name" type_name="gh_string" type_code="10">Move</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Move</item>
+ </items>
+ <chunks count="5">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2868</X>
+ <Y>2923</Y>
+ <W>141</W>
+ <H>44</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2936</X>
+ <Y>2945</Y>
+ </item>
+ </items>
+ </chunk>
+ <chunk name="param_input" index="0">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">Base geometry</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">7cab920d-d74d-4e0c-8312-2eeecf42c38b</item>
+ <item name="Name" type_name="gh_string" type_code="10">Geometry</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Geometry</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">true</item>
+ <item name="Source" index="0" type_name="gh_guid" type_code="9">3a20ff06-eeb1-4b64-926b-3dfaf9128bc9</item>
+ <item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
+ </items>
+ <chunks count="1">
+ <chunk name="Attributes">
+ <items count="2">
+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2870</X>
+ <Y>2925</Y>
+ <W>51</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2897</X>
+ <Y>2935</Y>
+ </item>
+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="param_input" index="1">
+ <items count="7">
+ <item name="Description" type_name="gh_string" type_code="10">Translation vector</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">cff43877-ee64-4b45-9621-9ab78fdbe784</item>
+ <item name="Name" type_name="gh_string" type_code="10">Motion</item>
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+ <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>
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+ <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">0ee0d29e-783d-4fcb-832e-e2bc26ea1e1d</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 Script</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="10">
+ <item name="AllowTreeAccess" type_name="gh_bool" type_code="1">true</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">e0b340a6-33e3-4438-bc60-5fea5b18f4fa</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>
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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="2">
+ <item name="Coordinate" type_name="gh_point3d" type_code="51">
+ <X>0</X>
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+ <Z>0</Z>
+ </item>
+ <item name="TypeName" type_name="gh_string" type_code="10">Grasshopper.Kernel.Types.GH_Point</item>
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+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="1">
+ <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 PtB</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">a74e4c29-c138-4cd0-b6ec-cd627a642509</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="SourceCount" type_name="gh_int32" type_code="3">0</item>
+ <item name="TypeHintID" type_name="gh_guid" type_code="9">e1937b56-b1da-4c12-8bd8-e34ee81746ef</item>
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+ <chunks count="1">
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+ <X>2334</X>
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+ </chunk>
+ <chunk name="InputParam" index="2">
+ <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 Pln</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">f4a02e94-d4ad-4590-84da-4f3345f5db67</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="SourceCount" type_name="gh_int32" type_code="3">0</item>
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+ </items>
+ <chunks count="2">
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+ <X>2334</X>
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+ </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>
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+ </items>
+ <chunks count="1">
+ <chunk name="Item" index="0">
+ <items count="2">
+ <item name="TypeName" type_name="gh_string" type_code="10">Grasshopper.Kernel.Types.GH_Plane</item>
+ <item name="plane" type_name="gh_plane" type_code="72">
+ <Ox>0</Ox>
+ <Oy>0</Oy>
+ <Oz>0</Oz>
+ <Xx>1</Xx>
+ <Xy>0</Xy>
+ <Xz>0</Xz>
+ <Yx>0</Yx>
+ <Yy>1</Yy>
+ <Yz>0</Yz>
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+ </chunk>
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+ </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">e8ad0a50-2a34-4c5c-abc5-fbeb62b12cf3</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>
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+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2334</X>
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+ <chunk name="InputParam" index="4">
+ <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 Wid</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">3d51ade1-9c1d-448d-ae91-7266d9eeadc1</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="Source" index="0" type_name="gh_guid" type_code="9">0c529f4b-39cf-4343-8565-04e4988cf6c0</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">
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+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
+ <X>2320</X>
+ <Y>3423</Y>
+ <W>25</W>
+ <H>20</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2334</X>
+ <Y>3433</Y>
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+ </items>
+ </chunk>
+ </chunks>
+ </chunk>
+ <chunk name="InputParam" index="5">
+ <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 Ht</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">42b3091b-80e1-471c-a7f5-f1248e8297a0</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="Source" index="0" type_name="gh_guid" type_code="9">e0ec9007-74c8-4451-9373-9d9815942542</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>
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+ <chunks count="1">
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+ <X>2320</X>
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+ <W>25</W>
+ <H>20</H>
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+ <X>2334</X>
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+ <chunk name="InputParam" index="6">
+ <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">8c2cb104-2fdb-463a-9d03-caa3dc8e6828</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="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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+ <W>25</W>
+ <H>20</H>
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+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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+ <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">f1b789aa-353e-4333-a570-95733cae4b39</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>
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+ <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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+ <W>25</W>
+ <H>20</H>
+ </item>
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+ <X>2334</X>
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+ <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">c95788d2-4a1a-44bf-a2f3-e275b3a140ea</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>
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+ <W>25</W>
+ <H>20</H>
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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">fa2597fb-ad52-4ad7-9f68-56f0ba98f216</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>
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+ <W>25</W>
+ <H>22</H>
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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">4fecf712-f978-4ff9-b599-c7123ce298cb</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>
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+ <Y>3365</Y>
+ <W>25</W>
+ <H>23</H>
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+ <X>2387.5</X>
+ <Y>3376.75</Y>
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+ </chunks>
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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">85964c8e-57ef-45e8-8254-561b34e4791d</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">
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+ <X>2375</X>
+ <Y>3388</Y>
+ <W>25</W>
+ <H>22</H>
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+ <item name="Description" type_name="gh_string" type_code="10">Output parameter L</item>
+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">ac6ba150-f790-44ec-a438-7c12be8544ee</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>
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+ <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
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+ <Y>3410</Y>
+ <W>25</W>
+ <H>23</H>
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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">685d261b-2e57-4de3-88c1-b53a7e4828c6</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>
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+ <W>25</W>
+ <H>22</H>
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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">99095cd4-3684-4b3e-bea7-c8ffb6520772</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>
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+ <Y>3455</Y>
+ <W>25</W>
+ <H>23</H>
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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">b9e6ad28-add8-420b-948a-b9279ad8639a</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>2375</X>
+ <Y>3478</Y>
+ <W>25</W>
+ <H>22</H>
+ </item>
+ <item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
+ <X>2387.5</X>
+ <Y>3489.25</Y>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">e8b32b49-9ae0-4958-b375-30f99fc9a1e5</item>
+ <item name="Name" type_name="gh_string" type_code="10">Reach Plane</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Reach Plane</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">dcdbf4e7-5dfc-4e6d-8716-a19152e42ade</item>
+ <item name="Name" type_name="gh_string" type_code="10">Offset Plane</item>
+ <item name="NickName" type_name="gh_string" type_code="10">Offset Plane</item>
+ <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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+ <item name="InstanceGuid" type_name="gh_guid" type_code="9">308874a3-735e-4350-901b-90ca30ecd1de</item>
+ <item name="Name" type_name="gh_string" type_code="10">Intersected</item>
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</bitmap>
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+</Archive>
\ No newline at end of file