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working tetrahedron intersections

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This commit is contained in:
David Allemang
2018-04-01 03:28:50 -04:00
parent fd017219b7
commit 26bd1d2606
6 changed files with 586 additions and 48 deletions
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204
Tetrahedrons/MVec3d.cs Normal file
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using System;
using OpenTK;
namespace Tetrahedrons
{
// ReSharper disable once InconsistentNaming
public struct MVec3d
{
public static readonly MVec3d Unit = new MVec3d(1, 0, 0, 0, 0, 0, 0, 0);
public static readonly MVec3d Unit1 = new MVec3d(0, 1, 0, 0, 0, 0, 0, 0);
public static readonly MVec3d Unit2 = new MVec3d(0, 0, 1, 0, 0, 0, 0, 0);
public static readonly MVec3d Unit3 = new MVec3d(0, 0, 0, 1, 0, 0, 0, 0);
public static readonly MVec3d Unit23 = new MVec3d(0, 0, 0, 0, 1, 0, 0, 0);
public static readonly MVec3d Unit31 = new MVec3d(0, 0, 0, 0, 0, 1, 0, 0);
public static readonly MVec3d Unit12 = new MVec3d(0, 0, 0, 0, 0, 0, 1, 0);
public static readonly MVec3d Unit123 = new MVec3d(0, 0, 0, 0, 0, 0, 0, 1);
public double E;
public double E1;
public double E2;
public double E3;
public double E23;
public double E31;
public double E12;
public double E123;
public MVec3d(double e, double e1, double e2, double e3, double e23, double e31, double e12, double e123)
{
E = e;
E1 = e1;
E2 = e2;
E3 = e3;
E23 = e23;
E31 = e31;
E12 = e12;
E123 = e123;
}
public MVec3d(MVec3d s, MVec3d v, MVec3d b, MVec3d t)
: this(s.E, v.E1, v.E2, v.E3, b.E23, b.E31, b.E12, t.E123)
{
}
public static MVec3d Scalar(double e)
{
return new MVec3d(e, 0, 0, 0, 0, 0, 0, 0);
}
public static MVec3d Vector(double e1, double e2, double e3)
{
return new MVec3d(0, e1, e2, e3, 0, 0, 0, 0);
}
public static MVec3d Vector(Vector3d v)
{
return new MVec3d(0, v.X, v.Y, v.Z, 0, 0, 0, 0);
}
public static MVec3d Bivector(double e23, double e31, double e12)
{
return new MVec3d(0, 0, 0, 0, e23, e31, e12, 0);
}
public static MVec3d Trivector(double e123)
{
return new MVec3d(0, 0, 0, 0, 0, 0, 0, e123);
}
public static MVec3d Complex(double real, double imag)
{
return new MVec3d(real, 0, 0, 0, 0, 0, 0, imag);
}
public static MVec3d Complex(double w, double i, double j, double k)
{
return new MVec3d(w, 0, 0, 0, i, j, k, 0);
}
public static MVec3d Complex(double angle, MVec3d plane)
{
return Math.Cos(angle) + Math.Sin(angle) * plane;
}
public static MVec3d Add(MVec3d m, MVec3d n)
{
return new MVec3d(m.E + n.E,
m.E1 + n.E1, m.E2 + n.E2, m.E3 + n.E3,
m.E23 + n.E23, m.E31 + n.E31, m.E12 + n.E12,
m.E123 + n.E123);
}
public static MVec3d Sub(MVec3d m, MVec3d n)
{
return new MVec3d(m.E - n.E,
m.E1 - n.E1, m.E2 - n.E2, m.E3 - n.E3,
m.E23 - n.E23, m.E31 - n.E31, m.E12 - n.E12,
m.E123 - n.E123);
}
public static MVec3d Mult(MVec3d m, MVec3d n)
{
return new MVec3d(
m.E * n.E + m.E1 * n.E1 + m.E2 * n.E2 + m.E3 * n.E3 - m.E23 * n.E23 - m.E31 * n.E31 - m.E12 * n.E12 - m.E123 * n.E123,
m.E * n.E1 + m.E1 * n.E - m.E2 * n.E12 + m.E3 * n.E31 - m.E23 * n.E123 - m.E31 * n.E3 + m.E12 * n.E2 - m.E123 * n.E23,
m.E * n.E2 + m.E1 * n.E12 + m.E2 * n.E - m.E3 * n.E23 + m.E23 * n.E3 - m.E31 * n.E123 - m.E12 * n.E1 - m.E123 * n.E31,
m.E * n.E3 - m.E1 * n.E31 + m.E2 * n.E23 + m.E3 * n.E - m.E23 * n.E2 + m.E31 * n.E1 - m.E12 * n.E123 - m.E123 * n.E12,
m.E * n.E23 + m.E1 * n.E123 + m.E2 * n.E3 - m.E3 * n.E2 + m.E23 * n.E - m.E31 * n.E12 + m.E12 * n.E31 + m.E123 * n.E1,
m.E * n.E31 - m.E1 * n.E3 + m.E2 * n.E123 + m.E3 * n.E1 + m.E23 * n.E12 + m.E31 * n.E - m.E12 * n.E23 + m.E123 * n.E2,
m.E * n.E12 + m.E1 * n.E2 - m.E2 * n.E1 + m.E3 * n.E123 - m.E23 * n.E31 + m.E31 * n.E23 + m.E12 * n.E + m.E123 * n.E3,
m.E * n.E123 + m.E1 * n.E23 + m.E2 * n.E31 + m.E3 * n.E12 + m.E23 * n.E1 + m.E31 * n.E2 + m.E12 * n.E3 + m.E123 * n.E
);
}
public double Norm2 => E * E + E1 * E1 + E2 * E2 + E3 * E3 + E23 * E23 + E31 * E31 + E12 * E12 + E123 * E123;
public double Norm => Math.Sqrt(Norm2);
public MVec3d Inv
{
get
{
var n2 = Norm2;
return new MVec3d(E / n2, -E1 / n2, -E2 / n2, -E3 / n2, -E23 / n2, -E31 / n2, -E12 / n2, E123 / n2);
// return new MVec3d(E / n2, E1 / n2, E2 / n2, E3 / n2, E23 / n2, E31 / n2, E12 / n2, E123 / n2);
}
}
public MVec3d Grade(int k)
{
switch (k)
{
case 0:
return Scalar(E);
case 1:
return Vector(E1, E2, E3);
case 2:
return Bivector(E23, E31, E12);
case 3:
return Trivector(E123);
default:
return new MVec3d();
}
}
public static MVec3d Inner(MVec3d m, MVec3d n)
{
var m0 = m.Grade(0);
var m1 = m.Grade(1);
var m2 = m.Grade(2);
var m3 = m.Grade(3);
var n0 = n.Grade(0);
var n1 = n.Grade(1);
var n2 = n.Grade(2);
var n3 = n.Grade(3);
return new MVec3d(
m0 * n0 + m1 * n1 + m2 * n2 + m3 * n3,
m0 * n1 + m1 * n2 + m2 * n3,
m0 * n2 + m1 * n3,
m0 * n3
);
}
public static MVec3d Outer(MVec3d m, MVec3d n)
{
var m0 = m.Grade(0);
var m1 = m.Grade(1);
var m2 = m.Grade(2);
var m3 = m.Grade(3);
var n0 = n.Grade(0);
var n1 = n.Grade(1);
var n2 = n.Grade(2);
var n3 = n.Grade(3);
return new MVec3d(
m0 * n0,
m1 * n0 + m0 * n1,
m2 * n0 + m1 * n1 + m0 * n2,
m3 * n0 + m2 * n1 + m1 * n2 + m0 * m3
);
}
public static MVec3d operator ~(MVec3d m) => m.Inv;
public static MVec3d operator *(MVec3d m, MVec3d n) => Mult(m, n);
public static MVec3d operator +(MVec3d m, MVec3d n) => Add(m, n);
public static MVec3d operator -(MVec3d m, MVec3d n) => Sub(m, n);
public static MVec3d operator &(MVec3d m, MVec3d n) => Inner(m, n);
public static MVec3d operator ^(MVec3d m, MVec3d n) => Outer(m, n);
public Vector3d VectorPart => new Vector3d(E1, E2, E3);
public static implicit operator MVec3d(Vector3 v) => new MVec3d(0, v.X, v.Y, v.Z, 0, 0, 0, 0);
public static implicit operator MVec3d(Vector3d v) => new MVec3d(0, v.X, v.Y, v.Z, 0, 0, 0, 0);
public static implicit operator MVec3d(double s) => new MVec3d(s, 0, 0, 0, 0, 0, 0, 0);
public override string ToString()
{
return $"({E:0.00} {E1:0.00}e1 {E2:0.00}e2 {E3:0.00}e3 {E23:0.00}e23 {E31:0.00}e31 {E12:0.00}e12 {E123:0.00}e123)";
}
}
}

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Tetrahedrons/OpenTK.dll.config Normal file
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<configuration>
<dllmap os="linux" dll="opengl32.dll" target="libGL.so.1"/>
<dllmap os="linux" dll="glu32.dll" target="libGLU.so.1"/>
<dllmap os="linux" dll="openal32.dll" target="libopenal.so.1"/>
<dllmap os="linux" dll="alut.dll" target="libalut.so.0"/>
<dllmap os="linux" dll="opencl.dll" target="libOpenCL.so"/>
<dllmap os="linux" dll="libX11" target="libX11.so.6"/>
<dllmap os="linux" dll="libXi" target="libXi.so.6"/>
<dllmap os="linux" dll="SDL2.dll" target="libSDL2-2.0.so.0"/>
<dllmap os="osx" dll="opengl32.dll" target="/System/Library/Frameworks/OpenGL.framework/OpenGL"/>
<dllmap os="osx" dll="openal32.dll" target="/System/Library/Frameworks/OpenAL.framework/OpenAL" />
<dllmap os="osx" dll="alut.dll" target="/System/Library/Frameworks/OpenAL.framework/OpenAL" />
<dllmap os="osx" dll="libGLES.dll" target="/System/Library/Frameworks/OpenGLES.framework/OpenGLES" />
<dllmap os="osx" dll="libGLESv1_CM.dll" target="/System/Library/Frameworks/OpenGLES.framework/OpenGLES" />
<dllmap os="osx" dll="libGLESv2.dll" target="/System/Library/Frameworks/OpenGLES.framework/OpenGLES" />
<dllmap os="osx" dll="opencl.dll" target="/System/Library/Frameworks/OpenCL.framework/OpenCL"/>
<dllmap os="osx" dll="SDL2.dll" target="libSDL2.dylib"/>
<!-- XQuartz compatibility (X11 on Mac) -->
<dllmap os="osx" dll="libGL.so.1" target="/usr/X11/lib/libGL.dylib"/>
<dllmap os="osx" dll="libX11" target="/usr/X11/lib/libX11.dylib"/>
<dllmap os="osx" dll="libXcursor.so.1" target="/usr/X11/lib/libXcursor.dylib"/>
<dllmap os="osx" dll="libXi" target="/usr/X11/lib/libXi.dylib"/>
<dllmap os="osx" dll="libXinerama" target="/usr/X11/lib/libXinerama.dylib"/>
<dllmap os="osx" dll="libXrandr.so.2" target="/usr/X11/lib/libXrandr.dylib"/>
</configuration>

8
Tetrahedrons/Program.cs
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@@ -1,9 +1,13 @@
namespace Tetrahedrons
using OpenTK;
namespace Tetrahedrons
{
internal class Program
internal class Program : GameWindow
{
public static void Main(string[] args)
{
using(var p = new TetrahedronWindow())
p.Run();
}
}
}

293
Tetrahedrons/TetrahedronWindow.cs Normal file
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using System;
using System.Collections.Generic;
using System.Drawing;
using System.Net.Mail;
using System.Security;
using OpenTK;
using OpenTK.Graphics.OpenGL;
using OpenTK.Input;
namespace Tetrahedrons
{
public struct Polygon
{
public Vector3d[] Points;
public Color Color;
public Polygon(Vector3d[] points) : this(points, Color.DodgerBlue)
{
}
public Polygon(Vector3d[] points, Color color)
{
Points = points;
Color = color;
}
public void Draw()
{
GL.Begin(PrimitiveType.TriangleStrip);
GL.Color3(Color);
foreach (var v in Points)
GL.Vertex3(v);
GL.End();
}
public static Polygon operator +(Polygon p, MVec3d m)
{
var pts = new Vector3d[p.Points.Length];
for (var i = 0; i < p.Points.Length; i++)
pts[i] = (p.Points[i] + m).VectorPart;
return new Polygon(pts, p.Color);
}
public static Polygon operator -(Polygon p, MVec3d m)
{
var pts = new Vector3d[p.Points.Length];
for (var i = 0; i < p.Points.Length; i++)
pts[i] = (p.Points[i] - m).VectorPart;
return new Polygon(pts, p.Color);
}
public static Polygon operator *(Polygon p, MVec3d m)
{
var pts = new Vector3d[p.Points.Length];
for (var i = 0; i < p.Points.Length; i++)
pts[i] = (p.Points[i] * m).VectorPart;
return new Polygon(pts, p.Color);
}
public static Polygon operator ^(Polygon p, MVec3d m)
{
var pts = new Vector3d[p.Points.Length];
for (var i = 0; i < p.Points.Length; i++)
pts[i] = (p.Points[i] ^ m).VectorPart;
return new Polygon(pts, p.Color);
}
public static Polygon operator &(Polygon p, MVec3d m)
{
var pts = new Vector3d[p.Points.Length];
for (var i = 0; i < p.Points.Length; i++)
pts[i] = (p.Points[i] & m).VectorPart;
return new Polygon(pts, p.Color);
}
}
public class Tetrahedron
{
public readonly Vector3d[] Points;
public Color Color;
public Color WireColor;
public Tetrahedron(Vector3d p1, Vector3d p2, Vector3d p3, Vector3d p4) : this(p1, p2, p3, p4, Color.GhostWhite)
{
}
public Tetrahedron(Vector3d p1, Vector3d p2, Vector3d p3, Vector3d p4, Color color) : this(p1, p2, p3, p4, color, Color.Maroon)
{
}
public Tetrahedron(Vector3d p1, Vector3d p2, Vector3d p3, Vector3d p4, Color color, Color wireColor)
{
Color = color;
WireColor = wireColor;
Points = new[] {p1, p2, p3, p4};
}
public void Draw(bool wire = true)
{
if (wire)
{
GL.Begin(PrimitiveType.Lines);
GL.Color3(WireColor);
for (var i = 0; i < 4; i++)
for (var j = i + 1; j < 4; j++)
{
GL.Vertex3(Points[i]);
GL.Vertex3(Points[j]);
}
GL.End();
}
else
{
GL.Begin(PrimitiveType.Triangles);
GL.Color3(Color);
for (var i = 0; i < 4; i++)
for (var j = i + 1; j < 4; j++)
for (var k = j + 1; k < 4; k++)
{
GL.Vertex3(Points[i]);
GL.Vertex3(Points[j]);
GL.Vertex3(Points[k]);
}
GL.End();
}
}
public Polygon Intersection(MVec3d blade, Vector3d pivot)
{
var pts = new Vector3d[4];
for (var i = 0; i < 4; i++)
{
pts[i] = Points[i] - pivot;
}
var a = blade * MVec3d.Unit123;
var sides = new double[4];
for (var i = 0; i < 4; i++)
{
sides[i] = (a & ((pts[i] ^ blade) * ~blade)).E; // normal dot rejection
}
var vecs = new List<Vector3d>(4);
for (var i = 0; i < 4; i++)
{
for (var j = i + 1; j < 4; j++)
{
if (sides[i] * sides[j] >= 0) continue; // both pts on same side
var t = ((blade ^ pts[i]) * ~(blade ^ (pts[j] - pts[i]))).E;
var point = pts[i] + t * (pts[j] - pts[i]);
vecs.Add(point + pivot);
}
}
return new Polygon(vecs.ToArray());
}
}
public class TetrahedronWindow : GameWindow
{
private Matrix4 _proj;
private Matrix4 _view;
private double _t;
private bool _pause;
private bool _div;
private Tetrahedron _tetra;
private Polygon _polyg;
private Polygon _square = new Polygon(new[] {new Vector3d(-1, -1, 0), new Vector3d(-1, 1, 0), new Vector3d(1, -1, 0), new Vector3d(1, 1, 0),}, Color.Red);
protected override void OnLoad(EventArgs e)
{
base.OnLoad(e);
X = (DisplayDevice.Default.Width - Width) / 2;
Y = (DisplayDevice.Default.Height - Height) / 2;
_tetra = new Tetrahedron(new Vector3d(1, 1, 1), new Vector3d(-1, -1, 1), new Vector3d(-1, 1, -1), new Vector3d(1, -1, -1));
_polyg = new Polygon(new[] {new Vector3d(-1, -1, 0), new Vector3d(-1, 1, 0), new Vector3d(1, -1, 0), new Vector3d(1, 1, 0)});
_view = Matrix4.LookAt(Vector3.Zero, -new Vector3(1, .6f, 1f), Vector3.UnitZ);
}
protected override void OnRenderFrame(FrameEventArgs e)
{
base.OnRenderFrame(e);
GL.Viewport(ClientRectangle);
GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit);
GL.PointSize(10f);
// _view = Matrix4.LookAt(Vector3.Zero, new Vector3((float) Math.Cos(_t / 5), (float) Math.Sin(_t / 5), -1), Vector3.UnitZ);
GL.PushMatrix();
GL.MatrixMode(MatrixMode.Projection);
GL.LoadMatrix(ref _proj);
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadMatrix(ref _view);
GL.Enable(EnableCap.DepthTest);
_tetra.Draw(wire: false);
GL.Disable(EnableCap.DepthTest);
if (_div)
{
GL.PushMatrix();
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadMatrix(ref Matrix4d.Identity);
_square.Draw();
_polyg.Draw();
GL.PopMatrix();
}
else
_polyg.Draw();
GL.Enable(EnableCap.DepthTest);
_tetra.Draw(wire: true);
GL.PopMatrix();
SwapBuffers();
}
protected override void OnUpdateFrame(FrameEventArgs e)
{
base.OnUpdateFrame(e);
_proj = Matrix4.CreateOrthographic(6, 6f * Height / Width, -2, 2);
_t += e.Time;
if (_pause)
return;
// var b1 = MVec3d.Unit2;
// var b2 = MVec3d.Unit3;
// var pivot = new Vector3d(Math.Cos(_t), 0, 0);
var b1 = MVec3d.Vector(0, Math.Cos(_t * .2), Math.Sin(_t * .5));
var b2 = MVec3d.Vector(Math.Cos(_t * .6), 0, Math.Sin(_t * .4));
var pivot = Vector3d.Zero;
// var b1 = MVec3d.Vector(Math.Cos(_t/2), Math.Sin(_t/2), 0);
// var b2 = MVec3d.Unit3;
// var pivot = Vector3d.Zero;
var blade = MVec3d.Outer(b1, b2);
// var rot = MVec3d.Complex(_t / 2, MVec3d.Unit12);
// var b1 = rot * MVec3d.Unit2 * ~rot;
// var b2 = rot * MVec3d.Unit3 * ~rot;
// var pln = MVec3d.Outer(b1, b2);
// var blade = pln;
// var pivot = Vector3d.Zero;
Console.Out.WriteLine("b1 = {0}", b1);
Console.Out.WriteLine("b2 = {0}", b2);
_polyg = _tetra.Intersection(blade, pivot);
if (_div)
{
for (var i = 0; i < _polyg.Points.Length; i++)
{
MVec3d p = _polyg.Points[i];
var x = ((p & b1) * ~b1) & b1;
var y = ((p ^ b1) * ~b1) & ((b2 ^ b1) * ~b1);
_polyg.Points[i] = new Vector3d(x.E, y.E, 0);
}
}
}
protected override void OnKeyDown(KeyboardKeyEventArgs e)
{
base.OnKeyDown(e);
switch (e.Key)
{
case Key.Space:
_pause = !_pause;
break;
case Key.A:
_div = !_div;
break;
}
}
}
}

100
Tetrahedrons/Tetrahedrons.csproj
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@@ -1,54 +1,62 @@
<?xml version="1.0" encoding="utf-8"?>
<Project ToolsVersion="12.0" DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
<Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props"
Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')"/>
<PropertyGroup>
<Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
<Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
<ProjectGuid>{D70DFA78-49B4-404B-BE1C-7CDC0DAE26FD}</ProjectGuid>
<OutputType>Exe</OutputType>
<AppDesignerFolder>Properties</AppDesignerFolder>
<RootNamespace>Tetrahedrons</RootNamespace>
<AssemblyName>Tetrahedrons</AssemblyName>
<TargetFrameworkVersion>v4.0</TargetFrameworkVersion>
<FileAlignment>512</FileAlignment>
</PropertyGroup>
<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
<PlatformTarget>AnyCPU</PlatformTarget>
<DebugSymbols>true</DebugSymbols>
<DebugType>full</DebugType>
<Optimize>false</Optimize>
<OutputPath>bin\Debug\</OutputPath>
<DefineConstants>DEBUG;TRACE</DefineConstants>
<ErrorReport>prompt</ErrorReport>
<WarningLevel>4</WarningLevel>
</PropertyGroup>
<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
<PlatformTarget>AnyCPU</PlatformTarget>
<DebugType>pdbonly</DebugType>
<Optimize>true</Optimize>
<OutputPath>bin\Release\</OutputPath>
<DefineConstants>TRACE</DefineConstants>
<ErrorReport>prompt</ErrorReport>
<WarningLevel>4</WarningLevel>
</PropertyGroup>
<ItemGroup>
<Reference Include="System"/>
<Reference Include="System.Core"/>
<Reference Include="System.Data"/>
<Reference Include="System.Xml"/>
</ItemGroup>
<ItemGroup>
<Compile Include="Program.cs"/>
<Compile Include="Properties\AssemblyInfo.cs"/>
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets"/>
<!-- To modify your build process, add your task inside one of the targets below and uncomment it.
<Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props" Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')" />
<PropertyGroup>
<Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
<Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
<ProjectGuid>{D70DFA78-49B4-404B-BE1C-7CDC0DAE26FD}</ProjectGuid>
<OutputType>Exe</OutputType>
<AppDesignerFolder>Properties</AppDesignerFolder>
<RootNamespace>Tetrahedrons</RootNamespace>
<AssemblyName>Tetrahedrons</AssemblyName>
<TargetFrameworkVersion>v4.0</TargetFrameworkVersion>
<FileAlignment>512</FileAlignment>
</PropertyGroup>
<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
<PlatformTarget>AnyCPU</PlatformTarget>
<DebugSymbols>true</DebugSymbols>
<DebugType>full</DebugType>
<Optimize>false</Optimize>
<OutputPath>bin\Debug\</OutputPath>
<DefineConstants>DEBUG;TRACE</DefineConstants>
<ErrorReport>prompt</ErrorReport>
<WarningLevel>4</WarningLevel>
</PropertyGroup>
<PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
<PlatformTarget>AnyCPU</PlatformTarget>
<DebugType>pdbonly</DebugType>
<Optimize>true</Optimize>
<OutputPath>bin\Release\</OutputPath>
<DefineConstants>TRACE</DefineConstants>
<ErrorReport>prompt</ErrorReport>
<WarningLevel>4</WarningLevel>
</PropertyGroup>
<ItemGroup>
<Reference Include="OpenTK, Version=3.0.0.0, Culture=neutral, PublicKeyToken=bad199fe84eb3df4">
<HintPath>..\packages\OpenTK.3.0.0-pre\lib\net20\OpenTK.dll</HintPath>
</Reference>
<Reference Include="System" />
<Reference Include="System.Core" />
<Reference Include="System.Data" />
<Reference Include="System.Drawing" />
<Reference Include="System.Xml" />
</ItemGroup>
<ItemGroup>
<Compile Include="MVec3d.cs" />
<Compile Include="Program.cs" />
<Compile Include="Properties\AssemblyInfo.cs" />
<Compile Include="TetrahedronWindow.cs" />
</ItemGroup>
<ItemGroup>
<None Include="OpenTK.dll.config" />
<None Include="packages.config" />
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
<!-- To modify your build process, add your task inside one of the targets below and uncomment it.
Other similar extension points exist, see Microsoft.Common.targets.
<Target Name="BeforeBuild">
</Target>
<Target Name="AfterBuild">
</Target>
-->
</Project>
</Project>

4
Tetrahedrons/packages.config Normal file
View File

@@ -0,0 +1,4 @@
<?xml version="1.0" encoding="utf-8"?>
<packages>
<package id="OpenTK" version="3.0.0-pre" targetFramework="net40" />
</packages>