internal override void Compute(List <Node> allNodes)
{
List <Point> vertices = new List <Point>();
foreach (int i in NodeIndices)
{
vertices.Add(allNodes[i].Position.ToPoint());
}
Mesh = Mesh.ByVerticesAndIndices(vertices, faces);
for (int i = 0; i < NodeCount; i++)
{
Moves[i] = Triple.Zero;
}
int faceCount = faces.Count / 3;
try
{
float currentVolume = (float)Mesh.Volume;
currentVolumeInversed = 1f / currentVolume;
}
catch
{
// ignored
}
for (int i = 0; i < faceCount; i++)
{
int iA = faces[i * 3 + 0];
int iB = faces[i * 3 + 1];
int iC = faces[i * 3 + 2];
Triple A = allNodes[NodeIndices[iA]].Position;
Triple B = allNodes[NodeIndices[iB]].Position;
Triple C = allNodes[NodeIndices[iC]].Position;
Triple n = (B - A).Cross(C - A);
Triple force = VolumePressureConstant * currentVolumeInversed * n * 0.16666666666666f;
Moves[iA] += force;
Moves[iB] += force;
Moves[iC] += force;
}
Weights.FillArray(Weight);
}
public static Dictionary <string, object> AuxeticRotatingTriangles(int xCount = 5, int yCount = 5, double thickness = 0.0)
{
List <Goal> shapeMatchingGoals = new List <Goal>();
List <Goal> mergeGoals = new List <Goal>();
List <GeometryBinder> meshBinders = new List <GeometryBinder>();
List <GeometryBinder> lineBinders = new List <GeometryBinder>();
List <Point> vertices = new List <Point>();
List <int> indices = new List <int>();
double offset = 0.001;
double cos30 = Math.Cos(Math.PI / 6.0);
for (int j = 0; j < yCount; j++)
{
for (int i = 0; i < xCount; i++)
{
double xOffset = 2 * i + 1;
double yOffset = 2 * j * cos30 + cos30;
Triple M = new Triple(xOffset, yOffset, 0.0);
List <Triple> v = new List <Triple>();
for (int k = 0; k < 6; k++)
{
v.Add(new Triple(xOffset + Math.Cos(k * Math.PI / 3.0), yOffset + Math.Sin(k * Math.PI / 3.0), 0.0));
}
for (int k = 0; k < 5; k++)
{
shapeMatchingGoals.Add(ProcessTriangle(M, v[k], v[k + 1], k % 2 == 0, offset, thickness, vertices, indices));
}
shapeMatchingGoals.Add(ProcessTriangle(M, v[5], v[0], false, offset, thickness, vertices, indices));
M = new Triple(xOffset + 1, yOffset, 0.0);
if (i < xCount - 1)
{
shapeMatchingGoals.Add(ProcessTriangle(
M,
new Triple(xOffset + 1.5, yOffset + cos30, 0.0),
new Triple(xOffset + 0.5, yOffset + cos30, 0.0),
false, offset, thickness, vertices, indices));
shapeMatchingGoals.Add(ProcessTriangle(
M,
new Triple(xOffset + 0.5, yOffset - cos30, 0.0),
new Triple(xOffset + 1.5, yOffset - cos30, 0.0),
true, offset, thickness, vertices, indices));
}
}
}
meshBinders.Add(new MeshBinder(Mesh.ByVerticesAndIndices(vertices, indices), new Color(.3f, .6f, .8f, 1f)));
//=======================================================================================
// Line Binders
//=======================================================================================
for (int j = 0; j < yCount; j++)
{
for (int i = 0; i < xCount * 2; i++)
{
double xOffset = i;
double yOffset = 2 * j * cos30 + cos30;
Triple M = new Triple(xOffset, yOffset, 0.0);
List <Triple> v = new List <Triple>();
for (int k = 1; k < 6; k += 2)
{
v.Add(new Triple(xOffset + offset * Math.Cos(k * Math.PI / 3.0), yOffset + offset * Math.Sin(k * Math.PI / 3.0), 0.0));
}
lineBinders.Add(new LineBinder(v[0], v[1]));
lineBinders.Add(new LineBinder(v[1], v[2]));
lineBinders.Add(new LineBinder(v[2], v[0]));
mergeGoals.Add(new MergeGoal(v, 0.1f));
}
}
for (int j = 0; j <= yCount; j++)
{
for (int i = 0; i < xCount * 2; i++)
{
double xOffset = i + 0.5;
double yOffset = 2 * j * cos30;
Triple M = new Triple(xOffset, yOffset, 0.0);
List <Triple> v = new List <Triple>();
for (int k = 1; k < 6; k += 2)
{
v.Add(new Triple(xOffset + offset * Math.Cos(k * Math.PI / 3.0), yOffset + offset * Math.Sin(k * Math.PI / 3.0), 0.0));
}
lineBinders.Add(new LineBinder(v[0], v[1]));
lineBinders.Add(new LineBinder(v[1], v[2]));
lineBinders.Add(new LineBinder(v[2], v[0]));
mergeGoals.Add(new MergeGoal(v, 0.1f));
}
}
return(new Dictionary <string, object>
{
{ "shapeMatchingGoals", shapeMatchingGoals },
{ "mergeGoals", mergeGoals },
{ "meshBinders", meshBinders },
{ "lineBinders", lineBinders },
});
}
public static Dictionary <string, object> AuxeticRotatingSquares(int xCount = 5, int yCount = 5, double thickness = 0.0)
{
List <Goal> shapeMatchingGoals = new List <Goal>();
List <GeometryBinder> meshBinders = new List <GeometryBinder>();
List <GeometryBinder> lineBinders = new List <GeometryBinder>();
List <Point> vertices = new List <Point>();
List <int> indices = new List <int>();
double offset = 0.001;
List <Triple> targetShape = new List <Triple>()
{
new Triple(0, 0, 0),
new Triple(1, 0, 0),
new Triple(1, 1, 0),
new Triple(0, 1, 0),
};
if (thickness > 0.0)
{
for (int i = 0; i < 4; i++)
{
targetShape.Add(targetShape[i] + thickness * Triple.BasisZ);
}
}
for (int i = 0; i < xCount; i++)
{
for (int j = 0; j < yCount; j++)
{
double k = 0.0;
List <Triple> tileVertices = new List <Triple>();
if ((i + j) % 2 == 0)
{
tileVertices = new List <Triple>()
{
new Triple(i, j + offset, k),
new Triple(i + 1f - offset, j, k),
new Triple(i + 1f, j + 1f - offset, k),
new Triple(i + offset, j + 1f, k),
}
}
;
else
{
tileVertices = new List <Triple>()
{
new Triple(i + offset, j, k),
new Triple(i + 1f, j + offset, k),
new Triple(i + 1f - offset, j + 1f, k),
new Triple(i, j + 1f - offset, k),
};
}
if (thickness > 0.0)
{
for (int ii = 0; ii < 4; ii++)
{
tileVertices.Add(tileVertices[ii] + thickness * Triple.BasisZ);
}
}
shapeMatchingGoals.Add(new ShapeMatchingGoal(tileVertices, targetShape));
vertices.Add(tileVertices[0].ToPoint());
vertices.Add(tileVertices[1].ToPoint());
vertices.Add(tileVertices[2].ToPoint());
vertices.Add(tileVertices[3].ToPoint());
int n = vertices.Count - 4;
indices.AddRange(new [] { n, n + 1, n + 2, n, n + 2, n + 3 });
}
}
List <Goal> lengthGoals = new List <Goal>();
for (int i = 1; i < xCount; i++)
{
for (int j = 0; j <= yCount; j++)
{
if ((i + j) % 2 == 1)
{
lengthGoals.Add(new LengthGoal(
new Triple(i - offset, j, 0),
new Triple(i + offset, j, 0)));
lineBinders.Add(new LineBinder(
new Triple(i - offset, j, 0),
new Triple(i + offset, j, 0)));
}
}
}
for (int i = 0; i <= xCount; i++)
{
for (int j = 1; j < yCount; j++)
{
if ((i + j) % 2 == 0)
{
lengthGoals.Add(new LengthGoal(
new Triple(i, j - offset, 0),
new Triple(i, j + offset, 0)));
lineBinders.Add(new LineBinder(
new Triple(i, j - offset, 0),
new Triple(i, j + offset, 0)));
}
}
}
meshBinders.Add(new MeshBinder(Mesh.ByVerticesAndIndices(vertices, indices), new Color(.3f, .6f, .8f, 1f)));
return(new Dictionary <string, object>
{
{ "shapeMatchingGoals", shapeMatchingGoals },
{ "lengthGoals", lengthGoals },
{ "meshBinders", meshBinders },
{ "lineBinders", lineBinders },
});
}
public static Dictionary <string, object> PlaneMesh(
[DefaultArgument("CoordinateSystem.ByOriginVectors(Point.Origin(), Vector.XAxis(), Vector.YAxis())")] CoordinateSystem cs,
[DefaultArgument("20.0")] double lengthX,
[DefaultArgument("20.0")] double lengthY,
[DefaultArgument("20")] int divX,
[DefaultArgument("20")] int divY,
[DefaultArgument("true")] bool alternatingDiagons)
{
if (divX < 1 || divY < 0)
{
throw new Exception("divX and divY must be larger than 0");
}
List <Point> vertices = new List <Point>((divX + 1) * (divY + 1));
Vector2Collection textureCoordinates = new Vector2Collection();
for (int j = 0; j <= divY; j++)
{
for (int i = 0; i <= divX; i++)
{
vertices.Add(
Point.ByCartesianCoordinates(
cs,
((double)i / divX - 0.5f) * lengthX,
((double)j / divY - 0.5f) * lengthY));
textureCoordinates.Add(new Vector2((float)i / (float)(divX), 1f - (float)j / (float)(divY)));
}
}
List <int> indices = new List <int>();
List <List <int> > quadFaceVertexIndices = new List <List <int> >();
for (int j = 0; j < divY; j++)
{
for (int i = 0; i < divX; i++)
{
int a = i + j * (divX + 1);
int b = i + 1 + j * (divX + 1);
int c = i + 1 + (j + 1) * (divX + 1);
int d = i + (j + 1) * (divX + 1);
quadFaceVertexIndices.Add(new List <int> {
a, b, c, d
});
if (alternatingDiagons)
{
if ((i + j) % 2 == 0)
{
indices.Add(a);
indices.Add(b);
indices.Add(c);
indices.Add(a);
indices.Add(c);
indices.Add(d);
}
else
{
indices.Add(a);
indices.Add(b);
indices.Add(d);
indices.Add(b);
indices.Add(c);
indices.Add(d);
}
}
else
{
indices.Add(a);
indices.Add(b);
indices.Add(c);
indices.Add(a);
indices.Add(c);
indices.Add(d);
}
}
}
return(new Dictionary <string, object>()
{
{ "mesh", Mesh.ByVerticesAndIndices(vertices, indices) },
{ "quadFaceVertexIndices", quadFaceVertexIndices },
{ "textureCoordinates", new TextureCoordinateSet(textureCoordinates) },
});
}
public static Dictionary <string, object> AuxeticRotatingSquares(int xCount = 5, int yCount = 5, double thickness = 0.0)
{
List <Goal> shapeMatchingGoals = new List <Goal>();
List <GeometryBinder> meshBinders = new List <GeometryBinder>();
List <GeometryBinder> lineBinders = new List <GeometryBinder>();
List <Point> vertices = new List <Point>();
List <int> indices = new List <int>();
double offset = 0.001;
for (int i = 0; i < xCount; i++)
{
for (int j = 0; j < yCount; j++)
{
double k = 0.0;
List <Triple> triples = new List <Triple>();
if ((i + j) % 2 == 0)
{
triples = new List <Triple>()
{
new Triple(i, j + offset, k),
new Triple(i + 1f - offset, j, k),
new Triple(i + 1f, j + 1f - offset, k),
new Triple(i + offset, j + 1f, k),
}
}
;
else
{
triples = new List <Triple>()
{
new Triple(i + offset, j, k),
new Triple(i + 1f, j + offset, k),
new Triple(i + 1f - offset, j + 1f, k),
new Triple(i, j + 1f - offset, k),
};
}
if (thickness > 0.0)
{
for (int ii = 0; ii < 4; ii++)
{
triples.Add(triples[ii] + thickness * Triple.BasisZ);
}
}
shapeMatchingGoals.Add(new ShapeMatchingGoal(triples, triples));
//goals.Add(new OnPlaneGoal(triples, Plane.XY()));
vertices.Add(triples[0].ToPoint());
vertices.Add(triples[1].ToPoint());
vertices.Add(triples[2].ToPoint());
vertices.Add(triples[3].ToPoint());
int n = vertices.Count - 4;
indices.AddRange(new [] { n, n + 1, n + 2, n, n + 2, n + 3 });
}
}
List <Goal> lengthGoals = new List <Goal>();
for (int i = 1; i < xCount; i++)
{
for (int j = 0; j <= yCount; j++)
{
if ((i + j) % 2 == 1)
{
lengthGoals.Add(new LengthGoal(
new Triple(i - offset, j, 0),
new Triple(i + offset, j, 0)));
lineBinders.Add(new LineBinder(
new Triple(i - offset, j, 0),
new Triple(i + offset, j, 0)));
}
}
}
for (int i = 0; i <= xCount; i++)
{
for (int j = 1; j < yCount; j++)
{
if ((i + j) % 2 == 0)
{
lengthGoals.Add(new LengthGoal(
new Triple(i, j - offset, 0),
new Triple(i, j + offset, 0)));
lineBinders.Add(new LineBinder(
new Triple(i, j - offset, 0),
new Triple(i, j + offset, 0)));
}
}
}
meshBinders.Add(new MeshBinder(Mesh.ByVerticesAndIndices(vertices, indices), new Color(.3f, .6f, .8f, 1f)));
List <Triple> allTriples = new List <Triple>();
foreach (Point point in vertices)
{
allTriples.Add(point.ToTriple());
}
return(new Dictionary <string, object>
{
{ "shapeMatchingGoals", shapeMatchingGoals },
{ "lengthGoals", lengthGoals },
//{"onSurfaceGoal", surface == null ? null : new OnSurfaceGoal(allTriples, surface, 1f)},
{ "onSurfaceGoal", null },
{ "meshBinders", meshBinders },
{ "lineBinders", lineBinders },
});
}
public static Dictionary <string, object> Shearing(int xCount = 5, int yCount = 5, double k = 0.2, double thickness = 0.5)
{
shapeMatchingGoals = new List <ShapeMatchingGoal>();
vertices = new List <Point>();
indices = new List <int>();
polylineBinders = new List <PolylineBinder>();
for (int i = 0; i < xCount; i++)
{
for (int j = 0; j < yCount; j++)
{
if ((i + j) % 2 == 0)
{
CreateUnit(new List <Triple>()
{
new Triple(i, j + k, 0f),
new Triple(i, j, 0f),
new Triple(i + 1f - k, j, 0f),
new Triple(i, j + k, thickness),
new Triple(i, j, thickness),
new Triple(i + 1f - k, j, thickness),
});
CreateUnit(new List <Triple>()
{
new Triple(i + 1f - k, j, 0f),
new Triple(i + 1f, j, 0f),
new Triple(i + 1f, j + 1f - k, 0f),
new Triple(i + 1f - k, j, thickness),
new Triple(i + 1f, j, thickness),
new Triple(i + 1f, j + 1f - k, thickness),
});
CreateUnit(new List <Triple>()
{
new Triple(i + 1f, j + 1f - k, 0f),
new Triple(i + 1f, j + 1f, 0f),
new Triple(i + k, j + 1f, 0f),
new Triple(i + 1f, j + 1f - k, thickness),
new Triple(i + 1f, j + 1f, thickness),
new Triple(i + k, j + 1f, thickness),
});
CreateUnit(new List <Triple>()
{
new Triple(i + k, j + 1f, 0f),
new Triple(i, j + 1f, 0f),
new Triple(i, j + k, 0f),
new Triple(i + k, j + 1f, thickness),
new Triple(i, j + 1f, thickness),
new Triple(i, j + k, thickness),
});
}
else
{
if (i == 0 || i == xCount - 1 || j == 0 || j == yCount - 1)
{
CreateUnit(new List <Triple>()
{
new Triple(i, j + 1f - k, 0f),
new Triple(i, j, 0f),
new Triple(i + k, j, 0f),
new Triple(i, j + 1f - k, thickness),
new Triple(i, j, thickness),
new Triple(i + k, j, thickness),
});
CreateUnit(new List <Triple>()
{
new Triple(i + k, j, 0f),
new Triple(i + 1f, j, 0f),
new Triple(i + 1f, j + k, 0f),
new Triple(i + k, j, thickness),
new Triple(i + 1f, j, thickness),
new Triple(i + 1f, j + k, thickness),
});
CreateUnit(new List <Triple>()
{
new Triple(i + 1f, j + k, 0f),
new Triple(i + 1f, j + 1f, 0f),
new Triple(i + 1f - k, j + 1f, 0f),
new Triple(i + 1f, j + k, thickness),
new Triple(i + 1f, j + 1f, thickness),
new Triple(i + 1f - k, j + 1f, thickness),
});
CreateUnit(new List <Triple>()
{
new Triple(i + 1f - k, j + 1f, 0f),
new Triple(i, j + 1f, 0f),
new Triple(i, j + 1f - k, 0f),
new Triple(i + 1f - k, j + 1f, thickness),
new Triple(i, j + 1f, thickness),
new Triple(i, j + 1f - k, thickness),
});
}
}
}
}
return(new Dictionary <string, object>
{
{ "shapeMatchingGoals", shapeMatchingGoals },
{ "meshBinders", new MeshBinder(Mesh.ByVerticesAndIndices(vertices, indices), new Color(0f, 0.7f, 1f, 0.9f)) },
{ "polylineBinders", KinetiX.polylineBinders },
});
}
public static Mesh PlaneMesh(
[DefaultArgument("CoordinateSystem.ByOriginVectors(Point.Origin(), Vector.XAxis(), Vector.YAxis())")] CoordinateSystem cs,
[DefaultArgument("20.0")] double lengthX,
[DefaultArgument("20.0")] double lengthY,
[DefaultArgument("20")] int divX,
[DefaultArgument("20")] int divY,
[DefaultArgument("true")] bool alternatingDiagons)
{
List <Point> vertices = new List <Point>((divX + 1) * (divY + 1));
for (int j = 0; j <= divY; j++)
{
for (int i = 0; i <= divX; i++)
{
vertices.Add(
Point.ByCartesianCoordinates(
cs,
((double)i / divX - 0.5f) * lengthX,
((double)j / divY - 0.5f) * lengthY));
}
}
List <int> indices = new List <int>();
if (alternatingDiagons)
{
for (int j = 0; j < divY; j++)
{
for (int i = 0; i < divX; i++)
{
int a = i + j * (divX + 1);
int b = i + 1 + j * (divX + 1);
int c = i + 1 + (j + 1) * (divX + 1);
int d = i + (j + 1) * (divX + 1);
if ((i + j) % 2 == 0)
{
indices.Add(a);
indices.Add(b);
indices.Add(c);
indices.Add(a);
indices.Add(c);
indices.Add(d);
}
else
{
indices.Add(a);
indices.Add(b);
indices.Add(d);
indices.Add(b);
indices.Add(c);
indices.Add(d);
}
}
}
}
else
{
for (int j = 0; j < divY; j++)
{
for (int i = 0; i < divX; i++)
{
int a = i + j * (divX + 1);
int b = i + 1 + j * (divX + 1);
int c = i + 1 + (j + 1) * (divX + 1);
int d = i + (j + 1) * (divX + 1);
indices.Add(a);
indices.Add(b);
indices.Add(c);
indices.Add(a);
indices.Add(c);
indices.Add(d);
}
}
}
return(Mesh.ByVerticesAndIndices(vertices, indices));
}
