/// <summary>
/// Connects the Vertices to the correct triangles for the chosen mesh type.
/// </summary>
/// <param name="mesh">The new TriangleMesh containing only the Vertices.</param>
/// <param name="steps">The number of steps to be taken.</param>
/// <returns>The completed TriangleMesh.</returns>
private TriangleMesh CreateTriangles(TriangleMesh mesh, int steps)
{
int point = 0;
if (meshType == 0)
{
steps *= 2;
do
{
// Creates eight triangles per square.
mesh.Add(new Triangle(point, point + 1, point + steps + 2));
mesh.Add(new Triangle(point + 1, point + 2, point + steps + 2));
mesh.Add(new Triangle(point + 2, point + steps + 3, point + steps + 2));
mesh.Add(new Triangle(point + steps + 3, point + 2 * steps + 4, point + steps + 2));
mesh.Add(new Triangle(point + 2 * steps + 4, point + 2 * steps + 3, point + steps + 2));
mesh.Add(new Triangle(point + 2 * steps + 3, point + 2 * steps + 2, point + steps + 2));
mesh.Add(new Triangle(point + 2 * steps + 2, point + steps + 1, point + steps + 2));
mesh.Add(new Triangle(point + steps + 1, point, point + steps + 2));
if (point % (2 * steps + 2) < steps - 2)
{
point += 2;
}
else
{
point += steps + 4;
}
} while (point <= mesh.Vertices.Count - (5 + 2 * steps));
}
else
{
do
{
// Creates two triangles per square.
mesh.Add(new Triangle(point, point + 1, point + steps + 2));
mesh.Add(new Triangle(point, point + steps + 2, point + steps + 1));
if (point % (steps + 1) < steps - 1)
{
point++;
}
else
{
point += 2;
}
} while (point <= mesh.Vertices.Count - (steps + 3));
}
mesh.Finish(true);
return(mesh);
}
/// <summary>
/// Creates the base tetrahedron.
/// </summary>
private TriangleMesh CreateBaseTetrahedron()
{
TriangleMesh baseMesh = new TriangleMesh();
baseMesh.Vertices.Add(new Vertex(0.5, 0.5, 0.5));
baseMesh.Vertices.Add(new Vertex(-0.5, -0.5, 0.5));
baseMesh.Vertices.Add(new Vertex(-0.5, 0.5, -0.5));
baseMesh.Vertices.Add(new Vertex(0.5, -0.5, -0.5));
baseMesh.Add(new Triangle(0, 1, 3));
baseMesh.Add(new Triangle(1, 0, 2));
baseMesh.Add(new Triangle(2, 0, 3));
baseMesh.Add(new Triangle(2, 3, 1));
return(baseMesh);
}
/// <summary>
/// Creates a rectangular base mesh.
/// </summary>
/// <returns>The rectangular base mesh</returns>
private TriangleMesh CreateSquareBase()
{
TriangleMesh baseMesh = new TriangleMesh();
int xSteps = (int)xStepsNumericUpDown.Value * 2;
int ySteps = (int)yStepsNumericUpDown.Value * 2;
double xLength = (double)xLengthNumericUpDown.Value;
double yLength = (double)yLengthNumericUpDown.Value;
double xMin = -(xLength * (int)xStepsNumericUpDown.Value) / 2;
double yMin = -(yLength * (int)yStepsNumericUpDown.Value) / 2;
baseMesh.Vertices.Add(new Vertex(xMin, yMin, 0));
for (int i = 0; i <= ySteps; i++)
{
for (int j = 0; j <= xSteps; j++)
{
if (i != 0)
{
baseMesh.Vertices.Add((baseMesh.Vertices[0] + new Vector(j * xLength * 0.5, i * yLength * 0.5, 0)).ToVertex());
}
else
{
if (j != 0)
{
baseMesh.Vertices.Add((baseMesh.Vertices[0] + new Vector(j * xLength * 0.5, i * yLength * 0.5, 0)).ToVertex());
}
}
}
}
int point = 0;
do
{
baseMesh.Add(new Triangle(point, point + 1, point + xSteps + 2));
baseMesh.Add(new Triangle(point + 1, point + 2, point + xSteps + 2));
baseMesh.Add(new Triangle(point + 2, point + xSteps + 3, point + xSteps + 2));
baseMesh.Add(new Triangle(point + xSteps + 3, point + 2 * xSteps + 4, point + xSteps + 2));
baseMesh.Add(new Triangle(point + 2 * xSteps + 4, point + 2 * xSteps + 3, point + xSteps + 2));
baseMesh.Add(new Triangle(point + 2 * xSteps + 3, point + 2 * xSteps + 2, point + xSteps + 2));
baseMesh.Add(new Triangle(point + 2 * xSteps + 2, point + xSteps + 1, point + xSteps + 2));
baseMesh.Add(new Triangle(point + xSteps + 1, point, point + xSteps + 2));
if (point % (2 * xSteps + 2) < xSteps - 2)
{
point += 2;
}
else
{
point += xSteps + 4;
}
} while (point <= baseMesh.Vertices.Count - (5 + 2 * xSteps));
return(baseMesh);
}
/// <summary>
/// Unites two TriangleMeshes making sure the Vertices remain unique.
/// </summary>
/// <param name="one">The first TriangleMesh</param>
/// <param name="two">The second TriangleMesh</param>
/// <returns>The united TriangleMesh</returns>
public static TriangleMesh Union(TriangleMesh one, TriangleMesh two)
{
TriangleMesh union = new TriangleMesh();
TriangleMesh big;
TriangleMesh small;
if (one.Vertices.Count >= two.Vertices.Count)
{
big = one;
small = two;
}
else
{
big = two;
small = one;
}
// The bigger TriangleMesh is part of the union.
union.Vertices.AddRange(big.Vertices.ToArray());
union.AddRange(big.ToArray());
List <Triangle> temp = new List <Triangle>(small.ToArray());
// The Vertices of the smaller TriangleMesh are included in the union.
for (int i = 0; i < small.Vertices.Count; i++)
{
Vertex vertex = small.Vertices[i];
// The indices of the Vertices in the Triangles of the smaller TriangleMesh
// are set to the corresponding indices in the union.
int index = big.Vertices.IndexOf(vertex);
if (index == -1)
{
union.Vertices.Add(vertex.Copy().ToVertex());
for (int j = 0; j < vertex.Triangles.Count; j++)
{
temp[vertex.Triangles[j]].Replace(i, union.Vertices.Count - 1);
}
}
else
{
for (int j = 0; j < vertex.Triangles.Count; j++)
{
temp[vertex.Triangles[j]].Replace(i, index);
}
}
}
// The Triangles of the smaller TriangleMesh are included in the union.
for (int k = 0; k < temp.Count; k++)
{
union.Add(new Triangle(temp[k][0], temp[k][1], temp[k][2]));
}
union.Finish(true);
return(union);
}
/// <summary>
/// Creates a hexagonal base mesh.
/// </summary>
/// <returns>The hexagonal base mesh</returns>
private TriangleMesh CreateHexBase()
{
TriangleMesh baseMesh = new TriangleMesh();
Cursor = System.Windows.Input.Cursors.Wait;
double baseLength = (double)lengthNumericUpDown.Value;
baseMesh.Vertices.Add(new Vertex(0, 0, 0));
baseMesh.Vertices.Add(new Vertex(baseLength, 0, 0));
baseMesh.Vertices.Add(new Vertex(baseLength / 2, baseLength * Math.Sqrt(3) / 2, 0));
baseMesh.Vertices.Add(new Vertex(-baseLength / 2, baseLength * Math.Sqrt(3) / 2, 0));
baseMesh.Vertices.Add(new Vertex(-baseLength, 0, 0));
baseMesh.Vertices.Add(new Vertex(-baseLength / 2, -baseLength * Math.Sqrt(3) / 2, 0));
baseMesh.Vertices.Add(new Vertex(baseLength / 2, -baseLength * Math.Sqrt(3) / 2, 0));
baseMesh.Add(new Triangle(0, 1, 2));
baseMesh.Add(new Triangle(0, 2, 3));
baseMesh.Add(new Triangle(0, 3, 4));
baseMesh.Add(new Triangle(0, 4, 5));
baseMesh.Add(new Triangle(0, 5, 6));
baseMesh.Add(new Triangle(0, 6, 1));
baseMesh.Subdivide((int)stepsNumericUpDown.Value);
Cursor = System.Windows.Input.Cursors.Arrow;
return(baseMesh);
}
/// <summary>
/// Creates the base octahedron.
/// </summary>
private TriangleMesh CreateBaseOctahedron()
{
TriangleMesh baseMesh = new TriangleMesh();
baseMesh.Vertices.Add(new Vertex(0, 0, 0.5));
baseMesh.Vertices.Add(new Vertex(0.5, 0, 0));
baseMesh.Vertices.Add(new Vertex(0, 0.5, 0));
baseMesh.Vertices.Add(new Vertex(-0.5, 0, 0));
baseMesh.Vertices.Add(new Vertex(0, -0.5, 0));
baseMesh.Vertices.Add(new Vertex(0, 0, -0.5));
baseMesh.Add(new Triangle(0, 1, 2));
baseMesh.Add(new Triangle(0, 2, 3));
baseMesh.Add(new Triangle(0, 3, 4));
baseMesh.Add(new Triangle(0, 4, 1));
baseMesh.Add(new Triangle(5, 2, 1));
baseMesh.Add(new Triangle(5, 3, 2));
baseMesh.Add(new Triangle(5, 4, 3));
baseMesh.Add(new Triangle(5, 1, 4));
return(baseMesh);
}
/// <summary>
/// Creates the base pyramid.
/// </summary>
private TriangleMesh CreateBasePyramid()
{
TriangleMesh baseMesh = new TriangleMesh();
baseMesh.Vertices.Add(new Vertex(0, 0, 0.5));
baseMesh.Vertices.Add(new Vertex(0.5, 0.5, -0.5));
baseMesh.Vertices.Add(new Vertex(-0.5, 0.5, -0.5));
baseMesh.Vertices.Add(new Vertex(-0.5, -0.5, -0.5));
baseMesh.Vertices.Add(new Vertex(0.5, -0.5, -0.5));
baseMesh.Add(new Triangle(0, 1, 2));
baseMesh.Add(new Triangle(0, 2, 3));
baseMesh.Add(new Triangle(0, 3, 4));
baseMesh.Add(new Triangle(0, 4, 1));
baseMesh.Add(new Triangle(1, 2, 3));
baseMesh.Add(new Triangle(3, 4, 1));
return(baseMesh);
}
/// <summary>
/// Creates the base icosahedron.
/// </summary>
private TriangleMesh CreateBaseIcosahedron()
{
TriangleMesh baseMesh = new TriangleMesh();
double phi = Math.PI * 26.56505 / 180.0;
double theta = 0;
double theta2 = Math.PI * 36.0 / 180.0;
double theta72 = Math.PI * 72.0 / 180;
baseMesh.Vertices.Add(new Vertex(0, 0, 1));
for (int i = 1; i < 6; i++)
{
Vertex newVertex = new Vertex(Math.Cos(theta) * Math.Cos(phi), Math.Sin(theta) * Math.Cos(phi), Math.Sin(phi));
newVertex.Normalize();
baseMesh.Vertices.Add(newVertex);
theta += theta72;
}
for (int j = 6; j < 11; j++)
{
Vertex newVertex = new Vertex(Math.Cos(theta2) * Math.Cos(-phi), Math.Sin(theta2) * Math.Cos(-phi), Math.Sin(-phi));
newVertex.Normalize();
baseMesh.Vertices.Add(newVertex);
theta2 += theta72;
}
baseMesh.Vertices.Add(new Vertex(0, 0, -1));
baseMesh.Add(new Triangle(0, 1, 2));
baseMesh.Add(new Triangle(0, 2, 3));
baseMesh.Add(new Triangle(0, 3, 4));
baseMesh.Add(new Triangle(0, 4, 5));
baseMesh.Add(new Triangle(0, 5, 1));
baseMesh.Add(new Triangle(11, 7, 6));
baseMesh.Add(new Triangle(11, 8, 7));
baseMesh.Add(new Triangle(11, 9, 8));
baseMesh.Add(new Triangle(11, 10, 9));
baseMesh.Add(new Triangle(11, 6, 10));
baseMesh.Add(new Triangle(1, 6, 2));
baseMesh.Add(new Triangle(2, 7, 3));
baseMesh.Add(new Triangle(3, 8, 4));
baseMesh.Add(new Triangle(4, 9, 5));
baseMesh.Add(new Triangle(5, 10, 1));
baseMesh.Add(new Triangle(6, 7, 2));
baseMesh.Add(new Triangle(7, 8, 3));
baseMesh.Add(new Triangle(8, 9, 4));
baseMesh.Add(new Triangle(9, 10, 5));
baseMesh.Add(new Triangle(10, 6, 1));
return(baseMesh);
}
/// <summary>
/// Creates the base dodecahedron.
/// </summary>
private TriangleMesh CreateBaseDodecahedron()
{
TriangleMesh baseMesh = new TriangleMesh();
double phi = (1 + Math.Sqrt(5)) / 2;
double phiInv = 2 / (1 + Math.Sqrt(5));
baseMesh.Vertices.Add(new Vertex(1, 1, 1)); // 0
baseMesh.Vertices.Add(new Vertex(-1, 1, 1)); // 1
baseMesh.Vertices.Add(new Vertex(1, -1, 1)); // 2
baseMesh.Vertices.Add(new Vertex(1, 1, -1)); // 3
baseMesh.Vertices.Add(new Vertex(-1, -1, 1)); // 4
baseMesh.Vertices.Add(new Vertex(-1, 1, -1)); // 5
baseMesh.Vertices.Add(new Vertex(1, -1, -1)); // 6
baseMesh.Vertices.Add(new Vertex(-1, -1, -1)); // 7
baseMesh.Vertices.Add(new Vertex(0, phiInv, phi)); // 8
baseMesh.Vertices.Add(new Vertex(0, -phiInv, phi)); // 9
baseMesh.Vertices.Add(new Vertex(0, phiInv, -phi)); // 10
baseMesh.Vertices.Add(new Vertex(0, -phiInv, -phi)); // 11
baseMesh.Vertices.Add(new Vertex(phiInv, phi, 0)); // 12
baseMesh.Vertices.Add(new Vertex(-phiInv, phi, 0)); // 13
baseMesh.Vertices.Add(new Vertex(phiInv, -phi, 0)); // 14
baseMesh.Vertices.Add(new Vertex(-phiInv, -phi, 0)); // 15
baseMesh.Vertices.Add(new Vertex(phi, 0, phiInv)); // 16
baseMesh.Vertices.Add(new Vertex(-phi, 0, phiInv)); // 17
baseMesh.Vertices.Add(new Vertex(phi, 0, -phiInv)); // 18
baseMesh.Vertices.Add(new Vertex(-phi, 0, -phiInv)); // 19
baseMesh.Vertices.Add(new Vertex(0, (2 * (1 + phi) + phiInv) / 5, (2 + phi) / 5)); // 20
baseMesh.Vertices.Add(new Vertex((2 + phi) / 5, 0, (2 * (1 + phi) + phiInv) / 5)); // 21
baseMesh.Vertices.Add(new Vertex((2 * (1 + phi) + phiInv) / 5, (2 + phi) / 5, 0)); // 22
baseMesh.Vertices.Add(new Vertex(-(2 * (1 + phi) + phiInv) / 5, (2 + phi) / 5, 0)); // 23
baseMesh.Vertices.Add(new Vertex(-(2 + phi) / 5, 0, -(2 * (1 + phi) + phiInv) / 5)); // 24
baseMesh.Vertices.Add(new Vertex(-(2 * (1 + phi) + phiInv) / 5, -(2 + phi) / 5, 0)); // 25
baseMesh.Vertices.Add(new Vertex(-(2 + phi) / 5, 0, (2 * (1 + phi) + phiInv) / 5)); // 26
baseMesh.Vertices.Add(new Vertex(0, -(2 * (1 + phi) + phiInv) / 5, (2 + phi) / 5)); // 27
baseMesh.Vertices.Add(new Vertex((2 * (1 + phi) + phiInv) / 5, -(2 + phi) / 5, 0)); // 28
baseMesh.Vertices.Add(new Vertex((2 + phi) / 5, 0, -(2 * (1 + phi) + phiInv) / 5)); // 29
baseMesh.Vertices.Add(new Vertex(0, -(2 * (1 + phi) + phiInv) / 5, -(2 + phi) / 5)); // 30
baseMesh.Vertices.Add(new Vertex(0, (2 * (1 + phi) + phiInv) / 5, -(2 + phi) / 5)); // 31
baseMesh.Add(new Triangle(0, 12, 20));
baseMesh.Add(new Triangle(12, 13, 20));
baseMesh.Add(new Triangle(13, 1, 20));
baseMesh.Add(new Triangle(1, 8, 20));
baseMesh.Add(new Triangle(8, 0, 20));
baseMesh.Add(new Triangle(0, 8, 21));
baseMesh.Add(new Triangle(8, 9, 21));
baseMesh.Add(new Triangle(9, 2, 21));
baseMesh.Add(new Triangle(2, 16, 21));
baseMesh.Add(new Triangle(16, 0, 21));
baseMesh.Add(new Triangle(0, 16, 22));
baseMesh.Add(new Triangle(16, 18, 22));
baseMesh.Add(new Triangle(18, 3, 22));
baseMesh.Add(new Triangle(3, 12, 22));
baseMesh.Add(new Triangle(12, 0, 22));
baseMesh.Add(new Triangle(19, 17, 23));
baseMesh.Add(new Triangle(17, 1, 23));
baseMesh.Add(new Triangle(1, 13, 23));
baseMesh.Add(new Triangle(13, 5, 23));
baseMesh.Add(new Triangle(5, 19, 23));
baseMesh.Add(new Triangle(19, 5, 24));
baseMesh.Add(new Triangle(5, 10, 24));
baseMesh.Add(new Triangle(10, 11, 24));
baseMesh.Add(new Triangle(11, 7, 24));
baseMesh.Add(new Triangle(7, 19, 24));
baseMesh.Add(new Triangle(19, 7, 25));
baseMesh.Add(new Triangle(7, 15, 25));
baseMesh.Add(new Triangle(15, 4, 25));
baseMesh.Add(new Triangle(4, 17, 25));
baseMesh.Add(new Triangle(17, 19, 25));
baseMesh.Add(new Triangle(1, 17, 26));
baseMesh.Add(new Triangle(17, 4, 26));
baseMesh.Add(new Triangle(4, 9, 26));
baseMesh.Add(new Triangle(9, 8, 26));
baseMesh.Add(new Triangle(8, 1, 26));
baseMesh.Add(new Triangle(2, 9, 27));
baseMesh.Add(new Triangle(9, 4, 27));
baseMesh.Add(new Triangle(4, 15, 27));
baseMesh.Add(new Triangle(15, 14, 27));
baseMesh.Add(new Triangle(14, 2, 27));
baseMesh.Add(new Triangle(2, 14, 28));
baseMesh.Add(new Triangle(14, 6, 28));
baseMesh.Add(new Triangle(6, 18, 28));
baseMesh.Add(new Triangle(18, 16, 28));
baseMesh.Add(new Triangle(16, 2, 28));
baseMesh.Add(new Triangle(3, 18, 29));
baseMesh.Add(new Triangle(18, 6, 29));
baseMesh.Add(new Triangle(6, 11, 29));
baseMesh.Add(new Triangle(11, 10, 29));
baseMesh.Add(new Triangle(10, 3, 29));
baseMesh.Add(new Triangle(6, 14, 30));
baseMesh.Add(new Triangle(14, 15, 30));
baseMesh.Add(new Triangle(15, 7, 30));
baseMesh.Add(new Triangle(7, 11, 30));
baseMesh.Add(new Triangle(11, 6, 30));
baseMesh.Add(new Triangle(3, 10, 31));
baseMesh.Add(new Triangle(10, 5, 31));
baseMesh.Add(new Triangle(5, 13, 31));
baseMesh.Add(new Triangle(13, 12, 31));
baseMesh.Add(new Triangle(12, 3, 31));
return(baseMesh);
}