// Make a torus without texture coordinates.
public static void AddTorus(this MeshGeometry3D mesh,
Point3D center, double R, double r, int numTheta, int numPhi,
bool smooth = false)
{
// Make a point dictionary if needed.
Dictionary <Point3D, int> pointDict = null;
if (smooth)
{
pointDict = new Dictionary <Point3D, int>();
}
// Generate the points.
double dtheta = 2 * Math.PI / numTheta;
double dphi = 2 * Math.PI / numPhi;
double theta = 0;
for (int t = 0; t < numTheta; t++)
{
double phi = 0;
for (int p = 0; p < numPhi; p++)
{
// Find this piece's points.
Point3D[] points =
{
G3.TorusPoint(center, R, r, theta + dtheta, phi),
G3.TorusPoint(center, R, r, theta + dtheta, phi + dphi),
G3.TorusPoint(center, R, r, theta, phi + dphi),
G3.TorusPoint(center, R, r, theta, phi),
};
// Make the polygon.
mesh.AddPolygon(pointDict, points);
phi += dphi;
}
theta += dtheta;
}
}
// Add a textured torus.
public static void AddTexturedTorus(this MeshGeometry3D mesh,
Point3D center, double R, double r, int numTheta, int numPhi,
bool smooth = false)
{
double dtheta = 2 * Math.PI / numTheta;
double dphi = 2 * Math.PI / numPhi;
double theta = Math.PI; // Puts the texture's top/bottom on the inside.
for (int t = 0; t < numTheta; t++)
{
double phi = 0;
for (int p = 0; p < numPhi; p++)
{
// Find this piece's points.
Point3D point1 = G3.TorusPoint(center, R, r, theta, phi).Round();
Point3D point2 = G3.TorusPoint(center, R, r, theta + dtheta, phi).Round();
Point3D point3 = G3.TorusPoint(center, R, r, theta + dtheta, phi + dphi).Round();
Point3D point4 = G3.TorusPoint(center, R, r, theta, phi + dphi).Round();
// Find this piece's normals.
Vector3D normal1 = G3.TorusNormal(D3.Origin, R, r, theta, phi);
Vector3D normal2 = G3.TorusNormal(D3.Origin, R, r, theta + dtheta, phi);
Vector3D normal3 = G3.TorusNormal(D3.Origin, R, r, theta + dtheta, phi + dphi);
Vector3D normal4 = G3.TorusNormal(D3.Origin, R, r, theta, phi + dphi);
// Find this piece's texture coordinates.
Point coords1 = new Point(1 - (double)p / numPhi, 1 - (double)t / numTheta);
Point coords2 = new Point(1 - (double)p / numPhi, 1 - (double)(t + 1) / numTheta);
Point coords3 = new Point(1 - (double)(p + 1) / numPhi, 1 - (double)(t + 1) / numTheta);
Point coords4 = new Point(1 - (double)(p + 1) / numPhi, 1 - (double)t / numTheta);
// Make the first triangle.
int index = mesh.Positions.Count;
mesh.Positions.Add(point1);
if (smooth)
{
mesh.Normals.Add(normal1);
}
mesh.TextureCoordinates.Add(coords1);
mesh.Positions.Add(point2);
if (smooth)
{
mesh.Normals.Add(normal2);
}
mesh.TextureCoordinates.Add(coords2);
mesh.Positions.Add(point3);
if (smooth)
{
mesh.Normals.Add(normal3);
}
mesh.TextureCoordinates.Add(coords3);
mesh.TriangleIndices.Add(index++);
mesh.TriangleIndices.Add(index++);
mesh.TriangleIndices.Add(index++);
// Make the second triangle.
mesh.Positions.Add(point1);
if (smooth)
{
mesh.Normals.Add(normal1);
}
mesh.TextureCoordinates.Add(coords1);
mesh.Positions.Add(point3);
if (smooth)
{
mesh.Normals.Add(normal3);
}
mesh.TextureCoordinates.Add(coords3);
mesh.Positions.Add(point4);
if (smooth)
{
mesh.Normals.Add(normal4);
}
mesh.TextureCoordinates.Add(coords4);
mesh.TriangleIndices.Add(index++);
mesh.TriangleIndices.Add(index++);
mesh.TriangleIndices.Add(index++);
phi += dphi;
}
theta += dtheta;
}
// Add texture coordinates 1.01 to prevent "seams."
mesh.Positions.Add(new Point3D());
mesh.TextureCoordinates.Add(new Point(1.01, 1.01));
}