public static void AddRegularPolygon(this MeshGeometry3D mesh,
int numSides, Point3D center, Vector3D vx, Vector3D vy,
Dictionary <Point3D, int> pointDict = null,
Point[] textureCoords = null)
{
// Generate the points.
Point3D[] points = G3.MakePolygonPoints(numSides, center, vx, vy);
// Make the polygon.
mesh.AddPolygon(points, textureCoords);
}
// Make a tetrahedron without texture coordinates or smoothing.
public static void AddTetrahedron(this MeshGeometry3D mesh, bool centered = true)
{
// Get the points.
Point3D A, B, C, D;
G3.TetrahedronPoints(out A, out B, out C, out D, centered);
// Make the triangles.
mesh.AddPolygon(A, B, C);
mesh.AddPolygon(A, C, D);
mesh.AddPolygon(A, D, B);
mesh.AddPolygon(D, C, B);
}
public static void VerifyTetrahedron()
{
// Get the points.
Point3D A, B, C, D;
G3.TetrahedronPoints(out A, out B, out C, out D, true);
// Verify the points.
G3.VerifyPoints(A, B, C, D);
// Verify the triangles.
G3.VerifyPolygon(A, B, C);
G3.VerifyPolygon(A, C, D);
G3.VerifyPolygon(A, D, B);
G3.VerifyPolygon(D, C, B);
}
// Define the model.
private void DefineModel(Model3DGroup group)
{
//// Verify the tetrahedron calculations.
//MeshExtensions.VerifyTetrahedron();
// Show the axes.
MeshExtensions.AddAxes(group);
const double scale = 5;
// Make a solid insphere.
MeshGeometry3D mesh1 = new MeshGeometry3D();
mesh1.AddSphere(D3.Origin, G3.TetrahedronInradius(), 60, 30, true);
mesh1.ApplyTransformation(new ScaleTransform3D(scale, scale, scale));
group.Children.Add(mesh1.MakeModel(Brushes.Red));
// Make a translucent tetrahedron.
MeshGeometry3D mesh2 = new MeshGeometry3D();
mesh2.AddTetrahedron();
mesh2.ApplyTransformation(new ScaleTransform3D(scale, scale, scale));
Brush brush = new SolidColorBrush(Color.FromArgb(128, 128, 255, 128));
MaterialGroup group2 = D3.MakeMaterialGroup(
new DiffuseMaterial(brush),
new SpecularMaterial(Brushes.White, 100));
group.Children.Add(mesh2.MakeModel(group2));
// Make a translucent circumsphere.
MeshGeometry3D mesh3 = new MeshGeometry3D();
mesh3.AddSphere(D3.Origin, G3.TetrahedronCircumradius(), 60, 30, true);
mesh3.ApplyTransformation(new ScaleTransform3D(scale, scale, scale));
MaterialGroup group3 = D3.MakeMaterialGroup(
new DiffuseMaterial(brush),
new SpecularMaterial(Brushes.White, 100));
group.Children.Add(mesh3.MakeModel(group3));
}
// 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));
}
// Add a sphere with texture coordinates.
public static void AddTexturedSphere(this MeshGeometry3D mesh,
Point3D center, double radius, int numTheta, int numPhi,
bool smooth = false)
{
double dtheta = 2 * Math.PI / numTheta;
double dphi = 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 point1 = G3.SpherePoint(center, radius, theta, phi).Round();
Point3D point2 = G3.SpherePoint(center, radius, theta, phi + dphi).Round();
Point3D point3 = G3.SpherePoint(center, radius, theta + dtheta, phi + dphi).Round();
Point3D point4 = G3.SpherePoint(center, radius, theta + dtheta, phi).Round();
// Find this piece's texture coordinates.
Point coords1 = new Point((double)t / numTheta, (double)p / numPhi);
Point coords2 = new Point((double)t / numTheta, (double)(p + 1) / numPhi);
Point coords3 = new Point((double)(t + 1) / numTheta, (double)(p + 1) / numPhi);
Point coords4 = new Point((double)(t + 1) / numTheta, (double)p / numPhi);
// Find this piece's normals.
Vector3D normal1 = (Vector3D)G3.SpherePoint(D3.Origin, 1, theta, phi).Round();
Vector3D normal2 = (Vector3D)G3.SpherePoint(D3.Origin, 1, theta, phi + dphi).Round();
Vector3D normal3 = (Vector3D)G3.SpherePoint(D3.Origin, 1, theta + dtheta, phi + dphi).Round();
Vector3D normal4 = (Vector3D)G3.SpherePoint(D3.Origin, 1, theta + dtheta, phi).Round();
// 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;
}
}