| public AddSphere ( Vector3D center, double radius ) : void | ||
| center | Vector3D | |
| radius | double | |
| return | void | |
public static void GenEuclidean()
{
Shapeways mesh = new Shapeways();
HashSet <H3.Cell.Edge> completed = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
int count = 2;
for (int i = -count; i < count; i++)
{
for (int j = -count; j < count; j++)
{
for (int k = -count; k < count; k++)
{
// Offset
double io = i + 0.5;
double jo = j + 0.5;
double ko = k + 0.5;
Vector3D p = new Vector3D(io, jo, ko);
// Add a sphere for this point.
Sphere s = new Sphere()
{
Center = p, Radius = 0.05
};
mesh.AddSphere(s.Center, s.Radius);
// Do every edge emanating from this point.
AddEuclideanEdge(mesh, completed, p, new Vector3D(io + 1, jo, ko));
AddEuclideanEdge(mesh, completed, p, new Vector3D(io - 1, jo, ko));
AddEuclideanEdge(mesh, completed, p, new Vector3D(io, jo + 1, ko));
AddEuclideanEdge(mesh, completed, p, new Vector3D(io, jo - 1, ko));
AddEuclideanEdge(mesh, completed, p, new Vector3D(io, jo, ko + 1));
AddEuclideanEdge(mesh, completed, p, new Vector3D(io, jo, ko - 1));
}
}
}
STL.SaveMeshToSTL(mesh.Mesh, "434.stl");
//PovRay.WriteEdges( new PovRay.Parameters() { AngularThickness = .05 }, Geometry.Euclidean, completed.ToArray(), "434.pov", append: false );
}
/// <summary>
/// A helper for adding a sphere. center should be passed in the ball model.
/// The approach is similar to how we do the bananas below.
/// </summary>
public static void AddSphere( Shapeways mesh, Vector3D center, H3.Settings settings )
{
Vector3D centerUHS = H3Models.BallToUHS( center );
// Find the Mobius we need.
// We'll do this in two steps.
// (1) Find a mobius taking center to (0,0,h).
// (2) Deal with scaling to a height of 1.
Vector3D flattened = centerUHS;
flattened.Z = 0;
Mobius m1 = new Mobius( flattened, Complex.One, Infinity.InfinityVector );
Vector3D centerUHS_transformed = m1.ApplyToQuaternion( centerUHS );
double scale = 1.0 / centerUHS_transformed.Z;
Mobius m2 = new Mobius( scale, Complex.Zero, Complex.Zero, Complex.One );
Mobius m = m2 * m1; // Compose them (multiply in reverse order).
// Add the sphere at the Ball origin.
// It will *always* be generated with the same radius.
Shapeways tempMesh = new Shapeways();
tempMesh.AddSphere( new Vector3D(), H3Models.Ball.SizeFunc( new Vector3D(), settings.AngularThickness ) );
// Unwind the transforms.
for( int i=0; i<tempMesh.Mesh.Triangles.Count; i++ )
{
tempMesh.Mesh.Triangles[i] = new Mesh.Triangle(
H3Models.BallToUHS( tempMesh.Mesh.Triangles[i].a ),
H3Models.BallToUHS( tempMesh.Mesh.Triangles[i].b ),
H3Models.BallToUHS( tempMesh.Mesh.Triangles[i].c ) );
}
Banana.TakePointsBack( tempMesh.Mesh, m.Inverse(), settings );
mesh.Mesh.Triangles.AddRange( tempMesh.Mesh.Triangles );
}