| public ApplyToQuaternion ( Vector3D q ) : Vector3D | ||
| q | Vector3D | |
| return | Vector3D | |
/// <summary>
/// Add a finite (truncated) banana to our mesh. Passed in edge should be in Ball model.
/// </summary>
public static void AddBanana( Shapeways mesh, Vector3D e1, Vector3D e2, H3.Settings settings )
{
Vector3D e1UHS = H3Models.BallToUHS( e1 );
Vector3D e2UHS = H3Models.BallToUHS( e2 );
// Endpoints of the goedesic on the z=0 plane.
Vector3D z1, z2;
H3Models.UHS.GeodesicIdealEndpoints( e1UHS, e2UHS, out z1, out z2 );
// XXX - Do we want to do a better job worrying about rotation here?
// (multiply by complex number with certain imaginary part as well)
//Vector3D z3 = ( z1 + z2 ) / 2;
//if( Infinity.IsInfinite( z3 ) )
// z3 = new Vector3D( 1, 0 );
Vector3D z3 = new Vector3D( Math.E, Math.PI ); // This should vary the rotations a bunch.
// Find the Mobius we need.
// We'll do this in two steps.
// (1) Find a mobius taking z1,z2 to origin,inf
// (2) Deal with scaling e1 to a height of 1.
Mobius m1 = new Mobius( z1, z3, z2 );
Vector3D e1UHS_transformed = m1.ApplyToQuaternion( e1UHS );
double scale = 1.0 / e1UHS_transformed.Z;
Mobius m2 = Mobius.Scale( scale );
Mobius m = m2 * m1; // Compose them (multiply in reverse order).
Vector3D e2UHS_transformed = m.ApplyToQuaternion( e2UHS );
// Make our truncated cone.
// For regular tilings, we really would only need to do this once for a given LOD.
List<Vector3D> points = new List<Vector3D>();
double logHeight = Math.Log( e2UHS_transformed.Z );
if( logHeight < 0 )
throw new System.Exception( "impl issue" );
int div1, div2;
H3Models.Ball.LOD_Finite( e1, e2, out div1, out div2, settings );
double increment = logHeight / div1;
for( int i=0; i<=div1; i++ )
{
double h = increment * i;
// This is to keep different bananas from sharing exactly coincident vertices.
double tinyOffset = 0.001;
if( i == 0 )
h -= tinyOffset;
if( i == div1 )
h += tinyOffset;
Vector3D point = new Vector3D( 0, 0, Math.Exp( h ) );
points.Add( point );
}
Shapeways tempMesh = new Shapeways();
tempMesh.Div = div2;
tempMesh.AddCurve( points.ToArray(), v => H3Models.UHS.SizeFunc( v, settings.AngularThickness ) );
// Unwind the transforms.
TakePointsBack( tempMesh.Mesh, m.Inverse(), settings );
mesh.Mesh.Triangles.AddRange( tempMesh.Mesh.Triangles );
}
/// <summary>
/// Helper to apply a Mobius to the ball model.
/// Vector is taken to UHS, mobius applied, then taken back.
/// </summary>
public static Vector3D ApplyMobius( Mobius m, Vector3D v )
{
v = BallToUHS( v );
v = m.ApplyToQuaternion( v );
return UHSToBall( v );
}
/// <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 );
}
internal static void TakePointsBack( Mesh mesh, Mobius m, H3.Settings settings )
{
for( int i=0; i<mesh.Triangles.Count; i++ )
{
mesh.Triangles[i] = new Mesh.Triangle(
m.ApplyToQuaternion( mesh.Triangles[i].a ),
m.ApplyToQuaternion( mesh.Triangles[i].b ),
m.ApplyToQuaternion( mesh.Triangles[i].c ) );
/*if( Infinity.IsInfinite( mesh.Triangles[i].a ) ||
Infinity.IsInfinite( mesh.Triangles[i].b ) ||
Infinity.IsInfinite( mesh.Triangles[i].c ) )
System.Diagnostics.Debugger.Break();*/
}
// Take all points back to Ball, if needed.
if( !settings.Halfspace )
{
for( int i=0; i<mesh.Triangles.Count; i++ )
{
mesh.Triangles[i] = new Mesh.Triangle(
H3Models.UHSToBall( mesh.Triangles[i].a ),
H3Models.UHSToBall( mesh.Triangles[i].b ),
H3Models.UHSToBall( mesh.Triangles[i].c ) );
}
}
}