| public Hyperbolic ( Geometry g, System.Numerics.Complex fixedPlus, double scale ) : void | ||
| g | Geometry | |
| fixedPlus | System.Numerics.Complex | |
| scale | double | |
| return | void | |
/// <summary>
/// This will trim back the tile using an equidistant curve.
/// It assumes the tile is at the origin.
/// </summary>
internal static void ShrinkTile( ref Tile tile, double shrinkFactor )
{
// This code is not correct in non-Euclidean cases!
// But it works reasonable well for small shrink factors.
// For example, you can easily use this function to grow a hyperbolic tile beyond the disk.
Mobius m = new Mobius();
m.Hyperbolic( tile.Geometry, new Vector3D(), shrinkFactor );
tile.Drawn.Transform( m );
return;
/*
// ZZZ
// Wow, all the work I did below was subsumed by 4 code lines above!
// I can't bring myself to delete it yet.
switch( tile.Geometry )
{
case Geometry.Spherical:
{
List<Tile> clipped = new List<Tile>();
clipped.Add( tile );
Polygon original = tile.Drawn.Clone();
foreach( Segment seg in original.Segments )
{
Debug.Assert( seg.Type == SegmentType.Arc );
if( true )
{
// Unproject to sphere.
Vector3D p1 = Spherical2D.PlaneToSphere( seg.P1 );
Vector3D p2 = Spherical2D.PlaneToSphere( seg.P2 );
// Get the poles of the GC, and project them to the plane.
Vector3D pole1, pole2;
Spherical2D.GreatCirclePole( p1, p2, out pole1, out pole2 );
pole1 = Spherical2D.SphereToPlane( pole1 );
pole2 = Spherical2D.SphereToPlane( pole2 );
// Go hyperbolic, dude.
double scale = 1.065; // ZZZ - needs to be configurable.
Complex fixedPlus = pole1;
Mobius hyperbolic = new Mobius();
hyperbolic.Hyperbolic( tile.Geometry, fixedPlus, scale );
Vector3D newP1 = hyperbolic.Apply( seg.P1 );
Vector3D newMid = hyperbolic.Apply( seg.Midpoint );
Vector3D newP2 = hyperbolic.Apply( seg.P2 );
Circle trimmingCircle = new Circle();
trimmingCircle.From3Points( newP1, newMid, newP2 );
Slicer.Clip( ref clipped, trimmingCircle, true );
}
else
{
// I think this block has logic flaws, but strangely it seems to work,
// so I'm leaving it in commented out for posterity.
Vector3D p1 = seg.P1;
Vector3D mid = seg.Midpoint;
Vector3D p2 = seg.P2;
//double offset = .1;
double factor = .9;
double f1 = Spherical2D.s2eNorm( (Spherical2D.e2sNorm( p1.Abs() ) * factor) );
double f2 = Spherical2D.s2eNorm( (Spherical2D.e2sNorm( mid.Abs() ) * factor) );
double f3 = Spherical2D.s2eNorm( (Spherical2D.e2sNorm( p2.Abs() ) * factor) );
p1.Normalize();
mid.Normalize();
p2.Normalize();
p1 *= f1;
mid *= f2;
p2 *= f3;
Circle trimmingCircle = new Circle();
trimmingCircle.From3Points( p1, mid, p2 );
Slicer.Clip( ref clipped, trimmingCircle, true );
}
}
Debug.Assert( clipped.Count == 1 );
tile = clipped[0];
return;
}
case Geometry.Euclidean:
{
double scale = .95;
Mobius hyperbolic = new Mobius();
hyperbolic.Hyperbolic( tile.Geometry, new Vector3D(), scale );
tile.Drawn.Transform( hyperbolic );
return;
}
case Geometry.Hyperbolic:
{
List<Tile> clipped = new List<Tile>();
clipped.Add( tile );
Circle infinity = new Circle();
infinity.Radius = 1.0;
Polygon original = tile.Drawn.Clone();
foreach( Segment seg in original.Segments )
{
Debug.Assert( seg.Type == SegmentType.Arc );
Circle segCircle = seg.GetCircle();
// Get the intersection points with the disk at infinity.
Vector3D p1, p2;
int count = Euclidean2D.IntersectionCircleCircle( infinity, segCircle, out p1, out p2 );
Debug.Assert( count == 2 );
Vector3D mid = seg.Midpoint;
//mid *= 0.75; // ZZZ - needs to be configurable.
double offset = .03;
double f1 = DonHatch.h2eNorm( DonHatch.e2hNorm( mid.Abs() ) - offset );
mid.Normalize();
mid *= f1;
Circle trimmingCircle = new Circle();
trimmingCircle.From3Points( p1, mid, p2 );
Slicer.Clip( ref clipped, trimmingCircle, false );
}
Debug.Assert( clipped.Count == 1 );
tile = clipped[0];
return;
}
}
*/
}