// Rotates a dodec about a vertex or edge to get a dual dodec.
private static Dodec GetDual(Dodec dodec, Vector3D rotationPoint)
{
//double rot = System.Math.PI / 2; // Edge-centered
double rot = 4 * (-Math.Atan((2 + Math.Sqrt(5) - 2 * Math.Sqrt(3 + Math.Sqrt(5))) / Math.Sqrt(3))); // Vertex-centered
Mobius m = new Mobius();
if (Infinity.IsInfinite(rotationPoint))
{
m.Elliptic(Geometry.Spherical, new Vector3D(), -rot);
}
else
{
m.Elliptic(Geometry.Spherical, rotationPoint, rot);
}
Dodec dual = new Dodec();
foreach (Vector3D v in dodec.Verts)
{
Vector3D rotated = m.ApplyInfiniteSafe(v);
dual.Verts.Add(rotated);
}
foreach (Vector3D v in dodec.Midpoints)
{
Vector3D rotated = m.ApplyInfiniteSafe(v);
dual.Midpoints.Add(rotated);
}
return(dual);
}
// https://plus.google.com/u/0/117663015413546257905/posts/BnCEkdNiTZ2
public static void TwinDodecs()
{
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig(5, 3);
tiling.GenerateInternal(config, Polytope.Projection.VertexCentered); // Vertex-centered makes infinities tricky
Dodec dodec = new Dodec();
foreach (Tile tile in tiling.Tiles)
{
foreach (Segment seg in tile.Boundary.Segments)
{
Vector3D p1 = seg.P1, p2 = seg.P2;
if (Infinity.IsInfinite(p1))
{
p1 = Infinity.InfinityVector;
}
if (Infinity.IsInfinite(p2))
{
p2 = Infinity.InfinityVector;
}
dodec.Verts.Add(p1);
dodec.Verts.Add(p2);
dodec.Midpoints.Add(Halfway(p1, p2));
}
}
// Now recursively add more vertices.
HashSet <Vector3D> allVerts = new HashSet <Vector3D>();
foreach (Vector3D v in dodec.Verts)
{
allVerts.Add(v);
}
RecurseTwins(allVerts, dodec, 0);
using (StreamWriter sw = File.CreateText("dual_dodecs_points_sphere.pov"))
{
foreach (Vector3D vert in allVerts)
{
Vector3D onSphere = Sterographic.PlaneToSphereSafe(vert);
sw.WriteLine(PovRay.Sphere(new Sphere()
{
Center = onSphere, Radius = 0.01
}));
//if( !Infinity.IsInfinite( vert ) )
// sw.WriteLine( PovRay.Sphere( new Sphere() { Center = vert, Radius = 0.01 } ) );
}
}
}
private static void RecurseTwins(HashSet <Vector3D> allVerts, Dodec dodec, int level)
{
level++;
if (level > 1)
{
return;
}
//foreach( Vector3D v in dodec.Midpoints )
foreach (Vector3D v in dodec.Verts)
{
Dodec dual = GetDual(dodec, v);
int count = allVerts.Count;
foreach (Vector3D dualV in dual.Verts)
{
allVerts.Add(dualV);
}
if (count != allVerts.Count)
{
RecurseTwins(allVerts, dual, level);
}
}
}
private static void RecurseTwins( HashSet<Vector3D> allVerts, Dodec dodec, int level )
{
level++;
if( level > 1 )
return;
//foreach( Vector3D v in dodec.Midpoints )
foreach( Vector3D v in dodec.Verts )
{
Dodec dual = GetDual( dodec, v );
int count = allVerts.Count;
foreach( Vector3D dualV in dual.Verts )
allVerts.Add( dualV );
if( count != allVerts.Count )
RecurseTwins( allVerts, dual, level );
}
}
// Rotates a dodec about a vertex or edge to get a dual dodec.
private static Dodec GetDual( Dodec dodec, Vector3D rotationPoint )
{
//double rot = System.Math.PI / 2; // Edge-centered
double rot = 4 * ( - Math.Atan( ( 2 + Math.Sqrt( 5 ) - 2 * Math.Sqrt( 3 + Math.Sqrt( 5 ) ) ) / Math.Sqrt( 3 ) ) ); // Vertex-centered
Mobius m = new Mobius();
if( Infinity.IsInfinite( rotationPoint ) )
m.Elliptic( Geometry.Spherical, new Vector3D(), -rot );
else
m.Elliptic( Geometry.Spherical, rotationPoint, rot );
Dodec dual = new Dodec();
foreach( Vector3D v in dodec.Verts )
{
Vector3D rotated = m.ApplyInfiniteSafe( v );
dual.Verts.Add( rotated );
}
foreach( Vector3D v in dodec.Midpoints )
{
Vector3D rotated = m.ApplyInfiniteSafe( v );
dual.Midpoints.Add( rotated );
}
return dual;
}
// https://plus.google.com/u/0/117663015413546257905/posts/BnCEkdNiTZ2
public static void TwinDodecs()
{
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig( 5, 3 );
tiling.GenerateInternal( config, Polytope.Projection.VertexCentered ); // Vertex-centered makes infinities tricky
Dodec dodec = new Dodec();
foreach( Tile tile in tiling.Tiles )
foreach( Segment seg in tile.Boundary.Segments )
{
Vector3D p1 = seg.P1, p2 = seg.P2;
if( Infinity.IsInfinite( p1 ) )
p1 = Infinity.InfinityVector;
if( Infinity.IsInfinite( p2 ) )
p2 = Infinity.InfinityVector;
dodec.Verts.Add( p1 );
dodec.Verts.Add( p2 );
dodec.Midpoints.Add( Halfway( p1, p2 ) );
}
// Now recursively add more vertices.
HashSet<Vector3D> allVerts = new HashSet<Vector3D>();
foreach( Vector3D v in dodec.Verts )
allVerts.Add( v );
RecurseTwins( allVerts, dodec, 0 );
using( StreamWriter sw = File.CreateText( "dual_dodecs_points_sphere.pov" ) )
{
foreach( Vector3D vert in allVerts )
{
Vector3D onSphere = Sterographic.PlaneToSphereSafe( vert );
sw.WriteLine( PovRay.Sphere( new Sphere() { Center = onSphere, Radius = 0.01 } ) );
//if( !Infinity.IsInfinite( vert ) )
// sw.WriteLine( PovRay.Sphere( new Sphere() { Center = vert, Radius = 0.01 } ) );
}
}
}
