/// <summary>
/// A correct implementation of shrink tile.
/// hmmmm, is "scaling" even well defined in non-E geometries? Am I really looking for an equidistant curve?
/// Sadly, even if I figure out what is best, I fear changing out usage of the incorrect one below in MagicTile,
/// because of the possibility of breaking existing puzzles.
/// </summary>
internal static void ShrinkTileCorrect( ref Tile tile, double shrinkFactor )
{
System.Func<Vector3D,double,Vector3D> scaleFunc = null;
switch( tile.Geometry )
{
case Geometry.Euclidean:
{
scaleFunc = ( v, s ) => v * s;
break;
}
case Geometry.Spherical:
{
scaleFunc = ( v, s ) =>
{
// Move to spherical norm, scale, then move back to euclidean.
double scale = Spherical2D.s2eNorm( ( Spherical2D.e2sNorm( v.Abs() ) * s ) );
v.Normalize();
return v * scale;
};
break;
}
case Geometry.Hyperbolic:
{
throw new System.NotImplementedException();
}
}
}
public Tile Clone()
{
Tile newTile = new Tile();
newTile.Boundary = Boundary.Clone();
newTile.Drawn = Drawn.Clone();
newTile.VertexCircle = VertexCircle.Clone();
newTile.Geometry = Geometry;
return newTile;
}
/// <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;
}
}
*/
}
public void CalculateFromTwoPolygons( Tile home, Polygon boundaryPolygon, Geometry g )
{
CalculateFromTwoPolygonsInternal( home.Boundary, boundaryPolygon, home.VertexCircle, g );
}
private static void MeshEdges( Mesh mesh, Tile tile, HashSet<Vector3D> completed, Polygon boundary )
{
for( int i=0; i<tile.Boundary.Segments.Count; i++ )
{
Segment boundarySeg = tile.Boundary.Segments[i];
Segment d1 = tile.Drawn.Segments[i];
if( completed.Contains( boundarySeg.Midpoint ) )
continue;
// Find the incident segment.
Segment seg2 = null, d2 = null;
foreach( Tile incident in tile.EdgeIncidences )
{
for( int j=0; j<incident.Boundary.Segments.Count; j++ )
{
if( boundarySeg.Midpoint == incident.Boundary.Segments[j].Midpoint )
{
seg2 = incident.Boundary.Segments[j];
d2 = incident.Drawn.Segments[j];
break;
}
}
if( seg2 != null )
break;
}
// Found our incident edge?
bool foundIncident = seg2 != null;
if( !foundIncident )
seg2 = d2 = boundarySeg;
// Do the endpoints mismatch?
if( boundarySeg.P1 != seg2.P1 )
{
Segment clone = d2.Clone();
clone.Reverse();
d2 = clone;
}
// Add the two vertices (careful of orientation).
if( foundIncident )
{
CheckAndAdd( mesh, new Mesh.Triangle( boundarySeg.P1, d1.P1, d2.P1 ), boundary );
CheckAndAdd( mesh, new Mesh.Triangle( boundarySeg.P2, d2.P2, d1.P2 ), boundary );
}
int num = 1 + (int)(d1.Length * m_divisions);
Vector3D[] list1 = d1.Subdivide( num );
Vector3D[] list2 = d2.Subdivide( num );
for( int j=0; j<num; j++ )
{
CheckAndAdd( mesh, new Mesh.Triangle( list1[j], list1[j + 1], list2[j + 1] ), boundary );
CheckAndAdd( mesh, new Mesh.Triangle( list2[j], list1[j], list2[j + 1] ), boundary );
}
completed.Add( boundarySeg.Midpoint );
}
}
/// <summary>
/// Will clone the tile, transform it and add it to our tiling.
/// </summary>
private bool TransformAndAdd( Tile tile )
{
// Will we want to include it?
if( !tile.IncludeAfterMobius( this.TilingConfig.M ) )
return false;
Tile clone = tile.Clone();
clone.Transform( this.TilingConfig.M );
m_tiles.Add( clone );
this.TilePositions[clone.Boundary.Center] = clone;
return true;
}
/// <summary>
/// Calculates an isometry by taking a tile boundary polygon to a home.
/// </summary>
public void CalculateFromTwoPolygons( Tile home, Tile tile, Geometry g )
{
Polygon poly = tile.Boundary;
CalculateFromTwoPolygons( home, poly, g );
}
/// <summary>
/// This will fill out all the tiles with the isometry that will take them back to a home tile.
/// </summary>
private static void FillOutIsometries( Tile home, List<Tile> tiles, Geometry g )
{
foreach( Tile tile in tiles )
tile.Isometry.CalculateFromTwoPolygons( home, tile, g );
}
/// <summary>
/// This will return whether we'll be a new tile after reflecting through a segment.
/// This allows us to do the check without having to do all the work of reflecting the entire tile.
/// </summary>
public bool NewTileAfterReflect( Tile t, Segment s, Dictionary<Vector3D, bool> completed )
{
/* This was too slow!
Polygon newPolyBoundary = t.Boundary.Clone();
newPolyBoundary.Reflect( s );
Vector3D testCenter = this.TilingConfig.M.Apply( newPolyBoundary.Center );*/
CircleNE newVertexCircle = t.VertexCircle.Clone();
newVertexCircle.Reflect( s );
Vector3D testCenter = this.TilingConfig.M.Apply( newVertexCircle.CenterNE );
return !completed.ContainsKey( testCenter );
}
public static Tile CreateBaseTile( TilingConfig config )
{
Polygon boundary = new Polygon(), drawn = new Polygon();
boundary.CreateRegular( config.P, config.Q );
drawn = boundary.Clone();
//boundary.CreateRegular( 3, 10 );
//drawn.CreateRegular( 3, 8 );
//boundary.CreateRegular( 3, 7 );
//drawn = Heart();
//for( int i=0; i<drawn.NumSides; i++ )
// drawn.Segments[i].Center *= 0.1;
// Good combos:
// ( 5, 5 ), ( 10, 10 )
// ( 3, 10 ), ( 3, 9 )
// ( 6, 4 ), ( 6, 8 )
// ( 7, 3 ), ( 7, 9 )
Tile tile = new Tile( boundary, drawn, config.Geometry );
Tile.ShrinkTile( ref tile, config.Shrink );
return tile;
}
private static void GetAssociatedTiling( EHoneycomb honeycomb, out Tiling tiling, out Tile baseTile )
{
int p, q;
GetPQ( honeycomb, out p, out q );
TilingConfig tilingConfig = new TilingConfig( p, q, maxTiles: m_params.MaxTiles );
tiling = new Tiling();
tiling.Generate( tilingConfig );
baseTile = Tiling.CreateBaseTile( tilingConfig );
}
private static double EdgeCenteredScale( Tile baseTile )
{
Segment seg = baseTile.Boundary.Segments[0];
return 1.0 / ( seg.Length / 2 );
}