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public Intersection ( |
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public static void GenImage()
{
int size = 1000;
Bitmap image = new Bitmap( size, size );
ImageSpace i = new ImageSpace( size, size );
double b = 1.1;
i.XMin = -b; i.XMax = b;
i.YMin = -b; i.YMax = b;
Vector3D cen = HoneycombPaper.CellCenBall;
cen = H3Models.BallToUHS( cen );
Sphere[] simplex = Simplex( ref cen );
Sphere inSphere = InSphere( simplex );
using( Graphics g = Graphics.FromImage( image ) )
foreach( int[] reflections in AllCells() )
{
Sphere clone = inSphere.Clone();
foreach( int r in reflections )
clone.Reflect( simplex[r] );
Sphere ball = new Sphere();
Circle3D inSphereIdealBall = ball.Intersection( clone );
Circle3D inSphereIdealUHS = H3Models.BallToUHS( inSphereIdealBall );
Circle inSphereIdeal = new Circle { Center = inSphereIdealUHS.Center, Radius = inSphereIdealUHS.Radius };
using( Brush brush = new SolidBrush( Color.Blue ) )
DrawUtils.DrawFilledCircle( inSphereIdeal, g, i, brush );
}
image.Save( "threefifty.png", ImageFormat.Png );
}
private static Circle3D HoneycombEdgeUHS(int p, int q, int r)
{
Sphere[] simplex = Mirrors(p, q, r, moveToBall: false);
Sphere s1 = simplex[0].Clone();
Sphere s2 = s1.Clone();
s2.Reflect(simplex[1]);
Circle3D intersection = s1.Intersection(s2);
return(intersection);
}
/// <summary>
/// This will return an altered facet to create true apparent 2D tilings (proper bananas) on the boundary.
/// Notes:
/// The input simplex must be in the ball model.
/// The first mirror of the simplex (the one that mirrors across cells) is the one we end up altering.
/// </summary>
public static Sphere AlteredFacetForTrueApparent2DTilings( Sphere[] simplex )
{
// We first need to find the size of the apparent 2D disk surrounding the leg.
// This is also the size of the apparent cell head disk of the dual.
// So we want to get the midsphere (insphere would also work) of the dual cell with that head,
// then calculate the intersection of that with the boundary.
Sphere cellMirror = simplex[0];
if( cellMirror.IsPlane )
throw new System.NotImplementedException();
// The point centered on a face is the closest point of the cell mirror to the origin.
// This will be the point centered on an edge on the dual cell.
Vector3D facePoint = cellMirror.ProjectToSurface( new Vector3D() );
// Reflect it to get 3 more points on our midsphere.
Vector3D reflected1 = simplex[1].ReflectPoint( facePoint );
Vector3D reflected2 = simplex[2].ReflectPoint( reflected1 );
Vector3D reflected3 = simplex[0].ReflectPoint( reflected2 );
Sphere midSphere = Sphere.From4Points( facePoint, reflected1, reflected2, reflected3 );
// Get the ideal circles of the cell mirror and midsphere.
// Note: The midsphere is not geodesic, so we can't calculate it the same.
Sphere cellMirrorUHS = H3Models.BallToUHS( cellMirror );
Circle cellMirrorIdeal = H3Models.UHS.IdealCircle( cellMirrorUHS );
Sphere ball = new Sphere();
Circle3D midSphereIdealBall = ball.Intersection( midSphere ); // This should exist because we've filtered for honeycombs with hyperideal verts.
Circle3D midSphereIdealUHS = H3Models.BallToUHS( midSphereIdealBall );
Circle midSphereIdeal = new Circle { Center = midSphereIdealUHS.Center, Radius = midSphereIdealUHS.Radius };
// The intersection point of our cell mirror and the disk of the apparent 2D tiling
// gives us "ideal" points on the apparent 2D boundary. These points will be on the new cell mirror.
Vector3D i1, i2;
if( 2 != Euclidean2D.IntersectionCircleCircle( cellMirrorIdeal, midSphereIdeal, out i1, out i2 ) )
{
//throw new System.ArgumentException( "Since we have hyperideal vertices, we should have an intersection with 2 points." );
// Somehow works in the euclidean case.
// XXX - Make this better.
return H3Models.UHSToBall( new Sphere() { Center = Vector3D.DneVector(), Radius = double.NaN } );
}
double bananaThickness = 0.025;
//bananaThickness = 0.15;
//bananaThickness = 0.04;
// Transform the intersection points to a standard Poincare disk.
// The midsphere radius is the scale of the apparent 2D tilings.
double scale = midSphereIdeal.Radius;
Vector3D offset = midSphereIdeal.Center;
i1 -= offset;
i2 -= offset;
i1 /= scale;
i2 /= scale;
Circle3D banana = H3Models.Ball.OrthogonalCircle( i1, i2 );
Vector3D i3 = H3Models.Ball.ClosestToOrigin( banana );
i3 = Hyperbolic2D.Offset( i3, -bananaThickness );
// Transform back.
i1 *= scale; i2 *= scale; i3 *= scale;
i1 += offset; i2 += offset; i3 += offset;
// Construct our new simplex mirror with these 3 points.
Circle3D c = new Circle3D( i1, i2, i3 );
Sphere result = new Sphere() { Center = c.Center, Radius = c.Radius };
return H3Models.UHSToBall( result );
}