Intersection() публичный Метод

Finds the intersection (a circle) between us and another sphere. Returns null if sphere centers are coincident or no intersection exists. Does not currently work for planes.
public Intersection ( Sphere s ) : Circle3D
s Sphere
Результат Circle3D
Пример #1
0
        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 );
        }
Пример #2
0
        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);
        }
Пример #3
0
        /// <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 );
        }