/// <summary>
/// Helper to construct some points we need for calculating simplex facets for a {p,q,r} honeycomb.
/// </summary>
private static void TilePoints(int p, int q, out Vector3D p1, out Vector3D p2, out Vector3D p3, out Segment seg)
{
if (Infinite(p) && Infinite(q) /*&& FiniteOrInfinite( r )*/)
{
p1 = new Vector3D(1, 0, 0);
p2 = new Vector3D(0, Math.Sqrt(2) - 1);
p3 = Vector3D.DneVector();
Circle3D arcCircle;
H3Models.Ball.OrthogonalCircleInterior(p2, p1, out arcCircle);
seg = Segment.Arc(p1, p2, arcCircle.Center, clockwise: true);
}
else
{
Segment[] baseTileSegments;
if (Infinite(q))
{
baseTileSegments = BaseTileSegments(p, q); // Can't use dual here.
}
else
{
baseTileSegments = BaseTileSegments(q, p); // Intentionally using dual.
}
seg = baseTileSegments.First();
p1 = seg.P1;
p2 = seg.Midpoint;
p3 = p2;
p3.RotateXY(-Math.PI / 2);
}
}
/// <summary>
/// Helper to return the smaller spliced arc.
/// </summary>
private static Segment SmallerSplicedArc(Circle c, List <IntersectionPoint> iPoints, ref int pair, bool increment, ref int nextSegIndex)
{
IntersectionPoint iPoint1, iPoint2;
GetPairPoints(iPoints, pair, increment, out iPoint1, out iPoint2);
Vector3D p1 = iPoint1.Location;
Vector3D p2 = iPoint2.Location;
nextSegIndex = iPoint2.Index;
Segment newSeg = Segment.Arc(p1, p2, c.Center, clockwise: true);
if (newSeg.Angle > System.Math.PI)
{
newSeg.Clockwise = false;
}
pair++;
if (pair == iPoints.Count / 2)
{
pair = 0;
}
return(newSeg);
}
public static Polygon Heart()
{
Polygon newPoly = new Polygon();
double size = 0.12;
double angle = -3 * Math.PI / 2;
Vector3D p1 = new Vector3D(0, -1.5 * size);
Vector3D p2 = new Vector3D(-size, 0);
Vector3D p3 = new Vector3D(-size / 2, size);
Vector3D p4 = new Vector3D(0, size / 2);
Vector3D p5 = new Vector3D(size / 2, size);
Vector3D p6 = new Vector3D(size, 0);
p1.RotateXY(angle);
p2.RotateXY(angle);
p3.RotateXY(angle);
p4.RotateXY(angle);
p5.RotateXY(angle);
p6.RotateXY(angle);
newPoly.Segments.Add(Segment.Line(p1, p2));
newPoly.Segments.Add(Segment.Arc(p2, p3, p4));
newPoly.Segments.Add(Segment.Arc(p4, p5, p6));
newPoly.Segments.Add(Segment.Line(p6, p1));
return(newPoly);
}
/// <summary>
/// Slicing function used for earthquake puzzles.
/// c should be geodesic (orthogonal to the disk boundary).
/// </summary>
public static void SlicePolygonWithHyperbolicGeodesic(Polygon p, CircleNE c, double thickness, out List <Polygon> output)
{
Geometry g = Geometry.Hyperbolic;
Segment seg = null;
if (c.IsLine)
{
Vector3D p1, p2;
Euclidean2D.IntersectionLineCircle(c.P1, c.P2, new Circle(), out p1, out p2);
seg = Segment.Line(p1, p2);
}
else
{
// Setup the two slicing circles.
// These are cuts equidistant from the passed in geodesic.
Vector3D closestToOrigin = H3Models.Ball.ClosestToOrigin(new Circle3D()
{
Center = c.Center, Radius = c.Radius, Normal = new Vector3D(0, 0, 1)
});
Vector3D p1, p2;
Euclidean2D.IntersectionCircleCircle(c, new Circle(), out p1, out p2);
seg = Segment.Arc(p1, closestToOrigin, p2);
}
Circle c1 = H3Models.Ball.EquidistantOffset(g, seg, thickness / 2);
Circle c2 = H3Models.Ball.EquidistantOffset(g, seg, -thickness / 2);
CircleNE c1NE = c.Clone(), c2NE = c.Clone();
c1NE.Center = c1.Center; c2NE.Center = c2.Center;
c1NE.Radius = c1.Radius; c2NE.Radius = c2.Radius;
SlicePolygonHelper(p, c1NE, c2NE, out output);
}
/// <summary>
/// Euclidean scale us relative to some center point.
/// NOTE: Currently only works for line segments.
/// </summary>
public void Scale(Vector3D center, double factor)
{
Translate(-center);
if (this.Type == SegmentType.Line)
{
this.P1 *= factor;
this.P2 *= factor;
}
else if (this.Type == SegmentType.Arc)
{
Vector3D p1 = this.P1;
Vector3D p2 = this.P2;
Vector3D mid = this.Midpoint;
p1 *= factor;
p2 *= factor;
mid *= factor;
Segment temp = Segment.Arc(p1, mid, p2);
this.P1 = p1;
this.P2 = p2;
this.Center = temp.Center;
}
Translate(center);
}