public static Mobius VertexCenteredMobius(int p, int q)
{
double angle = Math.PI / q;
if (Utils.Even(q))
{
angle *= 2;
}
Vector3D offset = new Vector3D(-1 * Geometry2D.GetNormalizedCircumRadius(p, q), 0, 0);
offset.RotateXY(angle);
Mobius m = new Mobius();
m.Isometry(Geometry2D.GetGeometry(p, q), angle, offset.ToComplex());
return(m);
}
public void CreateRegular(int numSides, int q)
{
int p = numSides;
Segments.Clear();
List <Vector3D> points = new List <Vector3D>();
Geometry g = Geometry2D.GetGeometry(p, q);
double circumRadius = Geometry2D.GetNormalizedCircumRadius(p, q);
double angle = 0;
for (int i = 0; i < p; i++)
{
Vector3D point = new Vector3D();
point.X = (circumRadius * Math.Cos(angle));
point.Y = (circumRadius * Math.Sin(angle));
points.Add(point);
angle += Utils.DegreesToRadians(360.0 / p);
}
// Turn this into segments.
for (int i = 0; i < points.Count; i++)
{
int idx1 = i;
int idx2 = i == points.Count - 1 ? 0 : i + 1;
Segment newSegment = new Segment();
newSegment.P1 = points[idx1];
newSegment.P2 = points[idx2];
if (g != Geometry.Euclidean)
{
newSegment.Type = SegmentType.Arc;
if (2 == p)
{
// Our magic formula below breaks down for digons.
double factor = Math.Tan(Math.PI / 6);
newSegment.Center = newSegment.P1.X > 0 ?
new Vector3D(0, -circumRadius, 0) * factor :
new Vector3D(0, circumRadius, 0) * factor;
}
else
{
// Our segments are arcs in Non-Euclidean geometries.
// Magically, the same formula turned out to work for both.
// (Maybe this is because the Poincare Disc model of the
// hyperbolic plane is stereographic projection as well).
double piq = q == -1 ? 0 : Math.PI / q; // Handle q infinite.
double t1 = Math.PI / p;
double t2 = Math.PI / 2 - piq - t1;
double factor = (Math.Tan(t1) / Math.Tan(t2) + 1) / 2;
newSegment.Center = (newSegment.P1 + newSegment.P2) * factor;
}
newSegment.Clockwise = Geometry.Spherical == g ? false : true;
}
// XXX - Make this configurable?
// This is the color of cell boundary lines.
//newSegment.m_color = CColor( 1, 1, 0, 1 );
Segments.Add(newSegment);
}
}
