/// <summary>
/// Allow a hyperbolic transformation using an absolute offset.
/// offset is specified in the respective geometry.
/// </summary>
public void Hyperbolic2(Geometry g, Complex fixedPlus, Complex point, double offset)
{
// To the origin.
Mobius m = new Mobius();
m.Isometry(g, 0, fixedPlus * -1);
double eRadius = m.Apply(point).Magnitude;
double scale = 1;
switch (g)
{
case Geometry.Spherical:
double sRadius = Spherical2D.e2sNorm(eRadius);
sRadius += offset;
scale = Spherical2D.s2eNorm(sRadius) / eRadius;
break;
case Geometry.Euclidean:
scale = (eRadius + offset) / eRadius;
break;
case Geometry.Hyperbolic:
double hRadius = DonHatch.e2hNorm(eRadius);
hRadius += offset;
scale = DonHatch.h2eNorm(hRadius) / eRadius;
break;
}
Hyperbolic(g, fixedPlus, scale);
}
public void AnimationSections(Settings config)
{
HoneycombDef imageData = new HoneycombDef(config.P, config.Q, config.R);
int p = imageData.P, q = imageData.Q, r = imageData.R;
string filename = imageData.FormatFilename();
Sphere[] mirrors = SimplexCalcs.Mirrors(p, q, r);
double bounds = 1.0; //config.UhsBoundary.Bounds;
bounds = 9.0;
// Calculate the color scale.
int size = 200;
CoxeterImages.Settings settings = new CoxeterImages.Settings()
{
Honeycomb = imageData,
Width = size,
Height = size,
Bounds = bounds,
Mirrors = mirrors,
FileName = imageData.FormatFilename(),
};
CoxeterImages imageCalculator = new CoxeterImages();
//imageCalculator.AutoCalcScale( settings );
if (settings.ColorScaling < 1)
{
settings.ColorScaling = 15;
}
settings.ColorScaling = 11;
Program.Log("\nGenerating sections...");
size = 500;
settings.Width = size;
settings.Height = size;
settings.FileName = filename;
double max = Spherical2D.e2sNorm(15);
double min = Spherical2D.e2sNorm(1.0 / 15);
DonHatch.e2hNorm(max);
int numSteps = 1800; // 1 minute
double step = (max - min) / numSteps;
for (int i = 0; i < 1; i++)
{
Program.Log("\nSection " + i);
imageCalculator.m_z = 1.0 / 0.5;
Spherical2D.s2eNorm(min + step * i);
DonHatch.h2eNorm(step * i);
settings.FileName = string.Format("533_{0:D4}.png", i);
imageCalculator.GenImage(settings);
}
}
/// <summary>
/// Equally subdivides a segment with a startpoint at the origin, in the respective geometry.
/// </summary>
private static Vector3D[] SubdivideRadialInGeometry(Segment radial, int divisions, Geometry g)
{
List <Vector3D> result = new List <Vector3D>();
if (radial.Type != SegmentType.Line)
{
Debug.Assert(false);
return(result.ToArray());
}
switch (g)
{
case Geometry.Spherical:
{
double eLength = radial.Length;
double sLength = Spherical2D.e2sNorm(eLength);
double divLength = sLength / divisions;
for (int i = 0; i <= divisions; i++)
{
double temp = Spherical2D.s2eNorm(divLength * i);
result.Add(radial.P2 * temp / eLength);
}
break;
}
case Geometry.Euclidean:
return(radial.Subdivide(divisions));
case Geometry.Hyperbolic:
{
double eLength = radial.Length;
double hLength = DonHatch.e2hNorm(eLength);
double divLength = hLength / divisions;
for (int i = 0; i <= divisions; i++)
{
double temp = DonHatch.h2eNorm(divLength * i);
result.Add(radial.P2 * temp / eLength);
}
break;
}
}
return(result.ToArray());
}
public static Sphere GeodesicOffset(Sphere s, double offset, bool ball = true)
{
Sphere offsetSphere;
if (ball)
{
// Geodesic offset (ball).
{ // Hyperbolic honeycomb
double mag = s.Center.Abs() - s.Radius;
mag = s.IsPlane ? DonHatch.h2eNorm(offset) :
DonHatch.h2eNorm(DonHatch.e2hNorm(mag) - offset);
Vector3D closestPointToOrigin = s.IsPlane ? s.Normal : s.Center;
closestPointToOrigin.Normalize();
closestPointToOrigin *= mag;
offsetSphere = H3Models.Ball.OrthogonalSphereInterior(closestPointToOrigin);
// There are multiple ultraparallel spheres.
// This experiments with picking others.
Mobius m = new Mobius();
m.Isometry(Geometry.Hyperbolic, 0, new Vector3D(0, -0.2));
//H3Models.TransformInBall2( offsetSphere, m );
}
{ // Spherical honeycomb
//offset *= -1;
double mag = -s.Center.Abs() + s.Radius;
Spherical2D.s2eNorm(Spherical2D.e2sNorm(mag) + offset);
offsetSphere = s.Clone();
offsetSphere.Radius += offset * 10;
}
}
else
{
// Geodesic offset (UHS).
// XXX - not scaled right.
offsetSphere = s.Clone();
offsetSphere.Radius += offset;
}
return(offsetSphere);
}
