private static Vector3D DiskToUpper( Vector3D input )
{
Mobius m = new Mobius();
m.UpperHalfPlane();
return m.Apply( input );
}
public static void Test()
{
S3.HopfOrbit();
Mobius m = new Mobius();
m.UpperHalfPlane();
Vector3D test = m.Apply( new Vector3D() );
test *= 1;
}
private Vector3D ApplyTransformationToSphere( Vector3D v, double t )
{
v = H3Models.BallToUHS( v );
// 437 (hyperbolic)
//v *= Math.Pow( 4.259171776329806, t*10-5 );
// 36i (parabolic)
//v += new Vector3D( Math.Cos( Math.PI / 6 ), Math.Sin( Math.PI / 6 ) ) * t;
// iii (loxodromic)
//Complex c = v.ToComplex();
//double x = Math.Sqrt( 2 ) - 1;
//Mobius m = new Mobius( new Complex( x, 0 ), Complex.One, new Complex( -x, 0 ) );
// 12,12,12 loxodromic
//m = new Mobius( new Complex( 0, 1 ), Complex.One, new Complex( 0, -1 ) );
/*
c = m.Apply( c );
c *= Complex.Exp( new Complex( 2.5, 4 * Math.PI ) * t );
c = m.Inverse().Apply( c );
v = Vector3D.FromComplex( c );
*/
// Center cell head in KolorEyes.
Mobius m = new Mobius();
m.UpperHalfPlane();
v = m.Inverse().Apply( v );
return H3Models.UHSToBall( v );
}
private static Mobius ToUpperHalfPlaneMobius()
{
Mobius m = new Mobius();
m.UpperHalfPlane();
return m;
}
/// <summary>
/// Using this to move the view around in interesting ways.
/// </summary>
private Vector3D ApplyTransformation( Vector3D v, double t = 0.0 )
{
//v.RotateXY( Math.PI / 4 + 0.01 );
bool applyNone = true;
if( applyNone )
return v;
Mobius m0 = new Mobius(), m1 = new Mobius(), m2 = new Mobius(), m3 = new Mobius();
Sphere unitSphere = new Sphere();
// self-similar scale for 437
//v*= 4.259171776329806;
double s = 6.5;
v *= s;
v += new Vector3D( s/3, -s/3 );
v = unitSphere.ReflectPoint( v );
v.RotateXY( Math.PI/6 );
//v /= 3;
//v.RotateXY( Math.PI );
//v.RotateXY( Math.PI/2 );
return v;
//v.Y = v.Y / Math.Cos( Math.PI / 6 ); // 637 repeatable
//return v;
// 12,12,12
m0.Isometry( Geometry.Hyperbolic, 0, new Complex( .0, .0 ) );
m1 = Mobius.Identity();
m2 = Mobius.Identity();
m3 = Mobius.Identity();
v = (m0 * m1 * m2 * m3).Apply( v );
return v;
// i64
m0.Isometry( Geometry.Hyperbolic, 0, new Complex( .5, .5 ) );
m1.UpperHalfPlane();
m2 = Mobius.Scale( 1.333333 );
m3.Isometry( Geometry.Euclidean, 0, new Vector3D( 0, -1.1 ) );
v = (m1 * m2 * m3).Apply( v );
return v;
// 464
// NOTE: Also, don't apply rotations during simplex generation.
m1.UpperHalfPlane();
m2 = Mobius.Scale( 1.3 );
m3.Isometry( Geometry.Euclidean, 0, new Vector3D( 1.55, -1.1 ) );
v = ( m1 * m2 * m3 ).Apply( v );
return v;
// iii
m1.Isometry( Geometry.Hyperbolic, 0, new Complex( 0, Math.Sqrt( 2 ) - 1 ) );
m2.Isometry( Geometry.Euclidean, -Math.PI / 4, 0 );
m3 = Mobius.Scale( 5 );
//v = ( m1 * m2 * m3 ).Apply( v );
// Vertical Line
/*v = unitSphere.ReflectPoint( v );
m1.MapPoints( new Vector3D(-1,0), new Vector3D(), new Vector3D( 1, 0 ) );
m2 = Mobius.Scale( .5 );
v = (m1*m2).Apply( v ); */
/*
m1 = Mobius.Scale( 0.175 );
v = unitSphere.ReflectPoint( v );
v = m1.Apply( v );
* */
// Inversion
//v = unitSphere.ReflectPoint( v );
//return v;
/*Mobius m1 = new Mobius(), m2 = new Mobius(), m3 = new Mobius();
m1.Isometry( Geometry.Spherical, 0, new Complex( 0, 1 ) );
m2.Isometry( Geometry.Euclidean, 0, new Complex( 0, -1 ) );
m3 = Mobius.Scale( 0.5 );
v = (m1 * m3 * m2).Apply( v );*/
//Mobius m = new Mobius();
//m.Isometry( Geometry.Hyperbolic, 0, new Complex( -0.88, 0 ) );
//m.Isometry( Geometry.Hyperbolic, 0, new Complex( 0, Math.Sqrt(2) - 1 ) );
//m = Mobius.Scale( 0.17 );
//m.Isometry( Geometry.Spherical, 0, new Complex( 0, 3.0 ) );
//v = m.Apply( v );
// 63i, 73i
m1 = Mobius.Scale( 6.0 ); // Scale {3,i} to unit disk.
m1 = Mobius.Scale( 1.0 / 0.14062592996431983 ); // 73i (constant is abs of midpoint of {3,7} tiling, if we want to calc later for other tilings).
m2.MapPoints( Infinity.InfinityVector, new Vector3D( 1, 0 ), new Vector3D() ); // swap interior/exterior
m3.UpperHalfPlane();
v *= 2.9;
// iii
/*m1.MapPoints( new Vector3D(), new Vector3D(1,0), new Vector3D( Math.Sqrt( 2 ) - 1, 0 ) );
m2.Isometry( Geometry.Euclidean, -Math.PI / 4, 0 );
m3 = Mobius.Scale( 0.75 );*/
Mobius m = m3 * m2 * m1;
v = m.Inverse().Apply( v ); // Strange that we have to do inverse here.
return v;
}
