/// <summary>
/// Helper to do a geodesic pan.
/// </summary>
private void GeodesicPan(Vector3D p1, Vector3D p2)
{
Mobius pan = new Mobius();
Isometry inverse = m_isometry.Inverse();
p1 = inverse.Apply(p1);
p2 = inverse.Apply(p2);
pan.Geodesic(m_geometry, p1, p2);
m_isometry.Mobius *= pan;
}
/// <summary>
/// Transforms us into a new macro based on a different click location.
/// </summary>
public Macro Transform(Cell clickedCell, Vector3D clickedPoint, Puzzle puzzle, bool mouseMotionReflected)
{
Macro m = this.CloneAllButTwists();
m.SetupMobius(clickedCell, clickedPoint, puzzle, mouseMotionReflected);
// Did we have an odd number of view reflections?
bool viewReflected = this.ViewReflected ^ m.ViewReflected;
Isometry iso1 = new Isometry(m.Mobius, null);
Isometry iso2 = new Isometry(this.Mobius, null);
if (viewReflected)
{
iso1 = Isometry.ReflectX() * iso1;
}
Isometry combined = iso1.Inverse() * iso2;
foreach (SingleTwist t in this.m_twists)
{
// Find the transformed twist data.
// NOTE: We choose the one which will be closest to the origin after transformation,
// which hopefully won't lead to performance problems.
// I initially just used the first TwistDataForStateCalcs list item,
// but that led to issues because sometimes it would get transformed
// to very near the disk boundary. We'd have run out of cells to
// find the correct closest, and the transformed macros got all messed up.
TwistData tdOriginal = t.IdentifiedTwistData.TwistDataForStateCalcs
.OrderBy(td => combined.Apply(td.Center).MagSquared())
.First();
Vector3D newCenter = combined.Apply(tdOriginal.Center);
TwistData tdNew = puzzle.ClosestTwistingCircles(newCenter);
SingleTwist tClone = t.Clone();
tClone.IdentifiedTwistData = tdNew.IdentifiedTwistData;
// If the reverse state of our transformed twist
// has changed, we may need to reverse the new twist.
bool reverse = tdOriginal.Reverse ^ tdNew.Reverse;
if (reverse ^ viewReflected) // NOTE: Very similar to code in Renderer.
{
tClone.ReverseTwist();
}
m.m_twists.Add(tClone);
}
return(m);
}
private static Isometry SetupIsometry(Cell clickedCell, Vector3D clickedPoint, Puzzle puzzle)
{
int p = puzzle.Config.P;
Geometry g = puzzle.Config.Geometry;
Isometry cellIsometry = clickedCell.Isometry.Clone();
// Take out reflections.
// ZZZ - Figuring out how to deal with these reflected isometries was a bit painful to figure out.
// I wish I had just taken more care to not have any cell isometries with reflections.
// Maybe I can rework that to be different at some point.
if (cellIsometry.Reflection != null)
{
cellIsometry = Isometry.ReflectX() * cellIsometry;
}
// Round to nearest vertex.
Vector3D centered = cellIsometry.Apply(clickedPoint);
double angle = Euclidean2D.AngleToCounterClock(centered, new Vector3D(1, 0));
double angleFromZeroToP = p * angle / (2 * Math.PI);
angleFromZeroToP = Math.Round(angleFromZeroToP, 0);
if (p == (int)angleFromZeroToP)
{
angleFromZeroToP = 0;
}
angle = 2 * Math.PI * angleFromZeroToP / p;
// This will take vertex to canonical position.
Mobius rotation = new Mobius();
rotation.Isometry(g, angle, new Complex());
Isometry rotIsometry = new Isometry(rotation, null);
return(rotIsometry * cellIsometry);
}
/// <summary>
/// Apply an isometry to us.
/// </summary>
public void Transform(Isometry isometry)
{
foreach (Segment s in this.Segments)
{
s.Transform(isometry);
}
Center = isometry.Apply(Center);
}
public static void DrawPolygonSolid(Polygon p, Isometry isometry, Color color)
{
GL.Color3(color);
GL.PolygonMode(MaterialFace.FrontAndBack, PolygonMode.Fill);
GL.Begin(BeginMode.TriangleFan);
{
Vector3D center = isometry.Apply(p.Center);
GL.Vertex2(center.X, center.Y);
Vector3D[] edgePoints = p.EdgePoints;
for (int i = 0; i < edgePoints.Length; i++)
{
Vector3D draw = isometry.Apply(edgePoints[i]);
GL.Vertex2(draw.X, draw.Y);
}
}
GL.End();
}
public static void DrawElements(HyperbolicModel model, Vector3D[] textureCoords, Vector3D[] textureVerts, int[] elements,
Isometry mouseIsometry, double textureScale)
{
////////////////////// ZZZ - Use VBOs
GL.Begin(BeginMode.Triangles);
{
double factor = textureScale;
int skipped = 0;
for (int i = 0; i < elements.Length; i++)
{
int idx = elements[i];
// In Poincare model.
GL.TexCoord2((textureCoords[idx].X * factor + 1) / 2, (textureCoords[idx].Y * factor + 1) / 2);
Complex transformed = textureVerts[idx].ToComplex();
if (mouseIsometry != null)
{
transformed = mouseIsometry.Apply(transformed);
}
switch (model)
{
case HyperbolicModel.Poincare:
{
Vertex(transformed);
break;
}
case HyperbolicModel.Klein:
{
Vector3D temp = Vector3D.FromComplex(transformed);
Vertex(PoincareToKlein(temp));
break;
}
case HyperbolicModel.Pseudosphere:
{
Mobius m = new Mobius();
m.UpperHalfPlane();
Complex u = m.Apply(transformed);
double x = u.Real;
double y = u.Imaginary;
double max = 1 * System.Math.PI;
double min = -1 * System.Math.PI;
if (0 == i % 3 && (x < min - 1 || x > max + 1 || y < 0))
{
skipped = 1;
continue;
}
if (skipped > 0 && skipped < 3)
{
skipped++;
continue;
}
skipped = 0;
GL.TexCoord2((textureCoords[idx].X * factor + 1) / 2, (textureCoords[idx].Y * factor + 1) / 2);
// Pseudosphere
Func <double, Complex> tractrix = new Func <double, Complex>(
(t) =>
{
return(new Complex(t - Math.Tanh(t), 1.0 / Math.Cosh(t)));
});
//Vector3D temp1 = Vector3D.FromComplex( u );
if (x < min)
{
x = min;
}
if (x > max)
{
x = max;
}
if (y < 1)
{
y = 1;
}
Vector3D temp1 = new Vector3D(x, y);
double logy = Math.Log(temp1.Y);
Complex tract = tractrix(logy);
Vector3D temp2 = new Vector3D(
Math.Cos(temp1.X) * tract.Imaginary,
Math.Sin(temp1.X) * tract.Imaginary,
tract.Real);
GL.Vertex3(temp2.X, temp2.Y, temp2.Z);
//temp1 = m.Inverse().Apply( temp1 );
//GL.Vertex3( temp1.X, temp1.Y, temp1.Z );
//Vertex( temp1 );
break;
}
case HyperbolicModel.Hyperboloid:
{
Vector3D hyper = Sterographic.PlaneToHyperboloid(Vector3D.FromComplex(transformed)); // Hyperboloid
GL.Vertex3(hyper.X, hyper.Y, hyper.Z);
break;
}
default:
{
System.Diagnostics.Debug.Assert(false);
break;
}
}
/* // PETALS
* int petals = 7;
* double newMag = transformed.Magnitude * ( 1 + 0.5 * Math.Sin( transformed.Phase * petals ) );
* double newPhase = transformed.Phase + ( -0.2 * newMag * Math.Pow( Math.Sin( newMag * 3 ), 1 ) * Math.Cos( transformed.Phase * petals ) );
* transformed = Complex.FromPolarCoordinates( newMag, newPhase );
*
* Vertex( transformed );
* */
//double mag = System.Math.Pow( transformed.Magnitude, 3 ) / transformed.Magnitude; // nice
//double mag = System.Math.Pow( transformed.Magnitude - 3, 2 ) + .0; // looks spherical
//double mag = transformed.Magnitude + 0.1* System.Math.Sin( transformed.Magnitude * 15 ); // Fun warping (20 is cool too)
//Vertex( transformed * mag );
/*double xmag = 1;
* double ymag = transformed.Imaginary + 0.1 * System.Math.Sin( transformed.Imaginary * 15 );
* xmag = System.Math.Abs( xmag );
* ymag = System.Math.Abs( ymag );
* Vertex( new Complex( transformed.Real * xmag, transformed.Imaginary * ymag ) ); */
//Vertex( 2 / System.Math.PI * Complex.Log( ( 1 + transformed ) / ( 1 - transformed ) ) ); // Band model
//Vertex( Complex.Pow( transformed, 3 ) / transformed.Magnitude ); // Spikey
// Spiral
//Complex band = 2 / System.Math.PI * Complex.Log( ( 1 + transformed ) / ( 1 - transformed ) );
//band = new Complex( band.Real, band.Imaginary + 0.3 * System.Math.Sin( band.Real * 2 ) );
//band = new Complex( band.Real * .5, band.Imaginary );
//band += new Complex( 0, .5 );
//Vertex( band );
/*
* double x = band.Real;
* double y = band.Imaginary;
*
* double r = System.Math.Exp( x );
* double theta = 3*( x + y/1.75 ); */
//Vertex( new Complex( r * System.Math.Sin( theta ), r * System.Math.Cos( theta ) ) ); // Spiral
}
}
GL.End();
}
public override void Transform(Isometry i)
{
base.Transform(i);
CenterNE = i.Apply(CenterNE);
}