//good to go
private void Square2Circle()
{
//center the square on the origin
int full = m_net.Size - 1;
int half = m_net.Size/2;
//constrain verticle and horizontal lines
Point2D N = new Point2D(0, 1);
Point2D S = new Point2D(0, -1);
Point2D E = new Point2D(1, 0);
Point2D W = new Point2D(-1, 0);
m_net.AlignEdge(m_net[half, full], m_net[half, 0], new AlignToSeg(N, S));
m_net.AlignEdge(m_net[full, half], m_net[0, half], new AlignToSeg(E, W));
//constrain diagonals
Point2D NE = new Point2D(Math.Sqrt(0.5), Math.Sqrt(0.5));
Point2D NW = new Point2D(Math.Sqrt(0.5), -Math.Sqrt(0.5));
Point2D SE = new Point2D(-Math.Sqrt(0.5), Math.Sqrt(0.5));
Point2D SW = new Point2D(-Math.Sqrt(0.5), -Math.Sqrt(0.5));
m_net.AlignEdge(m_net[full, full], m_net[0, 0], new AlignToSeg(NE, SW));
m_net.AlignEdge(m_net[full, 0], m_net[0, full], new AlignToSeg(NW, SE));
//constrain specific points
m_net[0, 0].Alignment = new AlignFixed(SW);
m_net[full, full].Alignment = new AlignFixed(NE);
m_net[full, 0].Alignment = new AlignFixed(NW);
m_net[0, full].Alignment = new AlignFixed(SE);
m_net[0, half].Alignment = new AlignFixed(W);
m_net[half, 0].Alignment = new AlignFixed(S);
m_net[full, half].Alignment = new AlignFixed(E);
m_net[half, full].Alignment = new AlignFixed(N);
m_net[half, half].Alignment = new AlignFixed(Point2D.Origin);
//constrain to circle
AlignToArc circle = new AlignToArc(Point2D.Origin, 1.0);
m_net.AlignEdge(m_net[0, 0], m_net[full, 0], circle);
m_net.AlignEdge(m_net[full, 0], m_net[full, full], circle);
m_net.AlignEdge(m_net[full, full], m_net[0, full], circle);
m_net.AlignEdge(m_net[0, full], m_net[0, 0], circle);
//setup initial position if first time
if (m_bFirstPass)
{
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] != null)
{
m_net[i, j].Position *= 2.0 / (double)full;
m_net[i, j].Position -= new Point2D(1.0, 1.0);
}
}
}
}
}
//will do in a pinch
private void Square2Heart()
{
Point2D
A = new Point2D(-2.0, 0),
B = new Point2D(-1.0, 0),
C = new Point2D(0, 0),
D = new Point2D(1.0, 0),
E = new Point2D(2.0, 0),
F = new Point2D(-Math.Sqrt(2.0), -Math.Sqrt(2.0)),
G = new Point2D(Math.Sqrt(2.0), -Math.Sqrt(2.0)),
H = new Point2D(0, -2.0 * Math.Sqrt(2));
Aligner HtoF = new AlignToSeg(H, F);
Aligner HtoG = new AlignToSeg(H, G);
Aligner FtoA = new AlignToArc(C, 2.0, A, F);
Aligner EtoG = new AlignToArc(C, 2.0, G, E);
Aligner AtoC = new AlignToArc(B, 1.0, C, A);
Aligner CtoE = new AlignToArc(D, 1.0, E, C);
AlignCombo Left = new AlignCombo();
Left.AddAligner(HtoF);
Left.AddAligner(FtoA);
Left.AddAligner(AtoC);
AlignCombo Right = new AlignCombo();
Right.AddAligner(HtoG);
Right.AddAligner(EtoG);
Right.AddAligner(CtoE);
m_net.AlignEdge(m_net[0, 0], m_net[m_net.Size - 1, m_net.Size - 1], new AlignToSeg(H, C));
m_net.AlignEdge(m_net[0, 0], m_net[0, m_net.Size - 1], Left);
m_net.AlignEdge(m_net[0, 0], m_net[m_net.Size - 1, 0], Right);
int quarter = m_net.Size / 4;
m_net.AlignEdge(m_net[0, m_net.Size - 1], m_net[quarter, m_net.Size - 1], Left);
m_net.AlignEdge(m_net[m_net.Size - 1, 0], m_net[m_net.Size - 1, quarter], Right);
for (int i = quarter; i < m_net.Size; i++)
{
double fraction = (double)(i - quarter) / (double)(m_net.Size - 1 - quarter);
fraction *= Math.PI;
#if false //fix top arc
m_net[i, m_net.Size - 1].Alignment = new AlignFixed(new Point2D(-1.0 - Math.Cos(fraction), Math.Sin(fraction)));
m_net[m_net.Size - 1, i].Alignment = new AlignFixed(new Point2D(1.0 + Math.Cos(fraction), Math.Sin(fraction)));
#else //initialize position
if (m_bFirstPass)
{
m_net[i, m_net.Size - 1].Position = new Point2D(-1.0 - Math.Cos(fraction), Math.Sin(fraction));
m_net[m_net.Size - 1, i].Position = new Point2D(1.0 + Math.Cos(fraction), Math.Sin(fraction));
}
#endif
}
//fix points
m_net[0, 0].Alignment = new AlignFixed(H);
m_net[m_net.Size - 1, m_net.Size - 1].Alignment = new AlignFixed(C);
}
//good to go
private void Hexagon2Circle()
{
int full = (m_net.Size - 1);
int third = m_net.Size / 3;
int twothirds = m_net.Size * 2 / 3;
if (m_bFirstPass)
{
m_net = new TriangularNet(m_net.Size);
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] != null)
{
m_net[i, j].Position *= 3.0 / m_net.Size;
m_net[i, j].Position += new Point2D(-2.0, -1.0);
}
}
}
}
//zero out what we don't need
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] != null)
{
if (i < j || // remove top half of triangle
i < third || // clip one corner
j > twothirds || // clip second corner
i > j + twothirds ) // clip third corner
{
m_net[i, j] = null;
}
}
}
}
m_net.SetNeighbors();
//align arcs
AlignToArc AlignToCircle = new AlignToArc(Point2D.Origin, 1.0);
m_net.AlignEdge(m_net[twothirds, twothirds], m_net[full, twothirds], AlignToCircle);
m_net.AlignEdge(m_net[full, twothirds], m_net[full, third], AlignToCircle);
m_net.AlignEdge(m_net[full, third], m_net[twothirds, 0], AlignToCircle);
m_net.AlignEdge(m_net[twothirds, 0], m_net[third, 0], AlignToCircle);
m_net.AlignEdge(m_net[third, 0], m_net[third, third], AlignToCircle);
m_net.AlignEdge(m_net[third, third], m_net[twothirds, twothirds], AlignToCircle);
//Align Points
m_net[full, third].Alignment = new AlignFixed( Point2D.FromPolar(1.0, 0.0 * Math.PI) );
m_net[full, twothirds].Alignment = new AlignFixed( Point2D.FromPolar(1.0, (1.0/3.0) * Math.PI) );
m_net[twothirds, twothirds].Alignment = new AlignFixed( Point2D.FromPolar(1.0, (2.0/3.0) * Math.PI) );
m_net[third, third].Alignment = new AlignFixed( Point2D.FromPolar(1.0, Math.PI) );
m_net[third, 0].Alignment = new AlignFixed( Point2D.FromPolar(1.0, (4.0/3.0) * Math.PI) );
m_net[twothirds, 0].Alignment = new AlignFixed( Point2D.FromPolar(1.0, (5.0/3.0) * Math.PI) );
}
//good to go
private void Diamond2Lens()
{
double Sqrt3 = Math.Sqrt(3.0);
int full = (m_net.Size-1);
int half = m_net.Size / 2;
int left = (int)((double)m_net.Size * (Sqrt3 - 1.0) / (2.0 * Sqrt3)) + 1;
int right = (int)((double)m_net.Size * (Sqrt3 + 1.0) / (2.0 * Sqrt3)) - 1;
//zero out what we don't need
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] != null)
{
if ((double)i + (double)j / Sqrt3 < (double)full * 0.5 - DMS.EPSILON ||
(double)i + (double)j / Sqrt3 > (double)full * (0.5 + 1.0/Sqrt3) + DMS.EPSILON ||
(double)i - (double)j /Sqrt3 > (double)full * 0.5 + DMS.EPSILON ||
(double)i - (double)j / Sqrt3 < (double)full * (0.5 - 1.0/Sqrt3) - DMS.EPSILON)
{
m_net[i, j] = null;
}
}
}
}
Point2D A = -Point2D.XAxis;
Point2D B = new Point2D(0, 1.0 / Sqrt3);
Point2D C = Point2D.XAxis;
Point2D D = new Point2D(0, -1.0 / Sqrt3);
Point2D E = Point2D.Origin;
AlignToArc AlignTop = new AlignToArc(D, 2.0 / Sqrt3, C, A);
AlignToArc AlignBottom = new AlignToArc(B, 2.0 / Sqrt3, A, C);
m_net.SetNeighbors();
//align arcs
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] != null)
{
if (m_net[i, j].North == null)
m_net[i, j].Alignment = AlignTop;
else if (m_net[i, j].South == null)
m_net[i, j].Alignment = AlignBottom;
else
m_net[i, j].Alignment = new Aligner(); //generic non-aligner
}
}
}
//align horizontal, align vertical axes
m_net.AlignEdge(m_net[half, 0], m_net[half, full], new AlignToSeg(B, D));
m_net.AlignEdge(m_net[left, half], m_net[right, half], new AlignToSeg(A, C));
//align points
m_net[half, 0].Alignment = new AlignFixed(D);
m_net[half, full].Alignment = new AlignFixed(B);
m_net[left, half].Alignment = new AlignFixed(A);
m_net[right, half].Alignment = new AlignFixed(C);
}
//good to go
private void Bitmap2Circle()
{
Aligner circle = new AlignToArc(Point2D.Origin, 1.0);
double full = m_net.Size - 1;
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
Point2D pt = new Point2D(i, j) / full;
if (m_mask.GetPixel(pt).ToArgb() == Color.Black.ToArgb())
m_net[i, j] = null;
}
}
m_net.SetNeighbors();
//calculate center, and determine which points are edges.
Point2D center = new Point2D();
bool[,] isedge = new bool[m_net.Size, m_net.Size];
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
isedge[i, j] = false;
if (m_net[i, j] == null)
continue;
if (m_net[i, j].East == null ||
m_net[i, j].West == null ||
m_net[i, j].South == null ||
m_net[i, j].North == null)
{
isedge[i, j] = true;
}
center += m_net[i, j].Position;
}
}
center /= m_net.Count;
//fix edge points to circle
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] == null)
continue;
if (isedge[i, j])
m_net[i, j].Alignment = circle;
if (m_bFirstPass)
{
m_net[i, j].Position -= center;
m_net[i, j].Position = m_net[i,j].Position / full;
}
}
}
}
private void XtoCircle()
{
int full = m_net.Size - 1;
int half = m_net.Size / 2;
int threequarters = m_net.Size / 4 * 3;
int quarter = m_net.Size / 4;
int third = m_net.Size / 3;
int twothirds = m_net.Size / 3 * 2;
int sixth = m_net.Size / 6;
Indicatrix
A = m_net[0, twothirds],
B = m_net[third, twothirds],
C = m_net[half, half],
D = m_net[twothirds, twothirds],
E = m_net[full, twothirds],
F = m_net[twothirds, third],
G = m_net[full, 0],
H = m_net[twothirds, 0],
I = m_net[half, sixth],
J = m_net[third, 0],
K = m_net[0, 0],
L = m_net[third, third];
AlignToArc TL = new AlignToArc(Point2D.Origin, 1.0, Point2D.YAxis, -Point2D.XAxis);
AlignToArc BL = new AlignToArc(Point2D.Origin, 1.0, -Point2D.XAxis, -Point2D.YAxis);
AlignToArc BR = new AlignToArc(Point2D.Origin, 1.0, -Point2D.YAxis, Point2D.XAxis);
AlignToArc TR = new AlignToArc(Point2D.Origin, 1.0, Point2D.XAxis, Point2D.YAxis);
m_net.AlignEdge(L, A, TL);
m_net.AlignEdge(A, B, TL);
m_net.AlignEdge(B, C, TL);
m_net.AlignEdge(C, D, TR);
m_net.AlignEdge(D, E, TR);
m_net.AlignEdge(E, F, TR);
m_net.AlignEdge(F, G, BR);
m_net.AlignEdge(G, H, BR);
m_net.AlignEdge(H, I, BR);
m_net.AlignEdge(I, J, BL);
m_net.AlignEdge(J, K, BL);
m_net.AlignEdge(K, L, BL);
m_net.AlignEdge(m_net[0, third], m_net[full, third], new AlignToSeg(-Point2D.XAxis, Point2D.XAxis));
m_net.AlignEdge(m_net[half, 0], m_net[half, full], new AlignToSeg(-Point2D.YAxis, Point2D.YAxis));
C.Alignment = new AlignFixed(Point2D.YAxis);
F.Alignment = new AlignFixed(Point2D.XAxis);
I.Alignment = new AlignFixed(-Point2D.YAxis);
L.Alignment = new AlignFixed(-Point2D.XAxis);
//now delete ones we don't need
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (j > twothirds)
m_net[i, j] = null;
if (Math.Abs(i + j - half - third) <= sixth)
continue;
if (i - j <= third && i - j >= 0)
continue;
m_net[i, j] = null;
}
}
//now scale them for a good start
if( m_bFirstPass)
for (int i = 0; i < m_net.Size; i++)
for (int j = 0; j < m_net.Size; j++)
if (m_net[i, j] != null)
m_net[i, j].Position = m_net[i, j].Position * 2.0 / m_net.Size - new Point2D(1.0, 1.0);
}
//good to go
private void Triangle2Rouleaux()
{
if (m_bFirstPass)
{
m_net = new TriangularNet(m_net.Size);
}
double Sqrt3 = Math.Sqrt(3.0);
int full = (m_net.Size - 1);
int half = m_net.Size / 2;
//zero out what we don't need
for (int i = 0; i < m_net.Size; i++)
{
for (int j = 0; j < m_net.Size; j++)
{
if (m_net[i, j] != null)
{
if ( i < j )
{
m_net[i, j] = null;
}
}
}
}
Point2D A = new Point2D(0, 1.0 / Math.Sqrt(2.0));
Point2D B = new Point2D(-Sqrt3 / (2.0 * Math.Sqrt(2.0)), -1.0 / (2.0 * Math.Sqrt(2.0)) );
Point2D C = new Point2D(Sqrt3 / (2.0 * Math.Sqrt(2.0)), -1.0 / (2.0 * Math.Sqrt(2.0)) );
double radius = (A - B).R;
AlignToArc AlignAB = new AlignToArc(C, radius, A, B);
AlignToArc AlignBC = new AlignToArc(A, radius, B, C);
AlignToArc AlignAC = new AlignToArc(B, radius, C, A);
m_net.SetNeighbors();
//align arcs
m_net.AlignEdge(m_net[full, full], m_net[full, 0], AlignAC);
m_net.AlignEdge(m_net[0, 0], m_net[full, full], AlignAB);
m_net.AlignEdge(m_net[0, 0], m_net[full, 0], AlignBC);
//align points
m_net[0, 0].Alignment = new AlignFixed(B);
m_net[full, full].Alignment = new AlignFixed(A);
m_net[full, 0].Alignment = new AlignFixed(C);
}