public List <Point> DetermineRotationCenter(PolygonSide s, double angle, double sensitivity = 0.00001)
{
List <Point> sortedPoints = new List <Point>();
Point newPoint = hTranslation(hRotation(s.B, s.A, angle), s.A);
if (ComparePoints(newPoint, s.closestA, sensitivity))
{
// rotation center
sortedPoints.Add(s.B);
// rotation point
sortedPoints.Add(s.A);
return(sortedPoints);
}
else
{
// rotation center
sortedPoints.Add(s.A);
// rotation point
sortedPoints.Add(s.B);
return(sortedPoints);
}
}
public void GetPolygon(ref List <PolygonSide> tesalation, PolygonSide s, int p, int q, int iteration)
{
if (iteration == 0)
{
return;
}
Point o = new Point(0, 0);
double angle = ConvertToDegrees((2 * Math.PI) / q);
List <Point> polygonVertex = new List <Point>();
List <PolygonSide> polygonSides = new List <PolygonSide>();
// By default sensitivity
List <Point> sortedPoints = DetermineRotationCenter(s, angle);
Point rotatedPoint = new Point();
int counter = 0;
Point rotationCenter = sortedPoints[0];
Point rotationPoint = sortedPoints[1];
polygonVertex.Add(rotationPoint);
polygonVertex.Add(rotationCenter);
// We need all points but p - 1 sides because we need to generate for PolygonSide
// Two polyigon vertex are knows so we need p - 2 more
while (counter < p - 2)
{
rotatedPoint = hTranslation(hRotation(rotationPoint, rotationCenter, angle), rotationCenter);
// Check if point of polyigon belongs to poencare disk
// New Polygon otherwise would be parcial in poencare disk
if (FindDistance(rotatedPoint, o) > 1)
{
return;
}
polygonVertex.Add(rotatedPoint);
rotationPoint = rotationCenter;
rotationCenter = rotatedPoint;
counter = counter + 1;
}
counter = 1;
// Skip first side because we dont need it for a process
while (counter < p)
{
PolygonSide polygonSide = new PolygonSide();
// p - 1 - beacuse counter starts from 0
// Check if it is last side od polygon (point)
if (counter == p - 1)
{
polygonSide.closestA = polygonVertex[counter - 1];
polygonSide.A = polygonVertex[counter];
polygonSide.B = polygonVertex[0];
polygonSide.closestB = polygonVertex[1];
polygonSides.Add(polygonSide);
counter = counter + 1;
continue;
}
// p - 2 - beacuse counter starts from 0
// Check if it is second lastest side od polygon (point)
if (counter == p - 2)
{
polygonSide.closestA = polygonVertex[counter - 1];
polygonSide.A = polygonVertex[counter];
polygonSide.B = polygonVertex[counter + 1];
polygonSide.closestB = polygonVertex[0];
polygonSides.Add(polygonSide);
counter = counter + 1;
continue;
}
polygonSide.closestA = polygonVertex[counter - 1];
polygonSide.A = polygonVertex[counter];
polygonSide.B = polygonVertex[counter + 1];
polygonSide.closestB = polygonVertex[counter + 2];
polygonSides.Add(polygonSide);
counter = counter + 1;
}
tesalation.AddRange(polygonSides);
foreach (PolygonSide side in polygonSides)
{
GetPolygon(ref tesalation, side, p, q, iteration - 1);
}
}
// p - number of sides of polygon
// q - number of polyigons that meet at single vertex
// Points added in context of OpenGL (added aditional z = 0 cordinate, added color)
public void tGetInitialRegularPolygon(ref List <PolygonSide> tesalation, int p, int q, int iteration)
{
double s = Math.Sqrt((1 - Math.Tan(Math.PI / p) * Math.Tan(Math.PI / q)) / (1 + Math.Tan(Math.PI / p) * Math.Tan(Math.PI / q)));
//s = 0.5;
List <Point> points = new List <Point>();
List <PolygonSide> polygonSides = new List <PolygonSide>();
Point orgin = new Point(0, 0);
Point newPoint = new Point();
int counter = 0;
while (counter < p)
{
newPoint = hRotation(new Point(s, 0), orgin, (counter + 1) * (360 / p));
points.Add(newPoint);
counter = counter + 1;
}
counter = 0;
// points.Count == p
while (counter < p)
{
PolygonSide polygonSide = new PolygonSide();
if (counter == 0)
{
polygonSide.closestA = points[points.Count - 1];
polygonSide.A = points[counter];
polygonSide.B = points[counter + 1];
polygonSide.closestB = points[counter + 2];
polygonSides.Add(polygonSide);
counter = counter + 1;
continue;
}
// p - 1 - beacuse counter starts from 0
// Check if it is last side od polygon (point)
if (counter == p - 1)
{
polygonSide.closestA = points[counter - 1];
polygonSide.A = points[counter];
polygonSide.B = points[0];
polygonSide.closestB = points[1];
polygonSides.Add(polygonSide);
counter = counter + 1;
continue;
}
// p - 2 - beacuse counter starts from 0
// Check if it is second lastest side od polygon (point)
if (counter == p - 2)
{
polygonSide.closestA = points[counter - 1];
polygonSide.A = points[counter];
polygonSide.B = points[counter + 1];
polygonSide.closestB = points[0];
polygonSides.Add(polygonSide);
counter = counter + 1;
continue;
}
polygonSide.closestA = points[counter - 1];
polygonSide.A = points[counter];
polygonSide.B = points[counter + 1];
polygonSide.closestB = points[counter + 2];
polygonSides.Add(polygonSide);
counter = counter + 1;
}
tesalation.AddRange(polygonSides);
foreach (PolygonSide side in polygonSides)
{
GetPolygon(ref tesalation, side, p, q, iteration);
}
}
