public Point FindStraightLineIntersection(StraightLine p, StraightLine q)
{
Point intersectionPoint = new Point();
if (p.k == q.k || (double.IsInfinity(q.k) && double.IsInfinity(p.k)))
{
throw new Exception("Method: FindStraightLineIntersection . Message: Straight lines are paralell");
}
if (double.IsInfinity(p.k))
{
intersectionPoint.x = ConvertToZero(p.x);
intersectionPoint.y = ConvertToZero(q.k * p.x + q.n);
return(intersectionPoint);
}
if (double.IsInfinity(q.k))
{
intersectionPoint.x = ConvertToZero(q.x);
intersectionPoint.y = ConvertToZero(p.k * q.x + p.n);
return(intersectionPoint);
}
intersectionPoint.x = ConvertToZero((q.n - p.n) / (p.k - q.k));
intersectionPoint.y = ConvertToZero(q.k * intersectionPoint.x + q.n);
return(intersectionPoint);
}
// Domain - sets of point that belong to R
// distanceD - distance between points on domain
public List <float> GenerateStraightLine(StraightLine p, double[] domain, List <float> color, double distanceD = 0.001)
{
List <float> straightLine = new List <float>();
double a = domain[0];
double b = domain[1];
double y;
while (a <= b)
{
if (double.IsInfinity(p.k))
{
y = p.k * a + p.n;
straightLine.Add((float)p.x);
straightLine.Add((float)a);
straightLine.Add(0);
straightLine.AddRange(color);
a = a + distanceD;
}
else
{
y = p.k * a + p.n;
straightLine.Add((float)a);
straightLine.Add((float)y);
straightLine.Add(0);
straightLine.AddRange(color);
a = a + distanceD;
}
}
return(straightLine);
}
public List <float> GenerateHiperbolicSegment(Point pointA, Point pointB, List <float> color)
{
// Center of inversion circle
Point o = new Point();
// Radius of inversion circle
double radius;
if (IsColinear(pointA, pointB, new Point(0, 0)) == true)
{
// This is when you want to generate hiperbolic straight line through center
List <Point> intersection = FindIntersectionBetweenStraightLineAndCircle(new Circle(new Point(0, 0), 1), new StraightLine(pointA, pointB));
// If points belongs to line paralel with y axis
// (pointA.x - pointB.x) < 0.00001
if (pointB.x == pointA.x)
{
double[] domain = { Math.Min(pointA.y, pointB.y), Math.Max(pointA.y, pointB.y) };
return(GenerateStraightLine(new StraightLine(pointA, pointB), domain, color, 0.001));
}
else
{
double[] domain = { Math.Min(pointA.x, pointB.x), Math.Max(pointA.x, pointB.x) };
return(GenerateStraightLine(new StraightLine(pointA, pointB), domain, color, 0.001));
}
}
else
{
Point pointA_inversе = CircleInversion(pointA);
Point midPointM = FindMidPoint(pointA, pointB);
Point midPointN = FindMidPoint(pointA_inversе, pointA);
StraightLine s = new StraightLine(pointA, pointB);
StraightLine d = new StraightLine(midPointM, -1 / s.k);
StraightLine p = new StraightLine(pointA, pointA_inversе);
StraightLine q = new StraightLine(midPointN, -1 / p.k);
o = FindStraightLineIntersection(d, q);
radius = FindDistance(pointA, o);
List <Point> points = FindIntersectionBetweenTwoCircles(new Circle(new Point(0, 0), 1), new Circle(o, radius));
double minAngle = Math.Min(FindAngle(pointA, o, radius), FindAngle(pointB, o, radius));
double maxAngle = Math.Max(FindAngle(pointA, o, radius), FindAngle(pointB, o, radius));
// angle between 2 points must be 180 deegres or less because arch lenght must be less then half of circumstance of inversion circle
if (maxAngle * minAngle < 0 && maxAngle - minAngle >= 180)
{
var auxiliarAngle = maxAngle;
maxAngle = 360 + minAngle;
minAngle = auxiliarAngle;
return(GenerateCircle(o, radius, color, minAngle, maxAngle));
}
return(GenerateCircle(o, radius, color, minAngle, maxAngle));
}
}
// Inversion circle is Poencare circle (Fundamental circle defined as x^2 + y^2 = 1)
public Point CircleInversion(Point point)
{
StraightLine p = new StraightLine(new Point(0, 0), point);
StraightLine v = new StraightLine(point, -1 / p.k);
List <Point> intersections = FindIntersectionBetweenStraightLineAndCircle(new Circle(new Point(0, 0), 1), v);
StraightLine q = new StraightLine(intersections[0], new Point(0, 0));
StraightLine s = new StraightLine(intersections[0], -1 / q.k);
return(FindStraightLineIntersection(p, s));
}
public List <Point> FindIntersectionBetweenStraightLineAndCircle(Circle k, StraightLine p, double sensitivity = 0.01)
{
// Regarding tesalation it should not happen that D <= 0
List <Point> intersectionPoints = new List <Point>();
// Case when p is parallel with y axis
if (double.IsInfinity(p.k))
{
double x1 = ConvertToZero(p.x);
double y1 = ConvertToZero(Math.Sqrt((1 - Math.Pow(p.x, 2))));
double x2 = ConvertToZero(p.x);
double y2 = ConvertToZero(-Math.Sqrt((1 - Math.Pow(p.x, 2))));
intersectionPoints.Add(new Point(x1, y1));
intersectionPoints.Add(new Point(x2, y2));
return(intersectionPoints);
}
Point kCenter = k.center;
// ax^2 + bx + c = 0
double a = 1 + Math.Pow(p.k, 2);
double b = 2 * (p.k * (p.n - kCenter.y) - kCenter.x);
double c = Math.Pow(kCenter.x, 2) + Math.Pow(kCenter.y, 2) + Math.Pow(p.n, 2) - Math.Pow(k.radius, 2) - (2 * p.n * kCenter.y);
double D = Math.Sqrt(Math.Pow(b, 2) - 4 * a * c);
if (D == 0)
{
double x = ConvertToZero(-b / (2 * a));
double y = ConvertToZero(p.k * x + p.n);
intersectionPoints.Add(new Point(x, y));
}
else if (D > 0)
{
double x1 = ConvertToZero((-b + D) / (2 * a));
double y1 = ConvertToZero(p.k * x1 + p.n);
double x2 = ConvertToZero((-b - D) / (2 * a));
double y2 = ConvertToZero(p.k * x2 + p.n);
intersectionPoints.Add(new Point(x1, y1));
intersectionPoints.Add(new Point(x2, y2));
}
// For D < 0 there are 2 solutions that belongs to C (set of complex numbers)
return(intersectionPoints);
}