static internal Point IntersectDiagonalWithRay(Point pivot, Point pointOnRay, Diagonal diagonal)
{
Point ray = pointOnRay - pivot;
Point source = diagonal.Start;
Point target = diagonal.End;
//let x(t-s)+s is on the ray, then for some y we x(t-s)+s=y*ray+pivot, or x(t-s)-y*ray=pivot-s
double x, y;
bool result = LinearSystem2.Solve(target.X - source.X, -ray.X, pivot.X - source.X, target.Y - source.Y, -ray.Y, pivot.Y - source.Y, out x, out y);
System.Diagnostics.Debug.Assert(result && -ApproximateComparer.Tolerance <= x && x <= 1 + ApproximateComparer.Tolerance);
return(pivot + y * ray);
}
Point IntersectEdgeWithRay(Point source, Point target, Point ray)
{
//let x(t-s)+s is on the ray, then for some y we x(t-s)+s=y*ray+pivot, or x(t-s)-y*ray=pivot-s
double x, y;
bool result = LinearSystem2.Solve(target.X - source.X, -ray.X, Pivot.X - source.X, target.Y - source.Y, -ray.Y, Pivot.Y - source.Y, out x, out y);
if (!(-ApproximateComparer.Tolerance <= x && x <= 1 + ApproximateComparer.Tolerance))
{
throw new Exception();
}
if (!result)
{
throw new InvalidOperationException();
}
return(Pivot + y * ray);
}
static public bool LineLineIntersection(Point a, Point b, Point c, Point d, out Point x)
{
//look for the solution in the form a+u*(b-a)=c+v*(d-c)
double u, v;
Point ba = b - a;
Point cd = c - d;
Point ca = c - a;
bool ret = LinearSystem2.Solve(ba.X, cd.X, ca.X, ba.Y, cd.Y, ca.Y, out u, out v);
if (ret)
{
x = a + u * ba;
return(true);
}
else
{
x = new Point();
return(false);
}
}
static public bool SegmentSegmentIntersection(Point a, Point b, Point c, Point d, out Point x)
{
//look for the solution in the form a+u*(b-a)=c+v*(d-c)
double u, v;
Point ba = b - a;
Point cd = c - d;
Point ca = c - a;
bool ret = LinearSystem2.Solve(ba.X, cd.X, ca.X, ba.Y, cd.Y, ca.Y, out u, out v);
double eps = ApproximateComparer.Tolerance;
if (ret && u > -eps && u < 1.0 + eps && v > -eps && v < 1.0 + eps)
{
x = a + u * ba;
return(true);
}
else
{
x = new Point();
return(false);
}
}