public Intersect Intersects(LineSegment2D other)
{
return(Math2D.AreIntersecting(this, other));
}
// Thanks to Mecki at https://stackoverflow.com/questions/217578/how-can-i-determine-whether-a-2d-point-is-within-a-polygon
public static Intersect AreIntersecting(LineSegment2D line1, LineSegment2D line2)
{
// Convert vector 1 to a line (line 1) of infinite length.
// We want the line in linear equation standard form: A*x + B*y + C = 0
// See: http://en.wikipedia.org/wiki/Linear_equation
float v1X1 = line1.P1.X,
v1Y1 = line1.P1.Y,
v1X2 = line1.P2.X,
v1Y2 = line1.P2.Y,
v2X1 = line2.P1.X,
v2Y1 = line2.P1.Y,
v2X2 = line2.P2.X,
v2Y2 = line2.P2.Y;
var a1 = v1Y2 - v1Y1;
var b1 = v1X1 - v1X2;
var c1 = (v1X2 * v1Y1) - (v1X1 * v1Y2);
// Every point (x,y), that solves the equation above, is on the line,
// every point that does not solve it, is not. The equation will have a
// positive result if it is on one side of the line and a negative one
// if is on the other side of it. We insert (x1,y1) and (x2,y2) of vector
// 2 into the equation above.
var d1 = (a1 * v2X1) + (b1 * v2Y1) + c1;
var d2 = (a1 * v2X2) + (b1 * v2Y2) + c1;
// If d1 and d2 both have the same sign, they are both on the same side
// of our line 1 and in that case no intersection is possible. Careful,
// 0 is a special case, that's why we don't test ">=" and "<=",
// but "<" and ">".
if (d1 > 0 && d2 > 0)
{
return(Intersect.No);
}
if (d1 < 0 && d2 < 0)
{
return(Intersect.No);
}
// The fact that vector 2 intersected the infinite line 1 above doesn't
// mean it also intersects the vector 1. Vector 1 is only a subset of that
// infinite line 1, so it may have intersected that line before the vector
// started or after it ended. To know for sure, we have to repeat the
// the same test the other way round. We start by calculating the
// infinite line 2 in linear equation standard form.
var a2 = v2Y2 - v2Y1;
var b2 = v2X1 - v2X2;
var c2 = (v2X2 * v2Y1) - (v2X1 * v2Y2);
// Calculate d1 and d2 again, this time using points of vector 1.
d1 = (a2 * v1X1) + (b2 * v1Y1) + c2;
d2 = (a2 * v1X2) + (b2 * v1Y2) + c2;
// Again, if both have the same sign (and neither one is 0),
// no intersection is possible.
if (d1 > 0 && d2 > 0)
{
return(Intersect.No);
}
if (d1 < 0 && d2 < 0)
{
return(Intersect.No);
}
// If we get here, only two possibilities are left. Either the two
// vectors intersect in exactly one point or they are collinear, which
// means they intersect in any number of points from zero to infinite.
if (Math.Abs((a1 * b2) - (a2 * b1)) < 0.01)
{
return(Intersect.Collinear);
}
// If they are not collinear, they must intersect in exactly one point.
return(Intersect.Yes);
}
