// this is the general case. Really really general
public static Vector2[] GetLineSegLineSegIntersectionInterval(Vector2 a1, Vector2 a2, Vector2 b1, Vector2 b2)
{
// PointEqualsEpsilon is needed, or this for example falsely returns true:
// MathUtil.CheckLineSegLineSegIntersection(new Vector2(-7.642176f, -3.406708f), new Vector2(-7.642176f, -3.406707f), new Vector2(0f, -3f), new Vector2(1f, -4f)));
if (a1.PointEqualEpsilon(a2) && b1.PointEqualEpsilon(b2))
{
// both "segments" are points, return either point
if (a1.PointEqualEpsilon(b1))
return new Vector2[] { a1 };
else // both "segments" are different points, return empty set
return new Vector2[] { };
}
else if (b1.PointEqualEpsilon(b2)) // b is a point, a is a segment
{
if (PointOnLine(b1, a1, a2))
return new Vector2[] { b1 };
else
return new Vector2[] { };
}
else if (a1.PointEqualEpsilon(a2)) // a is a point, b is a segment
{
if (PointOnLine(a1, b1, b2))
return new Vector2[] { a1 };
else
return new Vector2[] { };
}
// at this point we know both a and b are actual segments
float ua_t = (b2.x - b1.x) * (a1.y - b1.y) - (b2.y - b1.y) * (a1.x - b1.x);
float ub_t = (a2.x - a1.x) * (a1.y - b1.y) - (a2.y - a1.y) * (a1.x - b1.x);
float u_b = (b2.y - b1.y) * (a2.x - a1.x) - (b2.x - b1.x) * (a2.y - a1.y);
// Infinite lines intersect somewhere
if (!(-MyEpsilon < u_b && u_b < MyEpsilon)) // e.g. u_b != 0.0
{
float ua = ua_t / u_b;
float ub = ub_t / u_b;
if (0.0f <= ua && ua <= 1.0f && 0.0f <= ub && ub <= 1.0f)
{
// Intersection
return new Vector2[] {
new Vector2(a1.x + ua * (a2.x - a1.x),
a1.y + ua * (a2.y - a1.y)) };
}
else
{
// No Intersection
return new Vector2[] { };
}
}
else // lines (not just segments) are parallel or the same line
{
// Coincident
// find the common overlapping section of the lines
// first find the distance (squared) from one point (a1) to each point
if ((-MyEpsilon < ua_t && ua_t < MyEpsilon)
|| (-MyEpsilon < ub_t && ub_t < MyEpsilon))
{
if (a1.Equals(a2)) // danger!
return OneDIntersection(b1, b2, a1, a2);
else // safe
return OneDIntersection(a1, a2, b1, b2);
}
else
{
// Parallel
return new Vector2[] { };
}
}
}