public bool Intersects(LineSegment segment)
{
Vector2 intersectionPoint;
Vector2 intersectionEndPoint;
int result = Intersect(this, segment, out intersectionPoint, out intersectionEndPoint);
return result != 0;
}
// inSegment(): determine if a point is inside a segment
// Input: a point P, and a collinear segment S
// Return: 1 = P is inside S
// 0 = P is not inside S
// Ref: http://geomalgorithms.com/a05-_intersect-1.html
private static int InSegment(Vector2 P, LineSegment S)
{
if (S.PointA.X != S.PointB.X)
{
// S is not vertical
if (S.PointA.X <= P.X && P.X <= S.PointB.X)
return 1;
if (S.PointA.X >= P.X && P.X >= S.PointB.X)
return 1;
}
else
{
// S is vertical, so test y coordinate
if (S.PointA.Y <= P.Y && P.Y <= S.PointB.Y)
return 1;
if (S.PointA.Y >= P.Y && P.Y >= S.PointB.Y)
return 1;
}
return 0;
}
public static bool IsSimple(this Polygon polygon)
{
int polyCount = polygon.Count;
for (int i = 0; i < polyCount; ++i)
{
Vector2 a1 = polygon[i];
Vector2 a2 = polygon[(i + 1) % polyCount];
var seg1 = new LineSegment(a1, a2);
for (int j = 0; j < polyCount - 3; ++j)
{
Vector2 b1 = polygon[(i + 2 + j) % polyCount];
Vector2 b2 = polygon[(i + 3 + j) % polyCount];
var seg2 = new LineSegment(b1, b2);
if (seg1.Intersects(seg2))
return false;
}
}
return true;
}
// intersect2D_2Segments(): find the 2D intersection of 2 finite segments
// Input: two finite segments S1 and S2
// Output: *I0 = intersect point (when it exists)
// *I1 = endpoint of intersect segment [I0,I1] (when it exists)
// Return: 0=disjoint (no intersect)
// 1=intersect in unique point I0
// 2=overlap in segment from I0 to I1
// Ref: http://geomalgorithms.com/a05-_intersect-1.html
private static int Intersect(LineSegment S1, LineSegment S2, out Vector2 I0, out Vector2 I1)
{
I0 = Vector2.Zero;
I1 = Vector2.Zero;
Vector2 u = S1.PointB - S1.PointA;
Vector2 v = S2.PointB - S2.PointA;
Vector2 w = S1.PointA - S2.PointA;
float D = Calc.Cross(ref u, ref v);
// test if they are parallel (includes either being a point)
if (Math.Abs(D) < Epsilon)
{
// S1 and S2 are parallel
if (Calc.Cross(ref u, ref w) != 0 || Calc.Cross(ref v, ref w) != 0)
{
return 0; // they are NOT collinear
}
// they are collinear or degenerate
// check if they are degenerate points
float du = Vector2.Dot(u, u);
float dv = Vector2.Dot(v, v);
if (du == 0 && dv == 0)
{
// both segments are points
if (S1.PointA != S2.PointA) // they are distinct points
return 0;
I0 = S1.PointA; // they are the same point
return 1;
}
if (du == 0)
{
// S1 is a single point
if (InSegment(S1.PointA, S2) == 0) // but is not in S2
return 0;
I0 = S1.PointA;
return 1;
}
if (dv == 0)
{
// S2 a single point
if (InSegment(S2.PointA, S1) == 0) // but is not in S1
return 0;
I0 = S2.PointA;
return 1;
}
// they are collinear segments - get overlap (or not)
float t0, t1; // endpoints of S1 in eqn for S2
Vector2 w2 = S1.PointB - S2.PointA;
if (v.X != 0)
{
t0 = w.X/v.X;
t1 = w2.X/v.X;
}
else
{
t0 = w.Y/v.Y;
t1 = w2.Y/v.Y;
}
if (t0 > t1)
{
// must have t0 smaller than t1
float t = t0;
t0 = t1;
t1 = t; // swap if not
}
if (t0 > 1 || t1 < 0)
{
return 0; // NO overlap
}
t0 = t0 < 0 ? 0 : t0; // clip to min 0
t1 = t1 > 1 ? 1 : t1; // clip to max 1
if (t0 == t1)
{
// intersect is a point
I0 = S2.PointA + t0*v;
return 1;
}
// they overlap in a valid subsegment
I0 = S2.PointA + t0*v;
I1 = S2.PointA + t1*v;
return 2;
}
// the segments are skew and may intersect in a point
// get the intersect parameter for S1
float sI = Calc.Cross(ref v, ref w)/D;
if (sI < 0 || sI > 1) // no intersect with S1
return 0;
// get the intersect parameter for S2
float tI = Calc.Cross(ref u, ref w)/D;
if (tI < 0 || tI > 1) // no intersect with S2
return 0;
I0 = S1.PointA + sI*u; // compute S1 intersect point
return 1;
}
