//线段与凸多边形相交
//intersect2D_SegPoly():
// Input: S = 2D segment to intersect with the convex polygon
// n = number of 2D points in the polygon
// V[] = array of n+1 vertex points with V[n]=V[0]
// Note: The polygon MUST be convex and
// have vertices oriented counterclockwise (ccw).
// This code does not check for and verify these conditions.
// Output: *IS = the intersection segment (when it exists)
// Return: FALSE = no intersection
// TRUE = a valid intersection segment exists
int intersect2D_SegPoly(RgSegment S, RgPoint[] V, int n, RgSegment IS)
{
if (S.P0 == S.P1)
{ // the segment S is a single point
// test for inclusion of S.P0 in the polygon
IS = S; // same point if inside polygon
return(RgTopologicRelationship.cn_PnPoly(S.P0, V, n)); // March 2001 Algorithm
}
float tE = 0; // the maximum entering segment parameter
float tL = 1; // the minimum leaving segment parameter
float t, N, D; // intersect parameter t = N / D
Vector3d dS = S.P1 - S.P0; // the segment direction vector
Vector3d e; // edge vector
// Vector ne; // edge outward normal (not explicit in code)
for (int i = 0; i < n; i++) // process polygon edge V[i]V[i+1]
{
RgPoint ePt = V[i + 1] - V[i];
e = new Vector3d(ePt.X, ePt.Y, 0);
RgPoint temp = S.P0 - V[i];
N = (float)RgMath.perp(e, new Vector3d(temp.X, temp.Y, 0)); // = -dot(ne, S.P0-V[i])
D = (float)-RgMath.perp(e, dS); // = dot(ne, dS)
if (Math.Abs(D) < RgMath.SMALL_NUM)
{ // S is nearly parallel to this edge
if (N < 0) // P0 is outside this edge, so
{
return(0); // S is outside the polygon
}
else // S cannot cross this edge, so
{
continue; // ignore this edge
}
}
t = N / D;
if (D < 0)
{ // segment S is entering across this edge
if (t > tE)
{ // new max tE
tE = t;
if (tE > tL) // S enters after leaving polygon
{
return(0);
}
}
}
else
{ // segment S is leaving across this edge
if (t < tL)
{ // new min tL
tL = t;
if (tL < tE) // S leaves before entering polygon
{
return(0);
}
}
}
}
// tE <= tL implies that there is a valid intersection subsegment
IS.P0 = S.P0 + tE * dS; // = P(tE) = point where S enters polygon
IS.P1 = S.P0 + tL * dS; // = P(tL) = point where S leaves polygon
return(1);
}
// perp product (2D)
// intersect2D_2Segments(): the intersection of 2 finite 2D 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
public int Intersect2D_Segments(RgSegment S1, RgSegment S2, out Point3D I0, out Point3D I1)
{
Vector3d u = S1.P1 - S1.P0;
Vector3d v = S2.P1 - S2.P0;
Vector3d w = S1.P0 - S2.P0;
double D = RgMath.perp(u, v);
// test if they are parallel (includes either being a point)平行
if (Math.Abs(D) < RgMath.SMALL_NUM)
{
// S1 and S2 are parallel
if (RgMath.perp(u, w) != 0 || RgMath.perp(v, w) != 0)
{
I0 = null;
I1 = null;
return(0); // they are NOT collinear不共线
}
// they are collinear or degenerate两线段共线
// check if they are degenerate points
double du = RgMath.dot2(u, u);
double dv = RgMath.dot2(v, v);
if (du == 0 && dv == 0)
{ // both segments are points
if (S1.P0 != S2.P0) // they are distinct points不同的点
{
I0 = null;
I1 = null;
return(0);
}
I0 = S1.P0;
I1 = null;// they are the same point同一点
return(1);
}
if (du == 0)
{ // S1 is a single point
if (RgTopologicRelationship.InSegment(S1.P0, S2) == 0) // but is not in S2
{
I0 = null;
I1 = null;
return(0);
}
I0 = S1.P0;
I1 = null;
return(1);
}
if (dv == 0)
{ // S2 a single point
if (RgTopologicRelationship.InSegment(S2.P0, S1) == 0) // but is not in S1
{
I0 = null;
I1 = null;
return(0);
}
I0 = S2.P0;
I1 = null;
return(1);
}
// they are collinear segments - get overlap (or not)
double t0, t1; // endpoints of S1 in eqn for S2
Vector3d w2 = S1.P1 - S2.P0;
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
double t = t0; t0 = t1; t1 = t; // swap if not
}
if (t0 > 1 || t1 < 0)
{
I0 = null;
I1 = null;
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.P0 + t0 * v;
I1 = null;
return(1);
}
// they overlap in a valid subsegment
I0 = S2.P0 + t0 * v;
I1 = S2.P0 + t1 * v;
return(2);
}
// the segments are skew and may intersect in a point
// get the intersect parameter for S1
double sI = RgMath.perp(v, w) / D;
if (sI < 0 || sI > 1)
{// no intersect with S1
I0 = null;
I1 = null;
return(0);
}
// get the intersect parameter for S2
double tI = RgMath.perp(u, w) / D;
if (tI < 0 || tI > 1)
{// no intersect with S2
I0 = null;
I1 = null;
return(0);
}
I0 = S1.P0 + sI * u; // compute S1 intersect point
{
I1 = null;
return(1);
}
}