1 // Copyright 2000 softSurfer, 2012 Dan Sunday
 2 // This code may be freely used and modified for any purpose
 3 // providing that this copyright notice is included with it.
 4 // SoftSurfer makes no warranty for this code, and cannot be held
 5 // liable for any real or imagined damage resulting from its use.
 6 // Users of this code must verify correctness for their application.
 7  // a Point is defined by its coordinates {int x, y;}
 8 //===================================================================
 9  // isLeft(): tests if a point is Left|On|Right of an infinite line.
10 判断P2点在直线上（P0，P1）
11 //    Input:  three points P0, P1, and P2
12 //    Return: >0 for P2 left of the line through P0 and P1
13 //            =0 for P2  on the line
14 //            <0 for P2  right of the line
15 //    See: Algorithm 1 "Area of Triangles and Polygons"
16 inline int isLeft( Point P0, Point P1, Point P2 )
17 {
18     return ( (P1.x - P0.x) * (P2.y - P0.y)
19             - (P2.x -  P0.x) * (P1.y - P0.y) );
20 }
21 //===================================================================
22 射线法判断点在多边形内
23 // cn_PnPoly(): crossing number test for a point in a polygon
24 //      Input:   P = a point,
25 //               V[] = vertex points of a polygon V[n+1] with V[n]=V[0]
26 //      Return:  0 = outside, 1 = inside
27 // This code is patterned after [Franklin, 2000]
28 int cn_PnPoly( Point P, Point* V, int n )
29 {
30     int    cn = 0;    // the  crossing number counter
31 
32     // loop through all edges of the polygon
33     for (int i=0; i<n; i++) {    // edge from V[i]  to V[i+1]
34        if (((V[i].y <= P.y) && (V[i+1].y > P.y))     // an upward crossing
35         || ((V[i].y > P.y) && (V[i+1].y <=  P.y))) { // a downward crossing
36             // compute  the actual edge-ray intersect x-coordinate
37             float vt = (float)(P.y  - V[i].y) / (V[i+1].y - V[i].y);
38             if (P.x <  V[i].x + vt * (V[i+1].x - V[i].x)) // P.x < intersect
39                  ++cn;   // a valid crossing of y=P.y right of P.x
40         }
41     }
42     return (cn&1);    // 0 if even (out), and 1 if  odd (in)
43 
44 }
45 //===================================================================
46 
47 // wn_PnPoly(): winding number test for a point in a polygon
48 //      Input:   P = a point,
49 //               V[] = vertex points of a polygon V[n+1] with V[n]=V[0]
50 //      Return:  wn = the winding number (=0 only when P is outside)
51 int wn_PnPoly( Point P, Point* V, int n )
52 {
53     int    wn = 0;    // the  winding number counter
54 
55     // loop through all edges of the polygon
56     for (int i=0; i<n; i++) {   // edge from V[i] to  V[i+1]
57         if (V[i].y <= P.y) {          // start y <= P.y
58             if (V[i+1].y  > P.y)      // an upward crossing
59                  if (isLeft( V[i], V[i+1], P) > 0)  // P left of  edge
60                      ++wn;            // have  a valid up intersect
61         }
62         else {                        // start y > P.y (no test needed)
63             if (V[i+1].y  <= P.y)     // a downward crossing
64                  if (isLeft( V[i], V[i+1], P) < 0)  // P right of  edge
65                      --wn;            // have  a valid down intersect
66         }
67     }
68     return wn;
69 }
70 //===================================================================