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 P212 //    Return: >0 for P2 left of the line through P0 and P113 //            =0 for P2  on the line14 //            <0 for P2  right of the line15 //    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 polygon24 //      Input:   P = a point,25 //               V[] = vertex points of a polygon V[n+1] with V[n]=V[0]26 //      Return:  0 = outside, 1 = inside27 // 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 counter31 32     // loop through all edges of the polygon33     for (int i=0; i
     
       P.y))     // an upward crossing35         || ((V[i].y > P.y) && (V[i+1].y <=  P.y))) { // a downward crossing36             // compute  the actual edge-ray intersect x-coordinate37             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 < intersect39                  ++cn;   // a valid crossing of y=P.y right of P.x40         }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 polygon48 //      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 counter54 55     // loop through all edges of the polygon56     for (int i=0; i
      
        P.y)      // an upward crossing59                  if (isLeft( V[i], V[i+1], P) > 0)  // P left of  edge60                      ++wn;            // have  a valid up intersect61         }62         else {                        // start y > P.y (no test needed)63             if (V[i+1].y  <= P.y)     // a downward crossing64                  if (isLeft( V[i], V[i+1], P) < 0)  // P right of  edge65                      --wn;            // have  a valid down intersect66         }67     }68     return wn;69 }70 //===================================================================