判断点在多边形内

 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 //===================================================================