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点在多边形内算法的实现_点在多边形 apollo

作者：木道寻08 | 2024-07-29 17:00:15

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点在多边形 apollo
 
点在多边形内算法的实现
cheungmine
2007-9-22
 
本文是采用射线法判断点是否在多边形内的C语言程序。多年前，我自己实现了这样一个算法。但是随着时间的推移，我决定重写这个代码。参考周培德的《计算几何》一书，结合我的实践和经验，我相信，在这个算法的实现上，这是你迄今为止遇到的最优的代码。
这是个C语言的小算法的实现程序，本来不想放到这里。可是，当我自己要实现这样一个算法的时候，想在网上找个现成的，考察下来竟然一个符合需要的也没有。我对自己大学读书时写的代码没有信心，所以，决定重新写一个，并把它放到这里，以飨读者。也增加一下BLOG的点击量。
 
首先定义点结构如下：
/* Vertex structure */
typedef struct                      
{
     double x, y;
} vertex_t;
 
本算法里所指的多边形，是指由一系列点序列组成的封闭简单多边形。它的首尾点可以是或不是同一个点（不强制要求首尾点是同一个点）。这样的多边形可以是任意形状的，包括多条边在一条绝对直线上。因此，定义多边形结构如下：
/* Vertex list structure – polygon */
typedef struct                      
{
     int                num_vertices;      /* Number of vertices in list */
     vertex_t           *vertex;           /* Vertex array pointer */
} vertexlist_t;
 
为加快判别速度，首先计算多边形的外包矩形（ rect_t），判断点是否落在外包矩形内，只有满足落在外包矩形内的条件的点，才进入下一步的计算。为此，引入外包矩形结构rect_t和求点集合的外包矩形内的方法vertices_get_extent，代码如下：
/* bounding rectangle type */
typedef struct
{
     double min_x, min_y, max_x, max_y;
} rect_t;
 
/* gets extent of vertices */
void vertices_get_extent (const vertex_t* vl, int np, /* in vertices */
rect_t*  rc /* out extent*/ )
{
     int i;       
     if (np > 0){
         rc->min_x = rc->max_x = vl[0].x; rc->min_y = rc->max_y = vl[0].y;
     }else{
         rc->min_x = rc->min_y = rc->max_x = rc->max_y = 0; /* =0 ? no vertices at all */
     }
 
     for(i=1; i<np; i++)
     {
         if(vl[i].x < rc->min_x) rc->min_x = vl[i].x;
         if(vl[i].y < rc->min_y) rc->min_y = vl[i].y;      
         if(vl[i].x > rc->max_x) rc->max_x = vl[i].x;
         if(vl[i].y > rc->max_y) rc->max_y = vl[i].y;
     }
}
 
     当点满足落在多边形外包矩形内的条件，要进一步判断点（ v）是否在多边形（vl：np）内。本程序采用射线法，由待测试点（v）水平引出一条射线B（v，w），计算B与vl边线的交点数目，记为c，根据奇内偶外原则（c为奇数说明v在vl内，否则v不在vl内）判断点是否在多边形内。
具体原理就不多说。为计算线段间是否存在交点，引入下面的函数：
（ 1）is_same判断2（p、q）个点是（1）否（0）在直线l（l_start，l_end）的同侧；
（ 2）is_intersect用来判断2条线段（不是直线）s1、s2是（1）否（0）相交；
 
/* p, q is on the same of line l */
static int is_same(const vertex_t* l_start, const vertex_t* l_end, /* line l */
const vertex_t* p,
const vertex_t* q)
{
     double dx = l_end->x - l_start->x;
     double dy = l_end->y - l_start->y;
 
     double dx1= p->x - l_start->x;
     double dy1= p->y - l_start->y;
    
     double dx2= q->x - l_end->x;
     double dy2= q->y - l_end->y;
 
     return ((dx*dy1-dy*dx1)*(dx*dy2-dy*dx2) > 0? 1 : 0);
}
 
/* 2 line segments (s1, s2) are intersect? */
static int is_intersect(const vertex_t* s1_start, const vertex_t* s1_end,
const vertex_t* s2_start, const vertex_t* s2_end)
{
     return (is_same(s1_start, s1_end, s2_start, s2_end)==0 &&
is_same(s2_start, s2_end, s1_start, s1_end)==0)? 1: 0;
}
 
 
下面的函数 pt_in_poly就是判断点（v）是（1）否（0）在多边形（vl：np）内的程序：
 
int pt_in_poly (   const vertex_t* vl, int np,  /* polygon vl with np vertices  */
const vertex_t* v)
{
     int i, j, k1, k2, c;
     rect_t        rc; 
     vertex_t     w;
     if (np < 3)
         return 0;
    
     vertices_get_extent(vl, np, &rc);
     if (v->x < rc.min_x || v->x > rc.max_x || v->y < rc.min_y || v->y > rc.max_y)
         return 0;
 
     /* Set a horizontal beam l(*v, w) from v to the ultra right */  
     w.x = rc.max_x + DBL_EPSILON;
     w.y = v->y;
 
     c = 0;        /* Intersection points counter */
     for(i=0; i<np; i++)
     {
         j = (i+1) % np;
 
         if(is_intersect(vl+i, vl+j, v, &w))
         {
              c++;
         }
         else if(vl[i].y==w.y)
         {
              k1 = (np+i-1)%np;
              while(k1!=i && vl[k1].y==w.y)
                   k1 = (np+k1-1)%np;
 
              k2 = (i+1)%np;
              while(k2!=i && vl[k2].y==w.y)
                   k2 = (k2+1)%np;
             
              if(k1 != k2 && is_same(v, &w, vl+k1, vl+k2)==0)
                   c++;
 
              if(k2 <= i)
                   break;
 
              i = k2;
         }
     }
 
     return   c%2;
}
 
本想配些插图说明问题，但是， CSDN的文章里放图片我还没用过。以后再试吧！实践证明，本程序算法的适应性极强。但是，对于点正好落在多边形边上的极端情形，有可能得出2种不同的结果。

下面是python的版本： 
  1. #!/usr/bin/python
  2. #-*- coding: UTF-8 -*-
  3. #
  4. # pip.py
  5. #   point in polygon
  6. #
  7. # 2016-01-07
  8. #
  9. # point(pt) is inside polygon(poly)
  10. ########################################################################
  11.  
  12. # gets extent of vertices vl
  13. #
  14. def extent_vertices(vl):
  15.     min_x = 0.0
  16.     min_y = 0.0
  17.     max_x = 0.0
  18.     max_y = 0.0
  19.  
  20.     i = 0
  21.  
  22.     for (x, y) in vl:
  23.         if not i:
  24.             (min_x, min_y) = (x, y)
  25.             (max_x, max_y) = (x, y)
  26.             i = 1
  27.         else:
  28.             if x < min_x:
  29.                 min_x = x
  30.             if y < min_y:
  31.                 min_y = y
  32.             if x > max_x:
  33.                 max_x = x
  34.             if y > max_y:
  35.                 max_y = y
  36.  
  37.     return (min_x, min_y, max_x, max_y)
  38.  
  39.  
  40. # points p, q are on the same of line l
  41. #
  42. def same_side(l_start, l_end, p, q):
  43.     dx, dy = float(l_end[0] - l_start[0]), float(l_end[1] - l_start[1])
  44.     dx1, dy1 = float(p[0] - l_start[0]), float(p[1] - l_start[1])
  45.     dx2, dy2 = float(q[0] - l_end[0]), float(q[1] - l_end[1])
  46.  
  47.     d = (dx * dy1 - dy * dx1) * (dx * dy2 - dy * dx2)
  48.  
  49.     if d >= 0:
  50.         return 1
  51.     else:
  52.         return 0
  53.  
  54.  
  55. # are line segments s1, s2 intersect ?
  56. #
  57. def intersect_segs(s1_start, s1_end, s2_start, s2_end):
  58.     if not same_side(s1_start, s1_end, s2_start, s2_end) and not same_side(s2_start, s2_end, s1_start, s1_end):
  59.         return 1
  60.     else:
  61.         return 0
  62.  
  63.  
  64. # is point pt(x, y) in polygon poly
  65. #   returns:
  66. #     0 : not in
  67. #     1 : in
  68. def pt_in_poly(pt, poly):
  69.     np = len(poly)
  70.     if np < 3:
  71.         return 0
  72.  
  73.     (x, y) = pt
  74.     (min_x, min_y, max_x, max_y) = extent_vertices(poly)
  75.  
  76.     if x < min_x or x > max_x or y < min_y or y > max_y:
  77.         return 0
  78.  
  79.     # set a horizontal beam line (pt, w) from pt to the ultra right
  80.     w = (max_x + max_x*0.1 + 1, y)
  81.  
  82.     c = 0
  83.  
  84.     for i in range(0, np):
  85.         j = (i+1) % np
  86.  
  87.         if pt == poly[i]:
  88.             return 1
  89.         elif intersect_segs(poly[i], poly[j], pt, w):
  90.             c = c + 1
  91.         elif poly[i][1] == w[1]:
  92.             k1 = (np + i - 1) % np
  93.             while (k1 != i and poly[k1][1] == w[1]):
  94.                 k1 = (np + k1 - 1) % np
  95.  
  96.             k2 = (i+1) % np
  97.             while (k2 != i and poly[k2][1] == w[1]):
  98.                 k2 = (k2 + 1) % np
  99.  
  100.             if k1 != k2 and not same_side(pt, w, poly[k1], poly[k2]):
  101.                 c = c + 1
  102.  
  103.             if k2 <= i:
  104.                 break
  105.  
  106.             i = k2
  107.  
  108.     return c % 2
  109.  
  110. epsilon = 0.0000001
  111.  
  112. assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(1) appliaction error"
  113. assert pt_in_poly((-1, -1), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(2) appliaction error"
  114. assert pt_in_poly((-1, 1), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(3) appliaction error"
  115. assert pt_in_poly((-1 - epsilon, -1), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 0, "(4) appliaction error"
  116. assert pt_in_poly((-1 + epsilon, -1 + epsilon), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(5) appliaction error"
  117. assert pt_in_poly((-1 + epsilon, -1 + epsilon), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(6) appliaction error"
  118. assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, -1)]) == 1, "(7) appliaction error"
  119. assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 1), (2, -1)]) == 1, "(8) appliaction error"
  120. assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 1), (2, 0), (2, -1)]) == 1, "(9) appliaction error"
  121. assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 0), (3, 0), (2, -1)]) == 1, "(10) appliaction error"
  122. assert pt_in_poly((-2, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 0), (3, 0), (2, -1)]) == 0, "(11) appliaction error"
  123. assert pt_in_poly((3, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 0), (3, 0), (2, -1)]) == 1, "(12) appliaction error"


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