点在多边形内算法的实现

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mapaware 2023-01-11 01:43:01 博主文章分类：c ©著作权

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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
} 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 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
} rect_t;

  

/* gets extent of vertices */
void
 const vertex_t* vl, int np, /* in vertices */
rect_t*  rc /* out extent*/ )
{
int
if
         rc->min_x = rc->max_x = vl[0].x; rc->min_y = rc->max_y = vl[0].y;
else{
/* =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
double

  

double
double
     
double
double

  

return
}

  

/* 2 line segments (s1, s2) are intersect? */
static
 int is_intersect(const vertex_t* s1_start, const
const
 const
{
return
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
 const vertex_t* vl, int np,  /* polygon vl with np vertices  */
const
  vertex_t* v)
{
int
     rect_t        rc; 
     vertex_t     w;
if
return
     
     vertices_get_extent(vl, np, &rc);
if
return

  

/* Set a horizontal beam l(*v, w) from v to the ultra right */
     w.x = rc.max_x + DBL_EPSILON;
     w.y = v->y;

  

/* 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
}

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：

#!/usr/bin/python
#-*- coding: UTF-8 -*-
#
# pip.py
#   point in polygon
#
# 2016-01-07
#
# point(pt) is inside polygon(poly)
########################################################################

# gets extent of vertices vl
#
def extent_vertices(vl):
    min_x = 0.0
    min_y = 0.0
    max_x = 0.0
    max_y = 0.0

    i = 0

    for (x, y) in vl:
        if not i:
            (min_x, min_y) = (x, y)
            (max_x, max_y) = (x, y)
            i = 1
        else:
            if x < min_x:
                min_x = x
            if y < min_y:
                min_y = y
            if x > max_x:
                max_x = x
            if y > max_y:
                max_y = y

    return (min_x, min_y, max_x, max_y)


# points p, q are on the same of line l
#
def same_side(l_start, l_end, p, q):
    dx, dy = float(l_end[0] - l_start[0]), float(l_end[1] - l_start[1])
    dx1, dy1 = float(p[0] - l_start[0]), float(p[1] - l_start[1])
    dx2, dy2 = float(q[0] - l_end[0]), float(q[1] - l_end[1])

    d = (dx * dy1 - dy * dx1) * (dx * dy2 - dy * dx2)

    if d >= 0:
        return 1
    else:
        return 0


# are line segments s1, s2 intersect ?
#
def intersect_segs(s1_start, s1_end, s2_start, s2_end):
    if not same_side(s1_start, s1_end, s2_start, s2_end) and not same_side(s2_start, s2_end, s1_start, s1_end):
        return 1
    else:
        return 0


# is point pt(x, y) in polygon poly
#   returns:
#     0 : not in
#     1 : in
def pt_in_poly(pt, poly):
    np = len(poly)
    if np < 3:
        return 0

    (x, y) = pt
    (min_x, min_y, max_x, max_y) = extent_vertices(poly)

    if x < min_x or x > max_x or y < min_y or y > max_y:
        return 0

    # set a horizontal beam line (pt, w) from pt to the ultra right
    w = (max_x + max_x*0.1 + 1, y)

    c = 0

    for i in range(0, np):
        j = (i+1) % np

        if pt == poly[i]:
            return 1
        elif intersect_segs(poly[i], poly[j], pt, w):
            c = c + 1
        elif poly[i][1] == w[1]:
            k1 = (np + i - 1) % np
            while (k1 != i and poly[k1][1] == w[1]):
                k1 = (np + k1 - 1) % np

            k2 = (i+1) % np
            while (k2 != i and poly[k2][1] == w[1]):
                k2 = (k2 + 1) % np

            if k1 != k2 and not same_side(pt, w, poly[k1], poly[k2]):
                c = c + 1

            if k2 <= i:
                break

            i = k2

    return c % 2

epsilon = 0.0000001

assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(1) appliaction error"
assert pt_in_poly((-1, -1), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(2) appliaction error"
assert pt_in_poly((-1, 1), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(3) appliaction error"
assert pt_in_poly((-1 - epsilon, -1), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 0, "(4) appliaction error"
assert pt_in_poly((-1 + epsilon, -1 + epsilon), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(5) appliaction error"
assert pt_in_poly((-1 + epsilon, -1 + epsilon), [(-1, -1), (-1, 1), (1, 1), (1, -1)]) == 1, "(6) appliaction error"
assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, -1)]) == 1, "(7) appliaction error"
assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 1), (2, -1)]) == 1, "(8) appliaction error"
assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 1), (2, 0), (2, -1)]) == 1, "(9) appliaction error"
assert pt_in_poly((0, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 0), (3, 0), (2, -1)]) == 1, "(10) appliaction error"
assert pt_in_poly((-2, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 0), (3, 0), (2, -1)]) == 0, "(11) appliaction error"
assert pt_in_poly((3, 0), [(-1, -1), (-1, 1), (1, 1), (1, 0), (2, 0), (3, 0), (2, -1)]) == 1, "(12) appliaction error"