点在多边形内算法的实现
2007-09-24 10:19
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[align=center]点在多边形内算法的实现[/align][align=center]cheungmine[/align][align=center]2007-9-22[/align] 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:[align=left]/* Vertex structure */[/align][align=left]typedef struct [/align][align=left]{[/align][align=left] double x, y;[/align]} 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:[align=left]/* Vertex list structure – polygon */[/align][align=left]typedef struct [/align][align=left]{[/align][align=left] int num_vertices; /* Number of vertices in list */[/align][align=left] vertex_t *vertex; /* Vertex array pointer */[/align]} 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:[align=left]/* bounding rectangle type */[/align][align=left]typedef struct[/align][align=left]{[/align][align=left] double min_x, min_y, max_x, max_y;[/align]} rect_t; [align=left]/* gets extent of vertices */[/align][align=left]void vertices_get_extent (const vertex_t* vl, int np, /* in vertices */[/align][align=left]rect_t* rc /* out extent*/ )[/align][align=left]{[/align][align=left] int i; [/align][align=left] if (np > 0){[/align][align=left] rc->min_x = rc->max_x = vl[0].x; rc->min_y = rc->max_y = vl[0].y;[/align][align=left] }else{[/align][align=left] rc->min_x = rc->min_y = rc->max_x = rc->max_y = 0; /* =0 ? no vertices at all */[/align][align=left] }[/align][align=left] [/align][align=left] for(i=1; i<np; i++)[/align][align=left] {[/align][align=left] if(vl[i].x < rc->min_x) rc->min_x = vl[i].x;[/align][align=left] if(vl[i].y < rc->min_y) rc->min_y = vl[i].y; [/align][align=left] if(vl[i].x > rc->max_x) rc->max_x = vl[i].x;[/align][align=left] if(vl[i].y > rc->max_y) rc->max_y = vl[i].y;[/align][align=left] }[/align]} [align=left] 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。[/align][align=left]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:[/align][align=left](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;[/align](2)is_intersect用来判断2条线段(不是直线)s1、s2是(1)否(0)相交;[align=left] [/align][align=left]/* p, q is on the same of line l */[/align][align=left]static int is_same(const vertex_t* l_start, const vertex_t* l_end, /* line l */[/align][align=left]const vertex_t* p, [/align][align=left]const vertex_t* q)[/align][align=left]{[/align][align=left] double dx = l_end->x - l_start->x;[/align][align=left] double dy = l_end->y - l_start->y;[/align][align=left] [/align][align=left] double dx1= p->x - l_start->x;[/align][align=left] double dy1= p->y - l_start->y;[/align][align=left] [/align][align=left] double dx2= q->x - l_end->x;[/align][align=left] double dy2= q->y - l_end->y;[/align][align=left] [/align][align=left] return ((dx*dy1-dy*dx1)*(dx*dy2-dy*dx2) > 0? 1 : 0);[/align][align=left]}[/align][align=left] [/align][align=left]/* 2 line segments (s1, s2) are intersect? */[/align][align=left]static int is_intersect(const vertex_t* s1_start, const vertex_t* s1_end, [/align][align=left]const vertex_t* s2_start, const vertex_t* s2_end)[/align][align=left]{[/align][align=left] return (is_same(s1_start, s1_end, s2_start, s2_end)==0 && [/align][align=left]is_same(s2_start, s2_end, s1_start, s1_end)==0)? 1: 0;[/align]} [align=left]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: [/align][align=left] [/align][align=left]int pt_in_poly ( const vertex_t* vl, int np, /* polygon vl with np vertices */[/align][align=left]const vertex_t* v)[/align][align=left]{[/align][align=left] int i, j, k1, k2, c;[/align][align=left] rect_t rc; [/align][align=left] vertex_t w;[/align][align=left] if (np < 3)[/align][align=left] return 0; [/align][align=left] [/align][align=left] vertices_get_extent(vl, np, &rc);[/align][align=left] if (v->x < rc.min_x || v->x > rc.max_x || v->y < rc.min_y || v->y > rc.max_y)[/align][align=left] return 0;[/align][align=left] [/align][align=left] /* Set a horizontal beam l(*v, w) from v to the ultra right */ [/align][align=left] w.x = rc.max_x + DBL_EPSILON;[/align][align=left] w.y = v->y;[/align][align=left] [/align][align=left] c = 0; /* Intersection points counter */[/align][align=left] for(i=0; i<np; i++)[/align][align=left] {[/align][align=left] j = (i+1) % np;[/align][align=left] [/align][align=left] if(is_intersect(vl+i, vl+j, v, &w))[/align][align=left] {[/align][align=left] c++;[/align][align=left] }[/align][align=left] else if(vl[i].y==w.y)[/align][align=left] {[/align][align=left] k1 = (np+i-1)%np;[/align][align=left] while(k1!=i && vl[k1].y==w.y)[/align][align=left] k1 = (np+k1-1)%np;[/align][align=left] [/align][align=left] k2 = (i+1)%np;[/align][align=left] while(k2!=i && vl[k2].y==w.y)[/align][align=left] k2 = (k2+1)%np;[/align][align=left] [/align][align=left] if(k1 != k2 && is_same(v, &w, vl+k1, vl+k2)==0)[/align][align=left] c++;[/align][align=left] [/align][align=left] if(k2 <= i)[/align][align=left] break;[/align][align=left] [/align][align=left] i = k2;[/align][align=left] }[/align][align=left] }[/align][align=left] [/align][align=left] return c%2;[/align]} 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:
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"
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