我试图创建一个快速的2D点内多边形算法,用于命中测试(例如多边形.contains(p:点))。对有效技术的建议将不胜感激。
当前回答
以下是M. Katz基于Nirg方法的答案的JavaScript变体:
function pointIsInPoly(p, polygon) {
var isInside = false;
var minX = polygon[0].x, maxX = polygon[0].x;
var minY = polygon[0].y, maxY = polygon[0].y;
for (var n = 1; n < polygon.length; n++) {
var q = polygon[n];
minX = Math.min(q.x, minX);
maxX = Math.max(q.x, maxX);
minY = Math.min(q.y, minY);
maxY = Math.max(q.y, maxY);
}
if (p.x < minX || p.x > maxX || p.y < minY || p.y > maxY) {
return false;
}
var i = 0, j = polygon.length - 1;
for (i, j; i < polygon.length; j = i++) {
if ( (polygon[i].y > p.y) != (polygon[j].y > p.y) &&
p.x < (polygon[j].x - polygon[i].x) * (p.y - polygon[i].y) / (polygon[j].y - polygon[i].y) + polygon[i].x ) {
isInside = !isInside;
}
}
return isInside;
}
其他回答
这大概是一个稍微不那么优化的C代码版本,它来自于这个页面。
我的c++版本使用std::vector<std::pair<double, double>>和两个double作为x和y。逻辑应该与原始C代码完全相同,但我发现我的更容易阅读。我不能为表演说话。
bool point_in_poly(std::vector<std::pair<double, double>>& verts, double point_x, double point_y)
{
bool in_poly = false;
auto num_verts = verts.size();
for (int i = 0, j = num_verts - 1; i < num_verts; j = i++) {
double x1 = verts[i].first;
double y1 = verts[i].second;
double x2 = verts[j].first;
double y2 = verts[j].second;
if (((y1 > point_y) != (y2 > point_y)) &&
(point_x < (x2 - x1) * (point_y - y1) / (y2 - y1) + x1))
in_poly = !in_poly;
}
return in_poly;
}
原始的C代码是
int pnpoly(int nvert, float *vertx, float *verty, float testx, float testy)
{
int i, j, c = 0;
for (i = 0, j = nvert-1; i < nvert; j = i++) {
if ( ((verty[i]>testy) != (verty[j]>testy)) &&
(testx < (vertx[j]-vertx[i]) * (testy-verty[i]) / (verty[j]-verty[i]) + vertx[i]) )
c = !c;
}
return c;
}
以下是M. Katz基于Nirg方法的答案的JavaScript变体:
function pointIsInPoly(p, polygon) {
var isInside = false;
var minX = polygon[0].x, maxX = polygon[0].x;
var minY = polygon[0].y, maxY = polygon[0].y;
for (var n = 1; n < polygon.length; n++) {
var q = polygon[n];
minX = Math.min(q.x, minX);
maxX = Math.max(q.x, maxX);
minY = Math.min(q.y, minY);
maxY = Math.max(q.y, maxY);
}
if (p.x < minX || p.x > maxX || p.y < minY || p.y > maxY) {
return false;
}
var i = 0, j = polygon.length - 1;
for (i, j; i < polygon.length; j = i++) {
if ( (polygon[i].y > p.y) != (polygon[j].y > p.y) &&
p.x < (polygon[j].x - polygon[i].x) * (p.y - polygon[i].y) / (polygon[j].y - polygon[i].y) + polygon[i].x ) {
isInside = !isInside;
}
}
return isInside;
}
nirg回答的Swift版本:
extension CGPoint {
func isInsidePolygon(vertices: [CGPoint]) -> Bool {
guard !vertices.isEmpty else { return false }
var j = vertices.last!, c = false
for i in vertices {
let a = (i.y > y) != (j.y > y)
let b = (x < (j.x - i.x) * (y - i.y) / (j.y - i.y) + i.x)
if a && b { c = !c }
j = i
}
return c
}
}
from typing import Iterable
def pnpoly(verts, x, y):
#check if x and/or y is iterable
xit, yit = isinstance(x, Iterable), isinstance(y, Iterable)
#if not iterable, make an iterable of length 1
X = x if xit else (x, )
Y = y if yit else (y, )
#store verts length as a range to juggle j
r = range(len(verts))
#final results if x or y is iterable
results = []
#traverse x and y coordinates
for xp in X:
for yp in Y:
c = 0 #reset c at every new position
for i in r:
j = r[i-1] #set j to position before i
#store a few arguments to shorten the if statement
yneq = (verts[i][1] > yp) != (verts[j][1] > yp)
xofs, yofs = (verts[j][0] - verts[i][0]), (verts[j][1] - verts[i][1])
#if we have crossed a line, increment c
if (yneq and (xp < xofs * (yp - verts[i][1]) / yofs + verts[i][0])):
c += 1
#if c is odd store the coordinates
if c%2:
results.append((xp, yp))
#return either coordinates or a bool, depending if x or y was an iterable
return results if (xit or yit) else bool(c%2)
这个python版本是通用的。您可以为True/False结果输入单个x和单个y值,也可以使用x和y的范围来遍历整个点网格。如果使用范围,则返回所有True点的x/y对列表。vertices参数需要一个由x/y对组成的二维Iterable,例如:[(x1,y1), (x2,y2),…]
使用示例:
vertices = [(25,25), (75,25), (75,75), (25,75)]
pnpoly(vertices, 50, 50) #True
pnpoly(vertices, range(100), range(100)) #[(25,25), (25,26), (25,27), ...]
实际上,这些都可以。
pnpoly(vertices, 50, range(100)) #check 0 to 99 y at x of 50
pnpoly(vertices, range(100), 50) #check 0 to 99 x at y of 50
当使用qt (qt 4.3+)时,可以使用QPolygon的函数containsPoint
推荐文章
- 如何找到Java堆大小和内存使用(Linux)?
- 如何在HTML5中改变视频的播放速度?
- 我如何提高ASP。NET MVC应用程序性能?
- 列表推导式和函数式函数比for循环更快吗?
- 圆线段碰撞检测算法?
- Pandas loc vs iloc vs at vs iat?
- 当WebSockets可用时,为什么要使用AJAX ?
- SurfaceView和View的区别?
- 一个字符串的字符串列表
- .NET反射的成本有多高?
- 在c#中检查字符串是否只包含数字的最快方法
- JavaScript变量声明在循环外还是循环内?
- 为什么C语言这么快,为什么其他语言没有这么快或更快?
- String与StringBuilder
- 为什么引入无用的MOV指令会加速x86_64汇编中的紧循环?