如何确定多边形点列表是否按顺时针顺序排列？ [英] How to determine if a list of polygon points are in clockwise order?

问题描述

例如：

我有一个积分列表，如何查找它们是否按顺时针顺序排列？

  point [0] =（5,0）
 point [1] =（6,4）
 point [2] =（4,5） 
 point [3] =（1,5）
 point [4] =（1,0）
  

会说它是逆时针的（或者对于一些人是逆时针的）。

解决方案

一些建议的方法在非凸多边形（例如新月形）的情况下会失败。这是一个简单的方法，它可以与非凸多边形一起工作（它甚至可以像八分之一的自交多边形一样工作，告诉你它是否大多数情况下是顺时针方向）。

b
$ b

在边上求和，（x 2 - x 1）y（y 2 + y） > 1 ）。如果结果为正值，则曲线为顺时针，如果为负值，则曲线为逆时针。 （结果是封闭区域的两倍，带有+/-约定。）

  point [0] =（5,0 ）边缘[0]：（6-5）（4 + 0）= 4 
 point [1] =（6,4）边缘[1]：（4-6）（5 + 4）= -18 （1）（5 + 5）= -30 
 point [3] =（1,5）edge [3] ：（1-1）（0 + 5）= 0 
 point [4] =（1,0）edge [4]：（5-1）（0 + 0）= 0 
  -  -  
 -44逆时针
  

Having a list of points, how do I find if they are in clockwise order?

For example:

point[0] = (5,0)
point[1] = (6,4)
point[2] = (4,5)
point[3] = (1,5)
point[4] = (1,0)

would say that it is anti-clockwise (or counter-clockwise, for some people).

解决方案

Some of the suggested methods will fail in the case of a non-convex polygon, such as a crescent. Here's a simple one that will work with non-convex polygons (it'll even work with a self-intersecting polygon like a figure-eight, telling you whether it's mostly clockwise).

Sum over the edges, (x₂ − x₁)(y₂ + y₁). If the result is positive the curve is clockwise, if it's negative the curve is counter-clockwise. (The result is twice the enclosed area, with a +/- convention.)

point[0] = (5,0)   edge[0]: (6-5)(4+0) =   4
point[1] = (6,4)   edge[1]: (4-6)(5+4) = -18
point[2] = (4,5)   edge[2]: (1-4)(5+5) = -30
point[3] = (1,5)   edge[3]: (1-1)(0+5) =   0
point[4] = (1,0)   edge[4]: (5-1)(0+0) =   0
                                         ---
                                         -44  counter-clockwise

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