我认为为了使某些点顺时针方向，所有的边都必须是正的而不仅仅是边的和。如果一条边是负的，则逆时针方向给出至少3个点。

如果使用Matlab，如果多边形顶点按顺时针顺序排列，函数ispolycw将返回true。

求出这些点的质心。

假设有直线从这个点到你们的点。

求line0 line1的两条直线夹角

而不是直线1和直线2

...

...

如果这个角是单调递增的，而不是逆时针递增的，

如果是单调递减，则是顺时针递减

Else(它不是单调的)

你不能决定，所以这是不明智的

Javascript实现的lhf的答案 (再次强调，这只适用于简单的多边形，即不适用于图8)

let polygon = [ {x:5,y:0}, {x:6,y:4}, {x:4,y:5}, {x:1,y:5}, {x:1,y:0} ] document.body.innerHTML += `Polygon ${polygon.map(p=>`(${p.x}, ${p.y})`).join(", ")} is clockwise? ${isPolygonClockwise(polygon)}` let reversePolygon = [] polygon.forEach(point=>reversePolygon.unshift(point)) document.body.innerHTML += `<br/>Polygon ${reversePolygon.map(p=>`(${p.x}, ${p.y})`).join(", ")} is clockwise? ${isPolygonClockwise(reversePolygon)}` function isPolygonClockwise (polygon) { // From http://www.faqs.org/faqs/graphics/algorithms-faq/ "How do I find the orientation of a simple polygon?" // THIS SOMETIMES FAILS if the polygon is a figure 8, or similar shape where it crosses over itself // Take the lowest point (break ties with the right-most). if (polygon.length < 3) { return true // A single point or two points can't be clockwise/counterclockwise } let previousPoint = polygon[0] let lowestPoint = polygon[1] let nextPoint = polygon[2] polygon.forEach((point, index)=>{ if (point.y > lowestPoint.y || (point.y === lowestPoint.y && point.x > lowestPoint.x)) { // larger y values are lower, in svgs // Break ties with furthest right previousPoint = polygon[(index-1) >= (0) ? (index-1) : (polygon.length-1)] lowestPoint = polygon[index] nextPoint = polygon[(index+1) <= (polygon.length-1) ? (index+1) : (0)] } }) // Check the angle between the previous point, that point, and the next point. // If the angle is less than PI radians, the polygon is clockwise let angle = findAngle(previousPoint, lowestPoint, nextPoint) return angle < Math.PI } function findAngle(A,B,C) { var AB = Math.atan2(B.y-A.y, B.x-A.x); var BC = Math.atan2(C.y-B.y, C.x-B.x); if (AB < 0) AB += Math.PI*2 if (BC < 0) BC += Math.PI*2 return BC-AB; }

对于那些不想“重新发明轮子”的人，我认为值得一提的是，这个检查是在一个名为Shapely (github)的漂亮的Python包中实现的(它基于GEOS C/ c++库):

Shapely is a BSD-licensed Python package for manipulation and analysis of planar geometric objects. It is using the widely deployed open-source geometry library GEOS (the engine of PostGIS, and a port of JTS). Shapely wraps GEOS geometries and operations to provide both a feature rich Geometry interface for singular (scalar) geometries and higher-performance NumPy ufuncs for operations using arrays of geometries. Shapely is not primarily focused on data serialization formats or coordinate systems, but can be readily integrated with packages that are.

来源:https://shapely.readthedocs.io/en/stable/

一个给出OP坐标的小例子:

import numpy as np
from shapely.geometry import Polygon

points = np.array([
    (5,0),
    (6,4),
    (4,5),
    (1,5),
    (1,0)
])

P = Polygon(points)

这是新构造的多边形:

import matplotlib.pyplot as plt

x,y = P.exterior.coords.xy
plt.plot(x,y)
plt.axis('equal')
plt.grid()
plt.show()

你可以直接使用LinearRing的is_ccw属性来检查多边形是CW还是CCW:

type(P.exterior)
>: shapely.geometry.polygon.LinearRing

P.exterior.is_ccw
>: True

如果颠倒:

points = np.flipud(points)
points
>: 
array([[1, 0],
       [1, 5],
       [4, 5],
       [6, 4],
       [5, 0]])


P1 = Polygon(points)

P1.exterior.is_ccw
>: True

进一步阅读的文档和参考资料:

shaely is_ccw (github): https://github.com/shapely/shapely/blob/eba985c6e0170ecdd90c83592fd0afa7ae793cb8/shapely/predicates.py#L72-L108 Libgeos (github): https://github.com/libgeos/geos GEOS API参考:https://libgeos.org/doxygen/classgeos_1_1algorithm_1_1Orientation.html#a5af93795969b80f97d7997195974d7c8 GEOS实现(github): https://github.com/libgeos/geos/blob/ab0ce6dafdf7f75ec6d234b6c65bb209037dda17/src/algorithm/Orientation.cpp#L43-L133

我的c# / LINQ解决方案是基于下面@charlesbretana的交叉积建议的。你可以为线圈指定一个参考法线。只要曲线大部分在向上向量所定义的平面内，它就可以工作。

using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace SolidworksAddinFramework.Geometry
{
    public static class PlanePolygon
    {
        /// <summary>
        /// Assumes that polygon is closed, ie first and last points are the same
        /// </summary>
       public static bool Orientation
           (this IEnumerable<Vector3> polygon, Vector3 up)
        {
            var sum = polygon
                .Buffer(2, 1) // from Interactive Extensions Nuget Pkg
                .Where(b => b.Count == 2)
                .Aggregate
                  ( Vector3.Zero
                  , (p, b) => p + Vector3.Cross(b[0], b[1])
                                  /b[0].Length()/b[1].Length());

            return Vector3.Dot(up, sum) > 0;

        } 

    }
}

使用单元测试

namespace SolidworksAddinFramework.Spec.Geometry
{
    public class PlanePolygonSpec
    {
        [Fact]
        public void OrientationShouldWork()
        {

            var points = Sequences.LinSpace(0, Math.PI*2, 100)
                .Select(t => new Vector3((float) Math.Cos(t), (float) Math.Sin(t), 0))
                .ToList();

            points.Orientation(Vector3.UnitZ).Should().BeTrue();
            points.Reverse();
            points.Orientation(Vector3.UnitZ).Should().BeFalse();



        } 
    }
}