检查一个点是否在一个简单的多边形内

Question

我正在尝试确定一个点是否位于多边形内部。我使用来自this website 的以下（针对 Swift 修改的）算法：

func contains(polygon: [Point], test: Point) -> Bool {
    let count = polygon.count
    var i: Int, j: Int
    var contains = false
    for (i = 0, j = count - 1; i < count; j = i++) {
        if ( ((polygon[i].y >= test.y) != (polygon[j].y >= test.y)) &&
            (test.x <= (polygon[j].x - polygon[i].x) * (test.y - polygon[i].y) /
                (polygon[j].y - polygon[i].y) + polygon[i].x) ) {
                    contains = !contains;
        }
    }
    return contains;
}

但是，当有一个具有以下坐标的简单多边形时：(x: 0, y: 40), (x: 0, y: 0), (x: 20, y: 0), (x: 20, y: 20), (x: 40, y: 20), (x: 40, y: 40)，并检查点(x: 30, y: 20)，结果为真，因为当i 和j 为true 时，结果为真5 和 4（(x: 40, y: 40) 和 (x: 40, y: 20)），尽管该点仅位于多边形的边界。如果该点确实位于在多边形中，该函数实际上应该只评估true。感谢您对算法的任何帮助或改进/调整！

Answer 1

这是javascript代码（容易理解，你可以在swift上重写）。它对我来说非常有效，几乎 100%，即非常精确。

您的解决方案精度不佳。

function pointIsInPoly(v, polygon) {
    var edge_error = 1.192092896e-07; // epsilon i.e ~0.000000192
    var x = 0;
    var y = 1;
    var i, j;
    var r = false;
    for (i = 0, j = polygon.length - 1; i < polygon.length; j = i++)
    {
        var pi = polygon[i];
        var pj = polygon[j];
        if (Math.abs(pi[y] - pj[y]) <= edge_error && Math.abs(pj[y] - v[y]) <= edge_error && (pi[x] >= v[x]) != (pj[x] >= v[x]))
        {   
            return true;
        }

        if ((pi[y] > v[y]) != (pj[y] > v[y]))
        {
            var c = (pj[x] - pi[x]) * (v[y] - pi[y]) / (pj[y] - pi[y]) + pi[x];
            if (Math.abs(v[x] - c) <= edge_error)
            {
                return true;
            }
            if (v[x] < c)
            {
                r = !r;
            }
        }
    }
    return r;
}

Answer 2

如果这是用于 iOS 应用程序，请将您的多边形转换为 UIBezierPath，然后使用函数 containtsPoint() 验证您的点是否在该 bezierpath 中

示例（iOS）：

func contains(polygon: [CGPoint], test: CGPoint) -> Bool {
        if polygon.count <= 1 {
            return false //or if first point = test -> return true
        }

        var p = UIBezierPath()
        let firstPoint = polygon[0] as CGPoint

        p.moveToPoint(firstPoint)

        for index in 1...polygon.count-1 {
            p.addLineToPoint(polygon[index] as CGPoint)
        }

        p.closePath()

       return p.containsPoint(test)
    }

Answer 3

这是 PNPoly 算法的改进实现。我用过，效果很好。

func isPointInsidePolygon(polygon: [CGPoint], test:CGPoint) -> Bool {
 var  i:Int, j:Int = polygon.count - 1
 var  contains = false

 for (i = 0; i < polygon.count; i++) {
    if (((polygon[i].y < test.y && polygon[j].y >= test.y) || (polygon[j].y < test.y && polygon[i].y >= test.y))
        && (polygon[i].x <= test.x || polygon[j].x <= test.x)) {
            contains ^= (polygon[i].x + (test.y - polygon[i].y) / (polygon[j].y - polygon[i].y) * (polygon[j].x - polygon[i].x) < test.x)
    }

    j = i
 }

 return contains
}

进一步查询检查：http://alienryderflex.com/polygon/

Answer 4

也适合我，所以我不知道问题出在哪里

我还做了一个稍微修改过的版本来使用快速迭代器：

func contains(polygon: [Point], test: Point) -> Bool {

  var pJ=polygon.last!
  var contains = false
  for pI in polygon {
    if ( ((pI.y >= test.y) != (pJ.y >= test.y)) &&
    (test.x <= (pJ.x - pI.x) * (test.y - pI.y) / (pJ.y - pI.y) + pI.x) ){
          contains = !contains
    }
    pJ=pI
  }
  return contains
}

以下是您在 Playground 中的数组示例的结果：

contains(poly,Point(x:40,y:40))   -> true
contains(poly,Point(x:30,y:20))   -> false
contains(poly,Point(x:40,y:20))   -> true
contains(poly,Point(x:1,y:1))     -> true

Answer 5

swift中MKPolygon的简单扩展：

extension MKPolygon {
    func contain(coor: CLLocationCoordinate2D) -> Bool {
        let polygonRenderer = MKPolygonRenderer(polygon: self)
        let currentMapPoint: MKMapPoint = MKMapPoint(coor)
        let polygonViewPoint: CGPoint = polygonRenderer.point(for: currentMapPoint)
        if polygonRenderer.path == nil {
          return false
        }else{
          return polygonRenderer.path.contains(polygonViewPoint)
        }
    }
}