如何确定一个点是否在具有弧线的二维多边形内

问题描述

我一直在使用以下参考资料来尝试确定一个点是否在具有弧线的 2D 多边形内：

Is a point inside of 2D polygon,no curves

Is a point inside a compound polygon (C#)

Is a point inside a curve (Theory)

我的方法使用光线投射来确定一个点是否在多边形边界内。这是我尝试将引用串在一起的代码（C#）：

public static bool IsInsideBoundary(polyline pline,Point3d pnt,Document currentDoc)
    {
        try
        {
            if (pline.Closed == true)
            {
                Tools.Log("polyline is Closed");

                // Check if point is on the line -> WORKS
                if (IsPointOnCurve(pline,pnt))
                {
                    Log("Point is on the Boundary line");
                    return true;
                }
                else
                {
                    int numOfVerts = pline.NumberOfVertices;

                    // Get bounding Box of boundary
                    double minX = pline.GetPoint3dAt(0).X;
                    double maxX = pline.GetPoint3dAt(0).X;
                    double minY = pline.GetPoint3dAt(0).Y;
                    double maxY = pline.GetPoint3dAt(0).Y;

                    for (int i = 1; i < numOfVerts; i++)
                    {
                        Point3d q = pline.GetPoint3dAt(i);
                        minX = Math.Min(q.X,minX);
                        maxX = Math.Max(q.X,maxX);
                        minY = Math.Min(q.Y,minY);
                        maxY = Math.Max(q.Y,minY);
                    }

                    // Check if the given point outside of the bounding Box
                    if (pnt.X < minX || pnt.X > maxX || pnt.Y < minY || pnt.Y > maxY)
                    {
                        return false;
                    }
                    Log("Bounding Box check passed...");
                    bool inside = false;
                    for (int i = 0,j = numOfVerts - 1; i < numOfVerts; j = i++)
                    {
                        double a1 = pline.GetPoint3dAt(i).X,a2 = pline.GetPoint3dAt(i).Y;
                        double b1 = pnt.X,b2 = pnt.Y;
                        double c1 = pline.GetPoint3dAt(j).X,c2 = pline.GetPoint3dAt(j).Y;
                        // Use the Jordan Curve Theorem
                        double d1 = (c1 - a1) * (b2 - a2) / (c2 - a2) + a1;
                        
                        // Split arc into monotone parts and check bounds
                        if ((a2 > b2) != (c2 > b2) && b1 < d1)
                        {
                            inside = !inside;
                        }
                    }
                    Log("Point is within the boundary");
                    return inside;
                    
                }
            }
            else
            {
                Log("Boundary is not closed.");
            }
        }
        catch (System.Exception e)
        {
            Log("InsideBoundary() Failed. Exception: " + e.Message,true);
        }
        return false;
    }

请注意，我所做的一些调用（即 .GetPoint3dAt()）来自 AutoCAD .NET API。这种方法适用于任何没有弧的多边形，但是当引入弧并且该点位于多边形周长的边界内时，就会产生假阴性。

这是我正在测试的多边形示例：

如有任何帮助，将不胜感激，谢谢。

解决方法

我在 AutoDesk .NET 论坛中提出了这个问题并收到了这个解决方案： The Answer