如何判断点是否位于含圆弧的2D多边形内？C#实现假阴性问题求解

我一直在参考相关资料尝试实现点是否在含圆弧的2D多边形内的判断逻辑，参考的核心内容方向包括：

• 无曲线的普通2D多边形点包含判断方法
• C#语言下复合多边形的点包含判断实现方案
• 曲线包含点判断的相关理论

我的方案采用光线投射法判断点是否在多边形边界内，以下是我结合参考资料编写的C#代码：

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;
}

注：代码中用到的GetPoint3dAt()方法来自AutoCAD .NET API。该方案对不含圆弧的多边形运行正常，但引入圆弧后，若点位于多边形周长范围内会产生假阴性结果。

我测试的多边形示例如下：

内容的提问来源于stack exchange，提问作者wisenickel