c# - 如何识别多边形是wpf中的三角形

Question

我有 'n' 个多边形，如下所示。

    <Polygon Points="544,245,544,175,568,175,568,175" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="2,223,96,223,96,153,96,153" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="350,315,350,333,306,333,306,395,306,395" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="164,53,160,53,160,51,160,55,160,55" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="264,63,264,58,264,68,264,63,267,63,267,60,267,66,267,63,270,63,270,58,270,68,270,68" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="8,63,444,63,444,168,444,168" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="212,169,212,93,285,93,285,63,285,63" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="26,93,127,93,127,148,29,148,29,148" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="152,116,152,132,212,132,212,132" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="121,316,121,333,70,333,70,366,70,366" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="464,395,488,395,488,284,527,284,527,284" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="168,63,168,67,180,59,180,67,168,59,168,59" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="173,62,173,56,165,56,165,51,175,51,175,61,175,61" Stroke="Black" StrokeThickness="1" />
    <Polygon Points="3,285,121,285,121,316,211,316,211,304,211,304" Stroke="Black" StrokeThickness="1" />

请帮我辨别这些多边形中的三角形是什么

我试过像下面这样识别顶点..

        Polygon polygon = new Polygon();
        polygon.Points = new System.Windows.Media.PointCollection()
        {
            new Point(446,134),
            new Point(442,134),
            new Point(444,140),
            new Point(444,140),
        }; 

        List<double> verticesPoints = new List<double>();
        for (int i = 0; i < polygon.Points.Count - 1; i++)
        {
            var point1 = polygon.Points[i];
            var point2 = polygon.Points[i + 1];

            //calculate delta x and delta y between the two points
            var deltaX = Math.Pow((point2.X - point1.X), 2);
            var deltaY = Math.Pow((point2.Y - point1.Y), 2);

            //pythagras theorem for distance
            var distance = Math.Sqrt(deltaY + deltaX);

            //distance is zero..then same point
            if (distance != 0)
            {
                verticesPoints.Add(distance);
            }
        }
       ///Here is the code to calculate angle and consider the triangle
       ///three vertices then it might be triangle.
        if (verticesPoints.Count == 3)
        {
            ///use The Law of Cosines
            ///cos(C) = a2 + b2 − c2 /2ab
            ///cos(A) = b2 + c2 − a2 /bc
            ///cos(B) = c2 + a2 − b2 /ca
            var a = ((Math.Pow(verticesPoints[1], 2)) + (Math.Pow(verticesPoints[2], 2)) - (Math.Pow(verticesPoints[0], 2)))
                      / (2 * verticesPoints[1] * verticesPoints[2]);

            var b = ((Math.Pow(verticesPoints[0], 2)) + (Math.Pow(verticesPoints[2], 2)) - (Math.Pow(verticesPoints[1], 2)))
                     / (2 * verticesPoints[0] * verticesPoints[2]);

            var c = ((Math.Pow(verticesPoints[0], 2)) + (Math.Pow(verticesPoints[1], 2)) - (Math.Pow(verticesPoints[2], 2)))
                     / (2 * verticesPoints[0] * verticesPoints[1]);

            ///Inverse of cos
            var radians1 = Math.Acos(a);
            ///Convert radian to degree
            double degrees1 = (radians1 * 180.0) / Math.PI;

            ///Inverse of cos
            var radians2 = Math.Acos(b);
            //Convert radian to degree
            double degrees2 = (radians2 * 180.0) / Math.PI;

            ///Inverse of cos
            var radians3 = Math.Acos(c);
            ///Convert radian to degree
            double degrees3 = (radians3 * 180.0) / Math.PI;

            var totalDegrees = degrees1 + degrees2 + degrees3;
            if (totalDegrees == 180)
            {
               // Consider triangle
            }
        }

但上面的代码不适用于 <Polygon Points="446,134,442,134,444,140,444,140" Stroke="Black" StrokeThickness="1" />它只给出了两个顶点，但它是一个三角形，有些情况下有 3 个顶点，但 totalDegrees 不是 180

Answer 1

这里的代码遍历点并计算它们之间的梯度。如果两个连续点的梯度相同，则它们必须在同一直线上，因此 noOfPoints 不会递增，否则会递增。

第一个梯度存储在 firstGradient 中，以检查连接最后一个点和第一个点的梯度是否与第一个点和第二个点之间的梯度相同。

        Polygon polygon = new Polygon();
        polygon.Points = new System.Windows.Media.PointCollection()
    {
        new Point(446,134),
        new Point(442,134),
        new Point(444,140),
        new Point(444,140),
    };

        List<double> verticesPoints = new List<double>();
        double? firstGradient = null;
        double? gradient = null;
        double? newGradient = null;
        int noOfSides = 1;

        for (int i = 0; i < polygon.Points.Count - 1; i++)
        {
            var point1 = polygon.Points[i];
            var point2 = polygon.Points[i + 1];

            if(point1 == point2) { continue;}

            //calculate delta x and delta y between the two points
            var deltaX = point2.X - point1.X;
            var deltaY = point2.Y - point1.Y;

            //calculate gradient
            newGradient = (deltaY / deltaX);

            if (i == 0)
            {
                firstGradient = newGradient;
            }

            if ((gradient != newGradient) && (i != polygon.Points.Count - 2))
            {
                noOfSides++;
            }
            else if (i == polygon.Points.Count - 2)
            {
                if ((gradient != newGradient) && (firstGradient != newGradient)) //This now checks the gradient between the last and first point.
                {

                    point1 = polygon.Points[i+1];
                    point2 = polygon.Points[0];

                    if (point1 == point2) { continue; }

                    //calculate delta x and delta y between the two points
                    deltaX = point2.X - point1.X;
                    deltaY = point2.Y - point1.Y;

                    //calculate gradient
                    newGradient = (deltaY / deltaX);

                    if(newGradient != firstGradient)
                    {
                        noOfSides++;
                    }

                }


            gradient = newGradient;
        }