C# 如何检测多边形的角点？

我正在制作一个自动生成平面布置图的桌面应用程序。在本文中，首先我使用这种方法在点上绘制多边形

public void DrawPolygonPointF(PaintEventArgs e) {

// Create pen.
Pen blackPen = new Pen(Color.Black, 3);

// Create points that define polygon.
PointF point1 = new PointF(50.0F,  50.0F);
PointF point2 = new PointF(100.0F,  25.0F);
PointF point3 = new PointF(200.0F,   5.0F);
PointF point4 = new PointF(250.0F,  50.0F);
PointF point5 = new PointF(300.0F, 100.0F);
PointF point6 = new PointF(350.0F, 200.0F);
PointF point7 = new PointF(250.0F, 250.0F);
PointF[] curvePoints =
         {
             point1,
             point2,
             point3,
             point4,
             point5,
             point6,
             point7
         };

// Draw polygon curve to screen.
e.Graphics.DrawPolygon(blackPen, curvePoints);
}

注意：这些点不是实际点，它们仅用于演示目的。我正在从文本文件中读取点。

现在我需要生成一种特殊类型的网格。 在生成网格时，第一步是检测角点并延伸角线。 如何检测多边形的角点，以便进入生成网格的下一步

角落有标记。我需要在左侧水平延伸标有黑色的角，另一个在右侧延伸，直到它接触到线

附上一张截图

---

提前感谢

据我所知，您是在尝试延伸边缘，而不是角落。
程序可以是：

枚举边（每两个相邻点定义一条边）

对于每一条边，找出它是垂直的还是水平的（

abs（x1-x2）>abs（y1-y2）

）

确定边缘是否可以延伸，水平（左/右）和垂直（上/下）

布尔检查水平扩展性右（点[]曲线点，点角） { 返回曲线点.Any（cp=>cp.Y

---

据我所知，您是在尝试延伸边缘，而不是角落。
程序可以是：

枚举边（每两个相邻点定义一条边）

对于每一条边，找出它是垂直的还是水平的（

abs（x1-x2）>abs（y1-y2）

）

确定边缘是否可以延伸，水平（左/右）和垂直（上/下）

布尔检查水平扩展性右（点[]曲线点，点角） { 返回曲线点.Any（cp=>cp.Y

---

试试这个例子，看看你是否能适应它来解决你的问题

using System.Drawing;
using System.Windows.Forms;

namespace WindowsFormsApplication
{
    public partial class Form1 : Form
    {
        private struct LineSegment
        {
            private PointF _a, _b;

            public PointF A { get { return _a; } }
            public PointF B { get { return _b; } }

            public LineSegment(PointF a, PointF b)
            {
                _a = a; _b = b;
            }

            public float GetLengthSquared()
            {
                var dx = _a.X - _b.X;
                var dy = _a.Y - _b.Y;
                return dx * dx + dy * dy;
            }

            public bool RectContains(PointF a)
            {
                var x = a.X;
                var y = a.Y;
                var x1 = _a.X;
                var y1 = _a.Y;
                var x2 = _b.X;
                var y2 = _b.Y;
                return (x1 < x2 ? x1 <= x && x2 >= x : x2 <= x && x1 >= x) && (y1 < y2 ? y1 <= y && y2 >= y : y2 <= y && y1 >= y);
            }

            public bool ExtendToIntersectWith(LineSegment b)
            {
                var x1 = _a.X;
                var y1 = _a.Y;
                var x2 = _b.X;
                var y2 = _b.Y;

                var x3 = b._a.X;
                var y3 = b._a.Y;
                var x4 = b._b.X;
                var y4 = b._b.Y;

                var a1 = y2 - y1;
                var b1 = x1 - x2;
                var c1 = x1 * y2 - x2 * y1;

                var a2 = y4 - y3;
                var b2 = x3 - x4;
                var c2 = x3 * y4 - x4 * y3;

                var d = a1 * b2 - b1 * a2;
                if (d == 0)
                    return false;

                var x = (c1 * b2 - b1 * c2) / d;
                var y = (a1 * c2 - c1 * a2) / d;
                var p = new PointF(x, y);

                if (b.RectContains(p) && !RectContains(p))
                {
                    if (new LineSegment(_a, p).GetLengthSquared() < new LineSegment(_b, p).GetLengthSquared())
                        _a = p;
                    else
                        _b = p;
                    return true;
                }

                return false;
            }
        }

        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            PointF[] curvePoints =
            {
                /*
                new PointF(50.0F,  50.0F),
                new PointF(100.0F,  25.0F),
                new PointF(200.0F,   5.0F),
                new PointF(250.0F,  50.0F),
                new PointF(300.0F, 100.0F),
                new PointF(350.0F, 200.0F),
                new PointF(250.0F, 250.0F)
                */
                new PointF(30F,  10F),
                new PointF(60F,  10F),
                new PointF(60F,  20F),
                new PointF(90F,  20F),
                new PointF(90F,  60F),
                new PointF(10F,  60F),
                new PointF(10F,  40F),
                new PointF(30F,  40F),
            };
            int n = curvePoints.Length;
            LineSegment[] lineSegments = new LineSegment[n];
            int i = 0;
            for (; i < n - 1; ++i)
                lineSegments[i] = new LineSegment(curvePoints[i], curvePoints[i + 1]);
            lineSegments[i] = new LineSegment(curvePoints[i], curvePoints[0]);
            for (i = 0; i < n; ++i)
                for (int j = 0; j < n; ++j)
                    lineSegments[i].ExtendToIntersectWith(lineSegments[j]);
            for (i = 0; i < n; ++i)
            {
                var lineSegment = lineSegments[i];
                e.Graphics.DrawLine(Pens.Black, lineSegment.A, lineSegment.B);
            }
            //e.Graphics.DrawPolygon(Pens.Black, curvePoints);
        }
    }
}

使用系统图；
使用System.Windows.Forms；
命名空间Windows窗体应用程序
{
公共部分类Form1:Form
{
专用结构线段
{
私有点F_a，_b；
公共点f A{get{return{u A；}}
公共点B{get{return_B；}
公共线段（点F a、点F b）
{
_a=a；_b=b；
}
公共浮点GetLengthSquared（）
{
var dx=_a.X-_b.X；
变量dy=_a.Y-_b.Y；
返回dx*dx+dy*dy；
}
公共布尔值（点F a）
{
var x=a.x；
变量y=a.y；
var-x1=_a.X；
变量y1=_a.Y；
var x2=_b.X；
变量y2=_b.Y；
返回（x1

试试这个例子，看看你是否可以调整它来解决你的问题

using System.Drawing;
using System.Windows.Forms;

namespace WindowsFormsApplication
{
    public partial class Form1 : Form
    {
        private struct LineSegment
        {
            private PointF _a, _b;

            public PointF A { get { return _a; } }
            public PointF B { get { return _b; } }

            public LineSegment(PointF a, PointF b)
            {
                _a = a; _b = b;
            }

            public float GetLengthSquared()
            {
                var dx = _a.X - _b.X;
                var dy = _a.Y - _b.Y;
                return dx * dx + dy * dy;
            }

            public bool RectContains(PointF a)
            {
                var x = a.X;
                var y = a.Y;
                var x1 = _a.X;
                var y1 = _a.Y;
                var x2 = _b.X;
                var y2 = _b.Y;
                return (x1 < x2 ? x1 <= x && x2 >= x : x2 <= x && x1 >= x) && (y1 < y2 ? y1 <= y && y2 >= y : y2 <= y && y1 >= y);
            }

            public bool ExtendToIntersectWith(LineSegment b)
            {
                var x1 = _a.X;
                var y1 = _a.Y;
                var x2 = _b.X;
                var y2 = _b.Y;

                var x3 = b._a.X;
                var y3 = b._a.Y;
                var x4 = b._b.X;
                var y4 = b._b.Y;

                var a1 = y2 - y1;
                var b1 = x1 - x2;
                var c1 = x1 * y2 - x2 * y1;

                var a2 = y4 - y3;
                var b2 = x3 - x4;
                var c2 = x3 * y4 - x4 * y3;

                var d = a1 * b2 - b1 * a2;
                if (d == 0)
                    return false;

                var x = (c1 * b2 - b1 * c2) / d;
                var y = (a1 * c2 - c1 * a2) / d;
                var p = new PointF(x, y);

                if (b.RectContains(p) && !RectContains(p))
                {
                    if (new LineSegment(_a, p).GetLengthSquared() < new LineSegment(_b, p).GetLengthSquared())
                        _a = p;
                    else
                        _b = p;
                    return true;
                }

                return false;
            }
        }

        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            PointF[] curvePoints =
            {
                /*
                new PointF(50.0F,  50.0F),
                new PointF(100.0F,  25.0F),
                new PointF(200.0F,   5.0F),
                new PointF(250.0F,  50.0F),
                new PointF(300.0F, 100.0F),
                new PointF(350.0F, 200.0F),
                new PointF(250.0F, 250.0F)
                */
                new PointF(30F,  10F),
                new PointF(60F,  10F),
                new PointF(60F,  20F),
                new PointF(90F,  20F),
                new PointF(90F,  60F),
                new PointF(10F,  60F),
                new PointF(10F,  40F),
                new PointF(30F,  40F),
            };
            int n = curvePoints.Length;
            LineSegment[] lineSegments = new LineSegment[n];
            int i = 0;
            for (; i < n - 1; ++i)
                lineSegments[i] = new LineSegment(curvePoints[i], curvePoints[i + 1]);
            lineSegments[i] = new LineSegment(curvePoints[i], curvePoints[0]);
            for (i = 0; i < n; ++i)
                for (int j = 0; j < n; ++j)
                    lineSegments[i].ExtendToIntersectWith(lineSegments[j]);
            for (i = 0; i < n; ++i)
            {
                var lineSegment = lineSegments[i];
                e.Graphics.DrawLine(Pens.Black, lineSegment.A, lineSegment.B);
            }
            //e.Graphics.DrawPolygon(Pens.Black, curvePoints);
        }
    }
}

使用系统图；
使用System.Windows.Forms；
命名空间Windows窗体应用程序
{
公共部分类Form1:Form
{
专用结构线段
{
私有点F_a，_b；
公共点{