在正多边形的每条边上绘制三角形

Question

我曾尝试在正多边形的每条边上绘制三角形。

到目前为止，我已经制作了这样的多边形：

我要做的是多边形每个边缘上的那个小三角形：

我该怎么做？

如何绘制多边形的代码如下：

int sides = 5;
Graphics g = e.Graphics;
nPoints = CalculateVertices(sides, radius, angle, center);

g.DrawPolygon(navypen, nPoints);
g.FillPolygon(BlueBrush, nPoints);
Point center = new Point(ClientSize.Width / 2, ClientSize.Height / 2);

for(int i = 0; i < sides; i++) {
     g.DrawLine(new Pen(Color.Navy), center.X, center.Y, nPoints[i].X, nPoints[i].Y);

}

private PointF[] CalculateVertices(int sides, int radius, float startingAngle, Point center)
{
    if (sides < 3) {
        sides = 3;
    }
        //throw new ArgumentException("Polygon must have 3 sides or more.");

    List<PointF> points = new List<PointF>();
    float step = 360.0f / sides;

    float angle = startingAngle; //starting angle
    for (double i = startingAngle; i < startingAngle + 360.0; i += step) //go in a circle
    {
        points.Add(DegreesToXY(angle, radius, center));
        angle += step;
    }

    return points.ToArray();
}

private PointF DegreesToXY(float degrees, float radius, Point origin)
{
    PointF xy = new PointF();
    double radians = degrees * Math.PI / 180.0;

    xy.X = (int)(Math.Cos(radians) * radius + origin.X);
    xy.Y = (int)(Math.Sin(-radians) * radius + origin.Y);

    return xy;
}

Answer 1

试试这个...而不是计算三角形的绝对点，而是计算原点的“单位三角形”的点（使用你的函数！）。然后我只需旋转和移动图形表面并在我想要的位置绘制单位三角形：

public partial class Form1 : Form
{

    public Form1()
    {
        InitializeComponent();
    }

    private PointF[] nPoints;
    private PointF[] triangle;

    private int sides = 5;
    private int angle = 0;
    private int radius = 100;
    private int triangleLength = 10;

    private void Form1_Load(object sender, EventArgs e)
    {
        triangle = this.CalculateVertices(3, triangleLength, 0, new Point(0, 0)); // this "unit triangle" will get reused!
    }

    private void Form1_Paint(object sender, PaintEventArgs e)
    {

        Graphics g = e.Graphics;
        Point center = new Point(ClientSize.Width / 2, ClientSize.Height / 2);
        nPoints = CalculateVertices(sides, radius, angle, center);

        // draw the polygon
        g.FillPolygon(Brushes.Blue, nPoints);
        g.DrawPolygon(Pens.Black, nPoints);                  
        for (int i = 0; i < sides; i++)
        {
            g.DrawLine(Pens.Black, center.X, center.Y, nPoints[i].X, nPoints[i].Y);

        }

        // draw small triangles on each edge:
        float step = 360.0f / sides;
        float curAngle = angle + step / 2; // start in-between the original angles
        for (double i = curAngle; i < angle + (step / 2) + 360.0; i += step) //go in a circle
        {
            // move to the center and rotate:
            g.ResetTransform();
            g.TranslateTransform(center.X, center.Y);
            g.RotateTransform((float)i);

            // move out to where the triangle will be drawn and render it
            g.TranslateTransform(radius, 0);
            g.FillPolygon(Brushes.LightGreen, triangle);
            g.DrawPolygon(Pens.Black, triangle);
        }
    }

    // this is your code unchanged
    private PointF[] CalculateVertices(int sides, int radius, float startingAngle, Point center)
    {
        if (sides < 3)
        {
            sides = 3;
        }
        //throw new ArgumentException("Polygon must have 3 sides or more.");

        List<PointF> points = new List<PointF>();
        float step = 360.0f / sides;

        float angle = startingAngle; //starting angle
        for (double i = startingAngle; i < startingAngle + 360.0; i += step) //go in a circle
        {
            points.Add(DegreesToXY(angle, radius, center));
            angle += step;
        }

        return points.ToArray();
    }

    // this is your code unchanged
    private PointF DegreesToXY(float degrees, float radius, Point origin)
    {
        PointF xy = new PointF();
        double radians = degrees * Math.PI / 180.0;

        xy.X = (int)(Math.Cos(radians) * radius + origin.X);
        xy.Y = (int)(Math.Sin(-radians) * radius + origin.Y);

        return xy;
    }

}