c# - 如何在 C# 中绘制二维等高线图？

Question

我主要对能够将 Point3D[] 转换为可绘制的 gdi 线的算法感兴趣？

Answer 1

感谢@Anders Gustafsson，我能够构建一些东西:

public partial class FunctionGraph : UserControl
{
    private Rectangle _area = new Rectangle(-10, -10, 20, 20);

    private Func<float, float, float> _func;

    public FunctionGraph()
    {
        SetStyle(
            ControlStyles.UserPaint | ControlStyles.AllPaintingInWmPaint | ControlStyles.DoubleBuffer |
            ControlStyles.OptimizedDoubleBuffer |
            ControlStyles.ResizeRedraw, true);

        this.Padding.All=20;
        InitializeComponent();
    }


    public Rectangle Area
    {
        get { return _area; }
        set
        {
            _area = value;

            Invalidate();
        }
    }


    public Func<float, float, float> Function
    {
        get { return _func; }
        set
        {
            _func = value;
            Invalidate();
        }
    }


    public PointF GraphToClient(PointF p)
    {
        var xreal = this.ClientRectangle.Width - this.Padding.All * 2;
        var yreal = this.ClientRectangle.Height - this.Padding.All * 2;
         int n = (this.ClientRectangle.Width-this.Padding.All*2)/5;

            int m = (this.ClientRectangle.Height - this.Padding.All *2) / 5;

        return new PointF
                    {
                        X = this.Padding.All+p.X/ (xreal / (n * 5)),
                        Y = this.Padding.All + p.Y / (yreal / (m * 5))
                    };




    }

    protected override void OnPaint(PaintEventArgs e)
    {
        var graphics = e.Graphics;

        if (_func != null && !DesignMode&& Enabled)
        {

            float min = Single.MaxValue;

            float max = Single.MinValue;

            int n = (this.ClientRectangle.Width-this.Padding.All*2)/5;

            int m = (this.ClientRectangle.Height - this.Padding.All *2) / 5;

            var pts = new Point3F[n,m];

            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < m; j++)
                {




                    var xreal = this.ClientRectangle.Width - this.Padding.All * 2;
                    var yreal = this.ClientRectangle.Height - this.Padding.All * 2;


                    var pt=new Point3F(this.Padding.All+i * 5,this.Padding.All+ j * 5, _func((i * 5) * (xreal / (n * 5)), (j * 5) * (yreal / (m * 5))));

                    if (i == n-1)
                        pt.X = this.ClientRectangle.Width - this.Padding.All;
                    if(j==m-1)
                        pt.Y = this.ClientRectangle.Height - this.Padding.All;

                    pts[i, j] = pt;
                    if (pts[i, j].Z > max)
                        max = pts[i, j].Z;
                    if (pts[i, j].Z < min)
                        min = pts[i, j].Z;



                }

            }


            DrawContour(graphics, pts, min, max, 10);
            DrawColor(graphics, pts, min, max);

            var rect = this.ClientRectangle;

            rect.Inflate(-this.Padding.All+1,-this.Padding.All+1);

            ControlPaint.DrawBorder(graphics, rect, SystemColors.ControlDarkDark, ButtonBorderStyle.Dashed);

            int stepx = (this.ClientRectangle.Width - 2*this.Padding.All)/_area.Width;
            int stepy = (this.ClientRectangle.Height - 2 * this.Padding.All) / _area.Height;

            for (int i = _area.X; i < _area.Width; i++)
            {
              graphics.DrawString(i.ToString("0.0"),this.Font,Brushes.Black,this.Padding.All+(i-_area.X)*stepx,this.ClientRectangle.Height-this.Padding.All*0.75f);

            }
            using (var format = new StringFormat(StringFormatFlags.DirectionRightToLeft){Alignment = StringAlignment.Far})
            {
               // graphics.TranslateTransform(this.ClientRectangle.Width,0);
               // graphics.RotateTransform(90);

                for (int i = _area.Y; i < _area.Height; i++)
                {
                    graphics.DrawString(i.ToString("0.0"), this.Font, Brushes.Black, this.Padding.All*0.25f-this.Font.Size*0.5f
                        , this.ClientRectangle.Height-this.Padding.All- (i-_area.Y) * stepy,format);
                }
                graphics.ResetTransform();
            }
        }

        ControlPaint.DrawBorder(graphics, ClientRectangle, SystemColors.ActiveBorder, ButtonBorderStyle.Solid);
        base.OnPaint(e);
    }

    private struct Point3F
    {
        public float X { get; set; }
        public float Y { get; set; }
        public float Z { get; set; }


        public Point3F(float x,float y,float z) : this()
        {
            this.X = x;
            this.Y = y;
            this.Z = z;
        }

    }

    private static void DrawContour(Graphics g, Point3F[,] pts, float zmin, float zmax, int ncount)
    {
        using (var aPen = new Pen(Color.DimGray) {Width = 0.25f})
        {
            var pta = new PointF[2];


            var zlevels = new float[ncount];
            for (int i = 0; i < ncount; i++)
            {
                zlevels[i] = zmin + i*(zmax - zmin)/(ncount - 1);
            }
            int i0, i1, i2, j0, j1, j2;
            float zratio = 1; // Draw contour on the XY plane:
            for (int i = 0; i < pts.GetLength(0) - 1; i++)
            {
                for (int j = 0; j < pts.GetLength(1) - 1; j++)
                {
                    for (int k = 0; k < ncount; k++)
                    {
                        // Left triangle:
                        i0 = i;
                        j0 = j;
                        i1 = i;
                        j1 = j + 1;
                        i2 = i + 1;
                        j2 = j + 1;
                        if ((zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i1, j1].Z ||
                             zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i1, j1].Z) &&
                            (zlevels[k] >= pts[i1, j1].Z && zlevels[k] < pts[i2, j2].Z ||
                             zlevels[k] < pts[i1, j1].Z && zlevels[k] >= pts[i2, j2].Z))
                        {
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i1, j1].Z - pts[i0, j0].Z);
                            pta[0] =
                                new PointF(pts[i0, j0].X, (1 - zratio)*pts[i0, j0].Y + zratio*pts[i1, j1].Y);
                            zratio = (zlevels[k] - pts[i1, j1].Z)/(pts[i2, j2].Z - pts[i1, j1].Z);
                            pta[1] =
                                new PointF((1 - zratio)*pts[i1, j1].X + zratio*pts[i2, j2].X, pts[i1, j1].Y);
                            g.DrawLine(aPen, pta[0], pta[1]);
                        }
                        else if ((zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i2, j2].Z ||
                                  zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i2, j2].Z) &&
                                 (zlevels[k] >= pts[i1, j1].Z && zlevels[k] < pts[i2, j2].Z ||
                                  zlevels[k] < pts[i1, j1].Z && zlevels[k] >= pts[i2, j2].Z))
                        {
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i2, j2].Z - pts[i0, j0].Z);
                            pta[0] =
                                new PointF((1 - zratio)*pts[i0, j0].X + zratio*pts[i2, j2].X,
                                           (1 - zratio)*pts[i0, j0].Y + zratio*pts[i2, j2].Y);
                            zratio = (zlevels[k] - pts[i1, j1].Z)/(pts[i2, j2].Z - pts[i1, j1].Z);
                            pta[1] =
                                new PointF((1 - zratio)*pts[i1, j1].X + zratio*pts[i2, j2].X, pts[i1, j1].Y);
                            g.DrawLine(aPen, pta[0], pta[1]);
                        }
                        else if ((zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i1, j1].Z ||
                                  zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i1, j1].Z) &&
                                 (zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i2, j2].Z ||
                                  zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i2, j2].Z))
                        {
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i1, j1].Z - pts[i0, j0].Z);
                            pta[0] =
                                new PointF(pts[i0, j0].X, (1 - zratio)*pts[i0, j0].Y + zratio*pts[i1, j1].Y)
                                ;
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i2, j2].Z - pts[i0, j0].Z);
                            pta[1] =
                                new PointF(pts[i0, j0].X*(1 - zratio) + pts[i2, j2].X*zratio,
                                           pts[i0, j0].Y*(1 - zratio) + pts[i2, j2].Y*zratio);
                            g.DrawLine(aPen, pta[0], pta[1]);
                        } // right triangle:
                        i0 = i;
                        j0 = j;
                        i1 = i + 1;
                        j1 = j;
                        i2 = i + 1;
                        j2 = j + 1;
                        if ((zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i1, j1].Z ||
                             zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i1, j1].Z) &&
                            (zlevels[k] >= pts[i1, j1].Z && zlevels[k] < pts[i2, j2].Z ||
                             zlevels[k] < pts[i1, j1].Z && zlevels[k] >= pts[i2, j2].Z))
                        {
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i1, j1].Z - pts[i0, j0].Z);
                            pta[0] =
                                new PointF(pts[i0, j0].X*(1 - zratio) + pts[i1, j1].X*zratio, pts[i0, j0].Y);
                            zratio = (zlevels[k] - pts[i1, j1].Z)/(pts[i2, j2].Z - pts[i1, j1].Z);
                            pta[1] =
                                new PointF(pts[i1, j1].X, pts[i1, j1].Y*(1 - zratio) + pts[i2, j2].Y*zratio);
                            g.DrawLine(aPen, pta[0], pta[1]);
                        }
                        else if ((zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i2, j2].Z ||
                                  zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i2, j2].Z) &&
                                 (zlevels[k] >= pts[i1, j1].Z && zlevels[k] < pts[i2, j2].Z ||
                                  zlevels[k] < pts[i1, j1].Z && zlevels[k] >= pts[i2, j2].Z))
                        {
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i2, j2].Z - pts[i0, j0].Z);
                            pta[0] =
                                new PointF(pts[i0, j0].X*(1 - zratio) + pts[i2, j2].X*zratio,
                                           pts[i0, j0].Y*(1 - zratio) + pts[i2, j2].Y*zratio);
                            zratio = (zlevels[k] - pts[i1, j1].Z)/(pts[i2, j2].Z - pts[i1, j1].Z);
                            pta[1] =
                                new PointF(pts[i1, j1].X, pts[i1, j1].Y*(1 - zratio) + pts[i2, j2].Y*zratio);
                            g.DrawLine(aPen, pta[0], pta[1]);
                        }
                        else if ((zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i1, j1].Z ||
                                  zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i1, j1].Z) &&
                                 (zlevels[k] >= pts[i0, j0].Z && zlevels[k] < pts[i2, j2].Z ||
                                  zlevels[k] < pts[i0, j0].Z && zlevels[k] >= pts[i2, j2].Z))
                        {
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i1, j1].Z - pts[i0, j0].Z);
                            pta[0] =
                                new PointF(pts[i0, j0].X*(1 - zratio) + pts[i1, j1].X*zratio, pts[i0, j0].Y);
                            zratio = (zlevels[k] - pts[i0, j0].Z)/(pts[i2, j2].Z - pts[i0, j0].Z);
                            pta[1] =
                                new PointF(pts[i0, j0].X*(1 - zratio) + pts[i2, j2].X*zratio,
                                           pts[i0, j0].Y*(1 - zratio) + pts[i2, j2].Y*zratio);
                            g.DrawLine(aPen, pta[0], pta[1]);
                        }
                    }
                }
            }
        }
    }

    private static Color GetColor(float value, float maxValue, float minValue)
    {
        // Convert into a value between 0 and 1023.
        int int_value = (int) (1023*(value - maxValue)/(minValue - maxValue));

        // Map different color bands.
        if (int_value < 256)
        {
            // Red to yellow. (255, 0, 0) to (255, 255, 0).
            return Color.FromArgb(255, int_value, 0);
        }
        else if (int_value < 512)
        {
            // Yellow to green. (255, 255, 0) to (0, 255, 0).
            int_value -= 256;
            return Color.FromArgb(255 - int_value, 255, 0);
        }
        else if (int_value < 768)
        {
            // Green to aqua. (0, 255, 0) to (0, 255, 255).
            int_value -= 512;
            return Color.FromArgb(0, 255, int_value);
        }
        else
        {
            // Aqua to blue. (0, 255, 255) to (0, 0, 255).
            int_value -= 768;
            return Color.FromArgb(0, 255 - int_value, 255);
        }
    }

    private static void DrawColor(Graphics g, Point3F[,] pts, float zmin, float zmax)
    {          
        var pta = new PointF[4];

        for (int i = 0; i < pts.GetLength(0) - 1; i++)
        {
            for (int j = 0; j < pts.GetLength(1) - 1; j++)
            {
                pta[0] = new PointF(pts[i, j].X, pts[i, j].Y);
                pta[1] = new PointF(pts[i, j + 1].X, pts[i, j + 1].Y);
                pta[2] = new PointF(pts[i + 1, j + 1].X, pts[i + 1, j + 1].Y);
                pta[3] = new PointF(pts[i + 1, j].X, pts[i + 1, j].Y);
                using (var aBrush = new SolidBrush(Color.FromArgb(200, GetColor(pts[i, j].Z, zmin, zmax))))
                {
                    g.FillPolygon(aBrush, pta);
                }
            }
        }
    }