I'm mainly interested in algorithm which would enable me to convert Point3D[] into drawable gdi lines?
Thanks to @Anders Gustafsson I was able to build something:
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);
}
}
}
}