Graph3D: A Windows.Forms Render Control in C#

• Download Zip file (Sourcecode + Compiled Exe) - 580 kB - Version 26.may.2023

Features

• NEW: Resizing of 3D object when resizing 3D control
• NEW: Completely rewritten to allow display of multiple graphs at the same time
• NEW: Individual color scheme for each graph
• NEW: Surface plots can also be drawn as grid
• NEW: User messages can be drawn into the control
• NEW: Added scatter squares and triangles
• Copy Screenshot to Image
• Set Rho, Theta, Phi programmatically
• Drawing of scatterplots
• Coordinate system now also with negative values
• Universal ready-to-use 3D Graph control for System.Windows.Forms applications
• Derived from UserControl
• Target: Framework 4 (Visual Studio 2010 or higher)
• Display of 3 dimensional functions or binary data (X, Y, Z values)
• Very clean and reusable code written by an experienced programmer
• All code is in one single C# file with < 1200 lines
• Optional function compiler allows to enter formulas as strings
• Optional coordinate system with raster lines and labels
• Optionally multiple color schemes
• The user can rotate, elevate and zoom with the mouse or with 3 optional TrackBars
• Zooming is also possible with the mouse wheel, but only if the 3D Graph has the focus.
• The entire code is optimized for the maximum speed that is possible.
• An optional legend displays the current rotation angles to the user in the top left corner.
• An optional legend displays a user defined text for the axis in the bottom left corner.
• The black lines between the polygons can be turned off.
• Automatic normalization of 3D input data with 3 options

Why this Project?

I'am writing an ECU tunig software HUD ECU Hacker for which I need a 3D Viewer which displays the calibration tables.
I searched a ready-to-use 3D Control in internet but could not find what fits my needs.
Huge 3D software projects like Helix Toolkit are completely overbloated (220 MB) for my small project.
Commercial 3D software from $250 USD up to $2900 USD is also not an option.

WPF 3D Chart (from Jianzhong Zhang)

I found WPF 3D Chart on Codeproject.

It is very fast because WPF is based on ActiveX which uses hardware acceleration.
The graphics processor can render 3D surfaces which must be composed of triangles.
But it is difficult to render lines. Each line would have to be defined as 2 triangles.
I need lines for the coordinate system.
I also need lines which display discrete values on the 3D surface.
I want each value in a data table to be represented as a polygon on the 3D object.
The screenshot above shows the representation of a data table with 22 rows and 17 columns.
I found it too complicated to implement this in WPF.
Extra work must be done to integrate a WPF control into a Windows.Forms application. See this article.

Plot 3D (from Michal Brylka)

Then I found Plot 3D on Codeproject.
This is more what I'am looking for but the code is not reusable and has many issues.

It is one of these many projects on Codeproject or Github which the author never has finished, which are buggy and lack functionality.
There is no useful way to rotate the 3D object. Instead of specifying a rotation angle you must specify the 3D observer coordinates which is a complete misdesign.
After fixing this I found that rotation results in ugly drawing artifacts at certain angles.
The reason is that the polygons are not painted in the correct order.
The code has a bad performance because of wrong programming. For example in OnPaint() he creates each time 100 brushes and disposes them afterwards.
The code has been designed only for formulas but assigning fix values from a data table is not possible.

Graph3D (from me)

I ended up rewriting Plot 3D from the scratch, bug fixing and adding a lot of missing functionality.
The result is a UserControl which you can copy unchanged into your project and which you get working in a few minutes.
The features of my control are already listed above.
As my code does not use hardware acceleration the number of polygons that you display determines the drawing speed.
Without problem you can rotate and elevate the 3D objects of the demos in real time with the mouse without any delay. However if you want to render far more polygons it will be obviously slower.
For my purpose I need less than 2000 polygons which allows real time rotating with the mouse.
Download the ZIP file and then run the already compiled EXE file and play around with it and you will see the speed.

Demo: Surface Fill

The screenshot above shows the data from a data table with 22x17 values displayed as 3D surface with coordinate system.

int[,] s32_Values = new int[,]
{
    { 9059,   9634, 10617, 11141, ....., 15368, 15368, 15368, 15368, 15368 }, // row 1
    { 9684,  10387, 11141, 11796, ....., 15794, 15794, 15794, 15794, 15794 }, // row 2
    .........
    { 34669, 34210, 33653, 33096, ....., 27886, 26492, 25167, 25167, 25167 }, // row 21
    { 34767, 34210, 33718, 33096, ....., 27984, 26492, 25167, 25167, 25167 }  // row 22
};

Color[]      c_Colors = ColorSchema.GetSchema(eSchema.Rainbow);
cColorScheme i_Scheme = new cColorScheme(2, c_Colors);
cSurfaceData i_Data   = new cSurfaceData(eSurfaceMode.Fill, s32_Values.GetLength(0), s32_Values.GetLength(1), i_Scheme);

for (int C=0; C<i_Data.ms32_Cols; C++)
{
    for (int R=0; R<i_Data.ms32_Rows; R++)
    {
        double d_X = C *  10.0;
        double d_Y = R * 500.0;
        double d_Z = s32_Values[C,R] / 356.0;

        i_Data.SetPointAt(C, R,  d_X, d_Y, d_Z);
    }
}

graph3D.BeginUpdate();
graph3D.SetAxisLegends("MAP (kPa)", "Engine Speed (rpm)", "Volume Efficiency (%)");
graph3D.AddRenderData(i_Data);
graph3D.EndUpdate(eNormalize.Separate);

When you use discrete values for X,Y and Z which are not related like in this example make sure that X,Y and Z values are normalized separately by using the parameter eNormalize.Separate because the axes have different ranges.

Demo: Callback

Or you can write a C# callback function which calculates the Z values from the given X and Y values.

delRendererFunction f_Callback = delegate(double X, double Y)
{
    double r = 0.15 * Math.Sqrt(X * X + Y * Y);
    if (r < 1e-10) return 120;
    else           return 120 * Math.Sin(r) / r;
};

PointF k_Start = new PointF(-120, -80);
PointF k_End   = new PointF( 120,  80);
graph3D.BeginUpdate();
graph3D.AddFunctionPoints(f_Callback, k_Start, k_End, 5, eSurfaceMode.Fill, i_ColorScheme);
graph3D.EndUpdate(eNormalize.MaintainXYZ);

This code defines a modulated sinus function which is displayed on the X axis from -120 to +120 and on the Y axis from -80 to +80.
The fourth parameter (5) is the density which defines the count of polygons: (2* 120) / 5 + 1 = 49 polygons on the X axis and (2* 80) / 5 + 1 = 33 polygons for Y, which results in totally 1617 poygons.

When you use functions make sure that the relation between X,Y and Z values is not distorted by using the parameter eNormalize.MaintainXYZ.

Demo: Formula

Or you can let the user enter a string formula which will be compiled at run time:

String s_Formula = "12 * sin(x) * cos(y) / (sqrt(sqrt(x * x + y * y)) + 0.2)";

delRendererFunction f_Function = FunctionCompiler.Compile(s_Formula);

PointF k_Start = new PointF(-10, -10);
PointF k_End   = new PointF( 10,  10);

graph3D.BeginUpdate();
graph3D.AddFunctionPoints(f_Function, k_Start, k_End, 0.5, eSurfaceMode.Fill, i_ColorScheme);
graph3D.EndUpdate(eNormalize.MaintainXYZ);

Demo: Scatter Plot

Color[]      c_Colors = ColorSchema.GetSchema(eSchema.Rainbow);
cScatterData i_Data = new cScatterData(eScatterMode.Shapes, new cColorScheme(3, c_Colors));

for (double P = -22.0; P < 22.0; P += 0.1)
{
    double d_X = Math.Sin(P) * P;
    double d_Y = Math.Cos(P) * P;
    double d_Z = P;
    if (d_Z > 0.0) d_Z/= 3.0;

    i_Data.AddShape(d_X, d_Y, d_Z, eScatterShape.Circle, 3, null);
}

graph3D.BeginUpdate();
graph3D.AddRenderData(i_Data);
graph3D.EndUpdate(eNormalize.Separate);

Demo: Scatter Shapes

This demo shows negative values as red squares and positive values as green triangles.
The selected color scheme in the combobox is ignored.
Each point in this plot consists of 4 doubles: X,Y,Z and a value. The value defines the size of the square or triangle while X,Y,Z define the position.

Demo: Nested Graphs

This demo shows how to display 2 graphs at once.
It also shows how to add messages as a legend to the user.
The selected color scheme in the combobox is ignored.

const int POINTS = 8;
cSurfaceData i_Data1 = new cSurfaceData(eSurfaceMode.Lines, POINTS, POINTS, new cColorScheme(3, Color.Orange));
cSurfaceData i_Data2 = new cSurfaceData(eSurfaceMode.Lines, POINTS, POINTS, new cColorScheme(2, Color.Black));

for (int C=0; C<POINTS; C++)
{
    for (int R=0; R<POINTS; R++)
    {
        double d_X = (C - POINTS / 2.3) / (POINTS / 5.5);
        double d_Y = (R - POINTS / 2.3) / (POINTS / 5.5);
        double d_Radius = Math.Sqrt(d_X * d_X + d_Y * d_Y);
        double d_Z = Math.Cos(d_Radius) + 1.0;

        i_Data1.SetPointAt(C, R,  d_X, d_Y, d_Z);
        i_Data2.SetPointAt(C, R,  d_X, d_Y, d_Z * 0.6);
    }
}

cMessgData i_Mesg1 = new cMessgData("Graph with error data",   10, -10, Color.Orange);
cMessgData i_Mesg2 = new cMessgData("Graph with correct data", 10, -27, Color.Black);

graph3D.BeginUpdate();
graph3D.AddRenderData (i_Data1);
graph3D.AddRenderData (i_Data2);
graph3D.AddMessageData(i_Mesg1);
graph3D.AddMessageData(i_Mesg2);
graph3D.EndUpdate(eNormalize.MaintainXY);

Demo: Valentine

Well, this code has just been written on 14th february 2021.
Also here the selected color scheme in the combobox is ignored.

cColorScheme i_Scheme = new cColorScheme(5, Color.Red);
cScatterData i_Data   = new cScatterData(eScatterMode.Lines, i_Scheme);

// Upper (round) part of heart
double X = 0.0;
double Z = 0.0;
for (double P = 0.0; P <= Math.PI * 1.32; P += 0.025)
{
    X = Math.Cos(P) * 1.5 - 1.5;
    Z = Math.Sin(P) * 3.0 + 6.0;
    i_Data.AddLine( X, -X, Z, true,  null); // right side
    i_Data.AddLine(-X,  X, Z, false, null); // left  side
}

// Lower (linear) part of heart
double d_X = X / 70;
double d_Z = Z / 70;
while (Z >= 0.0)
{
    i_Data.AddLine( X, -X, Z, true,  null); // right side
    i_Data.AddLine(-X,  X, Z, false, null); // left  side
    X -= d_X;
    Z -= d_Z;
}

cMessgData i_Mesg = new cMessgData("Happy Valentine's day, Sweetheart!", -10, -10, Color.Red);

graph3D.BeginUpdate();
graph3D.AddRenderData(i_Data);
graph3D.AddMessageData(i_Mesg);
graph3D.EndUpdate(eNormalize.MaintainXYZ);