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Posted 21 Feb 2007

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# Plot 3D surfaces

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Simply render a 3D surface on your screen without OpenGL/DirectX.

## Introduction

This article describes a simple method of rendering 3D surfaces on a 2D plane. It doesn't use OpenGL or DirectX or stuff like that. It just utilizes the power of the CPU. Simplicity has, of course, its price - the rendering process isn't as fast as when using hardware acceleration.

Its application varies from simply admiring beautiful 3D surfaces to data visualization purposes, to stuff whatever one needs. I've used it in programs written for courses of Optimization Methods, Identification, Calculus (Mathematical Analysis), and Dimensional Analysis.

## Properties

• `Density` - Size of the spanning mesh.
• `PenColor` - Color of the drawing pen. Used to draw meshes.
• `StartPoint` - Plotting start point.
• `EndPoint` - Plotting end point.
• `Function` - Function used to calculate surface vertices.
• `ColorSchema` - Color schema assigned to mesh.

## Methods

• `ReCalculateTransformationsCoeficients` - Recalculates transformations' coefficients on the basis of new parameters.
• `Project` - Performs projection. Calculates screen coordinates for the 3D point.
• `RenderSurface` - Main method. Render the surface on given graphics.

## Points of Interest

Additional classes `ColorSchema` and `CompiledFunction` are interesting parts of the code. The first one encapsulates an array of `Color` entries. It has some predefined color palettes. The other one compiles a given formula to a function delegate, providing simple parser services.

## Usage

C#
```Surface3DRenderer sr = new Surface3DRenderer(70, 35, 40,
0, 0, ClientRectangle.Width,
ClientRectangle.Height, 0.5, 0, 0);
//new hue-based palette
sr.ColorSchema = new ColorSchema(120);
sr.SetFunction("sin(x1)*cos(x2)/(sqrt(sqrt(x1*x1+x2*x2))+1)*10");```

Use this to actually render something:

C#
`sr.RenderSurface(e.Graphics);`

And this, whenever plotting area size changes:

C#
```sr.ReCalculateTransformationsCoeficients(70, 35, 40, 0, 0,
ClientRectangle.Width, ClientRectangle.Height, 0.5, 0, 0);```

## History

• 22.02.2007 - first version.
• 23.02.2007 - sample images added.

## Sample (application)

Below, I'm publishing screenshots from an application that was written for my academic course of Optimization Methods (finding the minimum/maximum of functions). Labels are in Polish, but I hope that they are self-explaining.

Entering the formula:

Finding functions' minimum using the Greatest Slope method:

A list of licenses authors might use can be found here

## Share

 Architect Nokia Siemens Networks Poland
Michał is C# and whole .NET enthusiast. He graduated from computer science MSc studies at Wroclaw University of Technology, Poland.

He is interested in photography and diving. He is member of PADI, currently with divemaster certificate.

His favorite movies are Matrix, Amélie(Le Fabuleux Destin d'Amélie Poulain), Stargate SG-1 TV Serie and comedies of Mel Brooks.

Michał lives in Wroclaw, Poland. To contact Michał, email him at michal.brylka[mail-'"at'"-sign]op.pl.

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 This project is obsolete since today: A completely rewritten code is available now. Elmue4-Feb-21 7:15 Elmue 4-Feb-21 7:15
 Since many years this project did not get any update although there are several issues and a severe bug. Issues: Rotation is not implemented. Specifying 3D observer coordinates is a misdesign. The drawing has a bug which results in artifacts when rotating. When looking the 3D surface from the bottom it seems to be reversed. The drawing is slow because the code is not optimized for maximum speed. Only support for functions is implemented. Specifying 3D data from another data source is not possible. The code is just a demo. It cannot be reused in another project. I found it also very strange that formulas use variables x1 and x2 instead of x and y. Missing features: People ask here in the comments for features: The 3D surface cannot be moved, rotated, etc with the mouse. Axis and coordinate system are not implemented. A completely new project Therefore I invested a week to rewrite this project from the scratch. Form the original code nearly nothing is left. I fixed the bugs and added lots a of new features and cleaned up the code. I wrote a completely reusable Control which you can integrate easily into your application. In a few minutes you will get it working. It is lightning fast if you use up to 3000 polygons. You can rotate the 3D surface with the mouse without any delay. The completely rewritten version of this project can be found here: Windows.Forms 3D Graph Render Control in C#modified 4-Feb-21 13:23pm.
 Would you have VB.Net (VB2008) Member 837876926-Jun-15 0:01 Member 8378769 26-Jun-15 0:01
 3D Radio Wave Plot in space Member 232111821-Jan-15 9:44 Member 2321118 21-Jan-15 9:44
 3D line plot? DEGT13-Dec-14 9:13 DEGT 13-Dec-14 9:13
 nice, may be just what i'm after.. ibyk301-May-13 6:43 ibyk30 1-May-13 6:43
 Re: nice, may be just what i'm after.. ibyk303-May-13 4:57 ibyk30 3-May-13 4:57
 Re: Too many issues and bugs Elmue4-Feb-21 6:54 Elmue 4-Feb-21 6:54
 My vote of 5 ibyk301-May-13 6:28 ibyk30 1-May-13 6:28
 My vote of 5 victorbos4-Apr-13 14:18 victorbos 4-Apr-13 14:18
 How to achieve same grid effect as on second screenshot apaka31-Oct-12 22:14 apaka 31-Oct-12 22:14
 sr is null before initialization in mono j1s1e129-Oct-12 17:55 j1s1e1 29-Oct-12 17:55
 Adding mouse interaction xfx27-Mar-12 20:06 xfx 27-Mar-12 20:06
 Re: Adding mouse interaction Michal Brylka5-Apr-12 1:27 Michal Brylka 5-Apr-12 1:27
 Re: Adding mouse support Elmue4-Feb-21 6:51 Elmue 4-Feb-21 6:51
 My vote of 5 Manoj Kumar Choubey26-Feb-12 21:50 Manoj Kumar Choubey 26-Feb-12 21:50
 While obsX smaller than 0 transparency5-Apr-11 23:13 transparency 5-Apr-11 23:13
 Re: Drawing artifacts Elmue4-Feb-21 6:47 Elmue 4-Feb-21 6:47
 user interaction now7864-Apr-11 11:09 now786 4-Apr-11 11:09
 Excellent library; license question sirkne12322-Sep-09 8:35 sirkne123 22-Sep-09 8:35
 I can,t calculate the beginings coordinates of 3d plot artem0055-Apr-09 20:36 artem005 5-Apr-09 20:36
 Re: I can,t calculate the beginings coordinates of 3d plot Michal Brylka2-Sep-09 9:14 Michal Brylka 2-Sep-09 9:14
 Re: I can,t calculate the beginings coordinates of 3d plot artem0053-Sep-09 4:51 artem005 3-Sep-09 4:51
 Transformations Linuxman14-Jan-09 2:15 Linuxman 14-Jan-09 2:15
 Re: Rotation angle instead of observer coordinates Elmue4-Feb-21 6:43 Elmue 4-Feb-21 6:43
 Question about 3D graphic johndoelee1-Apr-08 5:30 johndoelee 1-Apr-08 5:30
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