## 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

Surface3DRenderer sr = new Surface3DRenderer(70, 35, 40,
0, 0, ClientRectangle.Width,
ClientRectangle.Height, 0.5, 0, 0);
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:

sr.RenderSurface(e.Graphics);

And this, whenever plotting area size changes:

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

## Copyright

## 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: