# Three-Dimensional Mathematica Graphics

### Extract from Mathematica Graphics: An Intensive Tutorial

#### by Tom Wickham-Jones

This HTML document is based on Mathematica Graphics: An Intensive Tutorial by Tom Wickham-Jones. It was adapted by Martin Kraus for non-commercial use.

Mathematica and MathLink are registered trademarks, and MathReader, MathSource and 3-Script are trademarks of Wolfram Research, Inc.

All other product names mentioned are trademarks of their producers.

Copyright 1992 by Wolfram Research, Inc.

All rights reserved. No part of this document may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright holder.

All three-dimensional Mathematica graphics in these notes are shown with the LiveGraphics3D Java applet. Therefore it is possible to rotate any of the graphics by dragging them. If a graphic is not displayed correctly, please try to reload the page. (Netscape users should keep the SHIFT-key pressed while clicking the reload button.)

## Introduction (36 KB)

### 1.1 Introduction to Mathematica

Mathematica is a computer system which integrates symbolic and numerical mathematics with powerful computer graphics. These are supported by a concise and flexible programming language. This first chapter consists of a brief description of Mathematica as a system and how to use it.

## Basic Graphics

### 2.4 Animation (100 KB)

This chapter looks at some of the simplest ways to obtain graphical output from Mathematica. If you are new to the system this is a good place to learn about Mathematica graphics. We first consider graphing of a funtion and move on to data plotting. This shows the basic types of images that Mathematica can create. Next we see how to change plots and work with the graphics options. This is followed by a look at some of the Mathematica graphics packages and the types of plots they provide. The chapter concludes with a brief look at animation.

## Graphics Output (20 KB)

### 3.2 Hardcopy Output

This chapter discusses the steps which are carried out when a Mathematica graphic is rendered. It first shows how the plotting commands construct primitives and produce a particular type of graphic. Then we see how the primitives are rendered into PostScript. This is followed with a discussion of the ways in which hardcopy output can be obtained.

## Chapter 4

### 4.3 Combining and Converting Images (102 KB)

This chapter describes more advanced graphics topics. The first section looks at primitives and directives for two- and three-dimensional graphics. We only look at some of the more complex primitives and directives and shall not review each of them. The following section discusses how to work with color and lighting in Mathematica graphics. The final section shows how to combine and convert pictures.

## Coordinate Systems

### 5.2 Three-Dimensional Coordinates (52 KB)

This chapter discusses the different coordinate systems which are used by Mathematica graphics. We see how Mathematica specifies coordinates. Then considerations specific to three-dimensional rendering are examined.

## Graphics Programming

### 6.4 Examples of Graphics Programming (18 KB)

This chapter provides an introduction to the use of graphics with the rest of the Mathematica system. First we quickly review programming in Mathematica. Then we consider building functions which draw on the power of the Mathematica system. This is followed by a discussion of animation. The chapter concludes with some examples of graphics programming.

 pages maintained by Martin Kraus