Graphics and Animations

Preface

To many users, one of the most important uses of computer algebra is exploration of mathematical structures and for this, often the prime tool is visualization. MuPAD® offers an extensive library for this purpose, which is described in the present paper.

This library is used for creating graphics in two and three dimensions, animated or still. In the following pages, we have tried to give you a thorough introduction to the many features available and to show you how to easily create beautiful graphics – we certainly hope you will also find them useful and informative.

When browsing the table of contents, do not despair: While there are over 100 “object types” and more than 400 “attributes,” most of the time you will only need a tiny fraction of all this. Many special features are only there for when you really need them, with what we hope are meaningful default settings for when you don't.

To help you find out which parts you may actually need, we have provided an extensive introduction you will find right after the Gallery, which follows this chapter. This introduction covers all topics from basic ideas up to exporting animations ready for web publishing and handling problems related to special or unusual OpenGL® drivers. Furthermore, all object descriptions and the explanations for each attribute are amply illustrated with examples where you may find a lot of MuPAD inputs ready to be changed and tweaked to your needs. Every object description contains a list of all the parameters you need, and each attribute description lists all the objects that react to this attribute, including the default settings. In general, examples go from the easy to the advanced usage and try to cover a broad range of applications.

Gallery

Introduction

Easy Plotting: Graphs of Functions

Advanced Plotting: Principles and First Examples

The Full Picture: Graphical Trees

Viewer, Browser, and Inspector: Interactive Manipulation

Primitives

Attributes

Colors

Layout of Canvas and Scenes

Animations

Groups of Primitives