Mathematica Cookbook

Chapter 7. Three-Dimensional Graphics and Plots

Maybe I’ll win Saved by zero Holding onto Winds that teach me I will conquer Space around me

—The Fixx, “Saved by Zero”

7.0 Introduction

Modern mathematics demands advanced visualization tools. Although Mathematica’s 2D graphics are impressive, 3D graphics is where Mathematica really distinguishes itself. As with 2D, 3D graphics are represented symbolically but with the head Graphics3D instead of Graphics. There are 3D counterparts to most 2D plotting functions. For example, Plot3D and ListPlot3D are the counterparts to the 2D functions Plot and ListPlot. There are also many functions unique to 3D space, such as SphericalPlot3D and RevolutionPlot3D.

Mathematica’s 3D graphics are interactive, although it is difficult to illustrate this in book form! Any 3D plot or drawing can be rotated, flipped, and stretched, allowing you to see different perspectives. Furthermore, Mathematica 6 added a host of options for controlling lighting, camera placement, and even how light reflects off of surfaces (see 7.12 Controlling Viewing Geometry and 7.13 Controlling Lighting and Surface Properties).

The Symbolic Nature of Graphics

I think most users are quite impressed with the breadth and depth of what Mathematica 7 can achieve with plotting functions (see 7.1 Plotting Functions of Two Variables in Cartesian Coordinates through 7.9 Plotting 3D Regions Where a Predicate Is Satisfied). However, as a programmer, I am even more taken with what can be achieved ...