Mathematica Demystified
Simple enough for a beginner, but challenging enough for an advanced user, this hands-on guide takes you from your very first calculation all the way to plotting complex fractals in Mathematica.
TABLE OF CONTENTS Mathematica Demystified
Chapter 6: Three-Dimensional Graphics
In Chap. 2, we saw how to plot a variety of two-dimensional objects. Almost all of the functions that were discussed there have a version that works similarly for three-dimensional objects. In this chapter we'll see how to plot curves and surfaces in three-dimensional space as well as other kinds of objects.
6.1 The Plot3D Function
Let's start with the Plot3D function which is the analog of the Plot function. We can use Plot3D to plot the graph of a two-variable function in three-dimensional space. Example 6.1.1 shows the graph of the function x 2 + y 2. The syntax for Plot3D is very similar to that of its two-dimensional cousin Plot. The first argument is the function that we want to plot the graph of, in this case x 2 + y 2. But now there are two independent variables, x and y, so the next thing we must tell Mathematica is the domain of each variable. We do this with the two lists { x, ?2, 2} and { y, ? 2, 2}. Mathematica draws a picture of the graph in perfect perspective as seen from a point called the ViewPoint. (Check out ViewPoint in the Help Files. You'll find that you can easily change this parameter, and hence the view of the object.) It also shades the surface and hides parts from view should one...
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