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Hughes/Computer Graphics, 3/E by Steven K. Feiner, Andries van Dam, John F. Hughes, Morgan McGuire, David F. Sklar, James D. Foley, Kurt Akeley

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Chapter 11. Transformations in Three Dimensions

11.1. Introduction

Transformations in 3-space are in many ways analogous to those in 2-space.

• Translations can be incorporated by treating three-dimensional space as the subset E3 defined by w = 1 in the four-dimensional space of points (x, y, z, w). A linear transformation whose matrix has the form Image, when restricted to E3, acts as a translation by [a b c]T on E3.

• If T is any continuous transformation that takes lines to lines, and O denotes the origin of 3-space, then we can define

Image

and the result ...

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