The Use of Projective Geometry in Computer Graphics

The ultimate goal of all 3D graphics systems is to render 3D
objects on a two-dimensional surface such as plotter output
or a workstation screen. The approach adopted by most
graphics systems is to perform a central or parallel
projection of the objects onto the view surface. These
systems have to make use of the mathematical results of
projective geometry.
This monograph has as its aim the derivation of a framework
for analyzing the behavior of projective transformations in
graphics systems. It is shown that a mathematically precise
description of the projective geometrical nature of a
graphics system leads not only to a deeper understanding of
the system but also to new approaches which result in faster
or more precise algorithms.
A further aim of the book is to show the importance of
advanced mathematics for computer science. Many problems
become easier to describe or to solve when the appropriate
mathematical tools are used. The author demonstrates that
projective geometry has a major role to play in computer
graphics.