Graphics Reference
In-Depth Information
Chapter 14
and Representations
The real world contains too much detail for us to simulate it efficiently from first
principles of physics and geometry. Mathematical models of the real world and
the data structures and algorithms that implement them are always approxima-
tions. These approximations make graphics computationally tractable but intro-
duce restrictions and error. The models and approximations are both geometric
and algorithmic. For example, a ball is a simple geometric model of an orange.
A simple computational model of light interaction might specify that the light
passing through glass does not refract or lose energy.
In this chapter, we survey some pervasive approximations and their limita-
tions. This chapter brings together a number of key assumptions about models
and data structures for representing them that are implicit in the rest of the topic
and throughout graphics. It contains some of the engineering conventional wisdom
and practical mathematical techniques accumulated over the past 50 years of com-
puter graphics. It is what you need to know to apply your existing mathematics
and computer science knowledge to computer graphics as it is practiced today. In
order to quickly communicate a breadth of material, we'll stay relatively shallow
on details. Where there are deep implications of choosing a particular approxima-
tion, a later chapter on each particular topic will explain those implications with
more nuance. To keep the text modular (and save you a lot of flipping), there is
some duplication of ideas from both prior and succeeding chapters, and we've
used some terms and units that have not yet been introduced, like steradians, but
whose precise details don't matter in a first reading at this stage.
The code samples in this chapter are based on the freely available OpenGL
API (
http://opengl.org)
and G3D Innovation Engine library (
http://g3d.sf.net)
. We
recommend examining the details in the documentation for those or equivalent
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