Game Development Reference
In-Depth Information
Chapter 3
Multiple Coordinate Spaces
The boundary lines have fallen for me in pleasant places;
surely I have a delightful inheritance.
— Psalm 16:6 (New International Version)
Chapter 1 discussed how we can establish a coordinate space anywhere we
want simply by picking a point to be the origin and deciding how we want
the axes to be oriented. We usually don't make these decisions arbitrarily;
we form coordinate spaces for specific reasons (one might say “different
spaces for different cases”). This chapter gives some examples of common
coordinate spaces that are used for graphics and games. We will then
discuss how coordinate spaces are nested within other coordinate spaces.
This chapter introduces the idea of multiple coordinate systems. It is
divided into five main sections.
•
Section 3.1
justifies the need for multiple coordinate systems.
•
Section 3.2
introduces some common coordinate systems. The main
concepts introduced are
◦
world space
◦
object space
◦
camera space
◦
upright space
•
Section 3.3
describes coordinate-space transformations.
◦
Section 3.3.1
exposes a duality between two ways of thinking
about coordinate-space transformations.
◦
Section 3.3.2
describes how to specify one coordinate system in
terms of another.
◦
Section 3.3.3
discusses the very important concept of basis vec-
tors.
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