Game Development Reference

In-Depth Information

abc

def

ghi

to

abc
0

def

where (
tx
,
ty
,
tz
) is the translation in the
x
-,
y
- and
z
-axes respectively.

This technique requires us to add a component to the vector

representation of a vertex. Now a vertex is defined as [
x
,
y
,
z
, 1]
T
. Such

coordinates are often referred to as homogeneous coordinates. The

matrix can now include the perspective transform that converts world

coordinates into the 2D screen coordinates that the viewer ultimately

sees. By concatenating the above matrix with a matrix that achieves this

perspective transform, all the calculations necessary to take a vertex from

model space through world space to camera space and finally to screen

space can be achieved by a single matrix.

0

ghi

0

tx

ty

tz

1

Summary

The basic operations presented here will act as building blocks as we

develop the character animation engine. To get the most out of this topic,

you need to be confident of the use of vectors, matrix multiplication and

the simple algebra manipulation we used in this chapter. I have tried to

present the material in a form that is suitable for those who are unfamiliar

with mathematical set texts. If the reader wishes to explore the

mathematics presented in this chapter in more depth, then please check

Appendix C, where further references are mentioned.

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