Transformations - Transformations and Projections in Computer Graphics - page 33

y

z

Left-handed

z

Right-handed

x

(a)

y

y

Object

Object

z x

z

Observer

Observer

x

(c) Right-handed

(b) Left-handed

Figure 1.18: Three-Dimensional Coordinate Systems.

Principle: Express co-ordinate ideas in similar form.
This principle, that of parallel construction, requires that expressions of similar con-
tent and function should be outwardly similar. The likeness of form enables the reader
to recognize more readily the likeness of content and function. Familiar instances from
the Bible are the Ten Commandments, the Beatitudes, and the petitions of the Lord's
Prayer.

—W. Strunk Jr. and E. B. White, The Elements of Style

1.4 Three-Dimensional Transformations

We develop three-dimensional transformations by extending the methods used in two-
dimensional transformations, especially the concept of homogeneous coordinates. A
three-dimensional point P =( x, y, z, 1) is transformed to a point P ∗ =( x ∗ ,y ∗ ,z ∗ , 1) by
multiplying it by a 4 × 4matrix

⎛ ⎞

abcp
defq
hijr
lmns

⎝ ⎠

T = . (1.23)