Practical Algorithms for 3D Computer Graphics, 2nd Edition

2.12. Transformations 31

x

φ + θ

P´

P

y

φ

Figure 2.12: Rotation of point P by a n angle θ round the z axis.

Rotation about the x axis To rotate round th e x axis by an angle θ, the transfor-

mation matrix is:

[T

x

(θ)] =









1 0 0 0

0 cosθ −sinθ 0

0 sinθ cosθ 0

0 0 0 1









Note that as illustrated in figure 2.11 θ is pos itive if the rotation takes place

in a clockwise sense when looking from the or igin along the axis of rotation. This

is consistent with a right-handed coordinate system.

2.12.4 Combining transformations

Section 2.12 introduced the key concept of a transformation applied to a pos ition

vector. In many cases we are interested in what happens when ...