GPGPU Programming for Games and Science

Linear and Affine Algebra 327

Thus, it is simple enough to compose matrices as a product. The more difficult

problem is how to decompose a matrix into translations, rotations, scalings,

and shearings. That is the topic of the next section.

A special set of transformations is the set of rigid transformations.These

consist of products of translations and rotations. An object for which all its

points are transformed by translations and rotations retains its shape—only

its location and orientation vary. A rigid transformation is of the form

H =



R

T

0

T

1



(6.134)

Another special set of transformations involve only translations, uniform

scalings, and rotations. I