Computer Graphics Through OpenGL, 2nd Edition

Appendix A

Projective Spaces and Transformations

Projective geometry is at the heart of computer graphics whichever view you take of it, practical or theoretical. The various transformations of real 3-space we learned to use for the purpose of animation in Chapter 4 and studied mathematically in Chapter 5 are, in fact, most naturally viewed as transformations of projective 3-space, following a so-called lifting of the scene from real to projective space. A consequence is that representing these transformations as projective is more efficient from a computational point of view, a fact that OpenGL takes constant advantage of in its design. Capturing the scene after a perspective projection on film – “shooting” as we imagine the OpenGL point ...