OpenGL Programming Guide

Chapter 9Texture Mapping

Advanced Features

The q Coordinate

The mathematics of the q coordinate in a general four-dimensional texture coordinate is as described in the previous section. You can make use of q in cases where more than one projection or perspective transformation is needed.

For example, suppose you want to model a spotlight that has some nonuniform pattern - brighter in the center, perhaps, or noncircular, because of flaps or lenses that modify the shape of the beam. You can emulate shining such a light on a flat surface by making a texture map that corresponds to the shape and intensity of a light, and then projecting it on the surface in question using projection transformations. Projecting the cone of light onto surfaces in the scene requires a perspective transformation (q ≠ 1), since the lights might shine on surfaces that aren't perpendicular to them. A second perspective transformation occurs because the viewer sees the scene from a different (but perspective) point of view. See Figure J-37 for an example, and see "Fast Shadows and Lighting Effects Using Texture Mapping" by Mark Segal, Carl Korobkin, Rolf van Widenfelt, Jim Foran, and Paul Haeberli, SIGGRAPH 1992 Proceedings, (Computer Graphics, 26:2, July 1992, p. 249-252) for more details.

Another example might arise if the texture map to be applied comes from a photograph that itself was taken in perspective. In the same way as for spotlights, the final view depends on the combination of two perspective transformations.

OpenGL Programming Guide