10.7 Bump Mapped Reflections

To the authors' knowledge, at least one hardware platform available at the time of writing supports environment mapped bump mapping. This technique provides visually interesting perturbed reflections, but is not yet available as an extension to OpenGL.

If the bump map is stored as displacements to the normal ( $\frac{\partial F}{\partial u}$ and $\frac{\partial F}{\partial u}$), rather than a height field, the displacements can be used as offsets added to the texture coordinates used in a second texture. This second texture represents the lighting environment, and can be the environment mapped approximation to phong lighting discussed in Section 10.1.1, or an environment map approximating reflections from the surface as discussed in Section 11.2.1.

The displacements in the ``bump map'' are related to the displacements to the normal used in bump mapping. The concept is that, instead of applying the spheremap equation to the vertex normals, the spheremap equation is applied to the displaced normals per vertex. In order to simplify hardware design, however, the displaced spheremap coordinates are approximated by applying the bump map displacements after the spheremap coordinates are computed for the vertex normals. The error introduced by this approximation is small at the center of the spheremap, but increases as the mapped normal approaches the edge of the spheremap. Pictures created with this technique look surprisingly realistic despite the dubious nature of the approximation.