OpenGL Programming Guide: The Official Guide to Learning OpenGL, Versions 3.0 and 3.1, Seventh Edition

Appendix H. Calculating Normal Vectors

This appendix describes how to calculate normal vectors for surfaces. You need to define normals to use the OpenGL lighting facility, which is described in Chapter 5. “Normal Vectors” in Chapter 2 introduces normals and the OpenGL command for specifying them. This appendix goes through the details of calculating them. It has the following major sections:

• “Finding Normals for Analytic Surfaces”

• “Finding Normals from Polygonal Data”

Since normals are perpendicular to a surface, you can find the normal at a particular point on a surface by first finding the flat plane that just touches the surface at that point. The normal is the vector that’s perpendicular to that plane. On a perfect sphere, ...