Normal Computation for Discrete Surfaces in 3D Space

Abstract

Associating normal vectors to surfaces is essential for many rendering algorithms. We introduce a new method to compute normals on discrete surfaces in object space. Assuming that the surface separates space locally into two disjoint subsets, each of these subsets contains implicitly information about the surface inclination. Considering one of these subsets in a small neighbourhood of a surface point enables us to derive the surface normal from this set. We show that this leads to exact results for C1 continuous surfaces in R3. Furthermore, we show that good approximations can be obtained numerically by sampling the considered area. Finally, we derive a method for normal computation on surfaces in discrete space.