Abstract

In this paper we analyze normal vector representations. We derive the error of the most widely used representa-
tion, namely 3D floating-point normal vectors. Based on this analysis, we show that, in theory, the discretization
error inherent to single precision floating-point normals can be achieved by 2^50.2 uniformly distributed normals,
addressable by 51 bits. We review common sphere parameterizations and show that octahedron normal vectors
perform best: They are fast and stable to compute, have a controllable error, and require only 1 bit more than the
theoretical optimal discretization with the same error.

Paper

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