On floating-point normal vectors

Authors:
Quirin Meyer;Jochen Süßmuth;Gerd Sußner;Marc Stamminger;Günther Greiner
Affiliations:
Computer Graphics Group Erlangen;Computer Graphics Group Erlangen;Realtime Technology AG;Computer Graphics Group Erlangen;Computer Graphics Group Erlangen
Venue:
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
Year:
2010

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Abstract

In this paper we analyze normal vector representations. We derive the error of the most widely used representation, 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 250:2 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.