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On Floating‐Point Normal Vectors
Author(s) -
Meyer Quirin,
Süßmuth Jochen,
Sußner Gerd,
Stamminger Marc,
Greiner Günther
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2010.01737.x
Subject(s) - discretization , normal , floating point , point (geometry) , algorithm , computer science , representation (politics) , discretization error , approximation error , mathematics , geometry , mathematical analysis , surface (topology) , politics , political science , law
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 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.