On Floating-Point Normal Vectors

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 b...

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Veröffentlicht in:Computer graphics forum Jg. 29; H. 4; S. 1405 - 1409
Hauptverfasser: Meyer, Quirin, Süßmuth, Jochen, Sußner, Gerd, Stamminger, Marc, Greiner, Günther
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford, UK Blackwell Publishing Ltd 01.06.2010
Schlagworte:
Analysis
C (programming language)
Computer graphics
Computer Graphics [I.3.6]: Methodology and Techniques-Graphics data structures and data types
Computer programming
Discretization
Errors
Floating point arithmetic
Mathematical analysis
Parametrization
Representations
Studies
Three dimensional
Vectors (mathematics)
ISSN:0167-7055, 1467-8659
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Zusammenfassung: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.
Bibliographie:ArticleID:CGF1737
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2010.01737.x