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On Floating-Point Normal Vectors.

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Title: On Floating-Point Normal Vectors.
Authors: Meyer, Quirin1, Süßmuth, Jochen1, Sußner, Gerd2, Stamminger, Marc1, Greiner, Günther1
Source: Computer Graphics Forum. Jun2010, Vol. 29 Issue 4, p1405-1409. 5p. 5 Diagrams, 1 Chart.
Subjects: Vector processing (Computer science), Three-dimensional imaging, Errors, Floating-point arithmetic, Computer arithmetic, Parameter estimation
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 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. [ABSTRACT FROM AUTHOR]
Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1111/j.1467-8659.2010.01737.x
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        Text: English
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