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Selective Degree Elevation for Multi-Sided Bézier Patches.

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Title: Selective Degree Elevation for Multi-Sided Bézier Patches.
Authors: Smith, J.1, Schaefer, S.1
Source: Computer Graphics Forum. May2015, Vol. 34 Issue 2, p609-615. 7p. 10 Diagrams.
Subjects: Computer graphics, Vector graphics, Polytopes, Polygons, Computer-generated imagery
Abstract: This paper presents a method to selectively elevate the degree of an S-Patch of arbitrary dimension. We consider not only S-Patches with 2D domains but 3D and higher-dimensional domains as well, of which volumetric cage deformations are a subset. We show how to selectively insert control points of a higher degree patch into a lower degree patch while maintaining the polynomial reproduction order of the original patch. This process allows the user to elevate the degree of only one portion of the patch to add new degrees of freedom or maintain continuity with adjacent patches without elevating the degree of the entire patch, which could create far more degrees of freedom than necessary. Finally we show an application to cage-based deformations where we increase the number of control points by elevating the degree of a subset of cage faces. The result is a cage deformation with higher degree triangular Bézier functions on a subset of cage faces but no interior control points. [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: This paper presents a method to selectively elevate the degree of an S-Patch of arbitrary dimension. We consider not only S-Patches with 2D domains but 3D and higher-dimensional domains as well, of which volumetric cage deformations are a subset. We show how to selectively insert control points of a higher degree patch into a lower degree patch while maintaining the polynomial reproduction order of the original patch. This process allows the user to elevate the degree of only one portion of the patch to add new degrees of freedom or maintain continuity with adjacent patches without elevating the degree of the entire patch, which could create far more degrees of freedom than necessary. Finally we show an application to cage-based deformations where we increase the number of control points by elevating the degree of a subset of cage faces. The result is a cage deformation with higher degree triangular Bézier functions on a subset of cage faces but no interior control points. [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/cgf.12588
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        Text: English
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        PageCount: 7
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      – SubjectFull: Vector graphics
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      – SubjectFull: Polytopes
        Type: general
      – SubjectFull: Polygons
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      – SubjectFull: Computer-generated imagery
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      – TitleFull: Selective Degree Elevation for Multi-Sided Bézier Patches.
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              Text: May2015
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