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Smooth piecewise polynomial blending operations for implicit shapes

Li, Q.



In this paper, we present a new set of blending operations for implicitly defined geometric shapes. The proposed shape operators are piecewise polynomial and blending range controllable, and can be constructed to any required degree of smoothness. The key idea behind these techniques is the introduction of the concept of the smooth absolute functions, which in turn lead to the definition of smooth maximum functions. These novel generalized absolute functions can be constructed recursively or through a recursively defined functions, and can thus be computed cheaply. In addition, the underlying mathematical descriptions of these shape operations are very simple and elegant.


Li, Q. (2007). Smooth piecewise polynomial blending operations for implicit shapes. Computer graphics forum : journal of the European Association for Computer Graphics, 26(2), 157-171.

Journal Article Type Article
Acceptance Date Oct 1, 2006
Online Publication Date May 21, 2007
Publication Date 2007-06
Journal Computer Graphics Forum
Print ISSN 0167-7055
Electronic ISSN 1467-8659
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 26
Issue 2
Pages 157-171
Keywords Implicit curve; Implicit surface; Blending operation; Shape modeling; Constructive solid geometry; I.3.5 [Computational Geometry and Object Modeling]; Boundary representations; Constructive solid geometry; Curve; Surface; Solid; Object representations
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