Smooth piecewise polynomial blending operations for implicit shapes

Li, Q.

Abstract

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.

Citation

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. https://doi.org/10.1111/j.1467-8659.2007.01011.x

• 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
• DOI: https://doi.org/10.1111/j.1467-8659.2007.01011.x
• 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
• Public URL: https://hull-repository.worktribe.com/output/391238
• Publisher URL: https://onlinelibrary.wiley.com/doi/full/10.1111/j.1467-8659.2007.01011.x