Smooth piecewise polynomial blending operations for implicit shapes

Li, Qingde

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.

• Journal Article Type: Article
• Publication Date: Dec 31, 2007
• Journal: COMPUTER GRAPHICS FORUM
• Print ISSN: 0167-7055
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 2
• Pages: 157 - 171
• APA6 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
• DOI: https://doi.org/10.1111/j.1467-8659.2007.01011.x
• Publisher URL: https://onlinelibrary.wiley.com/doi/full/10.1111/j.1467-8659.2007.01011.x