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Smooth Piecewise Polynomial Blending Operations for Implicit Shapes
Author(s) -
Li Q.
Publication year - 2007
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2007.01011.x
Subject(s) - piecewise , smoothness , polynomial , set (abstract data type) , simple (philosophy) , range (aeronautics) , computer science , key (lock) , mathematics , algorithm , mathematical optimization , mathematical analysis , philosophy , materials science , computer security , epistemology , composite material , programming language
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.