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Smooth Piecewise Polynomial Blending Operations for Implicit Shapes

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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.
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Keywords: Boundary representations; Constructive solid geometry; Curve; I.3.5 [Computational Geometry and Object Modeling]; blending operation; constructive solid geometry; implicit curve; implicit surface; object representations; shape modeling; solid; surface

Document Type: Research Article

Affiliations: Department of Computer Science, University of Hull, Hull, HU6 7RX, UK, Email: [email protected]

Publication date: June 1, 2007

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