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CONTROLLABLE BINARY CSG OPERATORS FOR "SOFT OBJECTS"

LOÏC BARTHE

SIRV Group, IRIT/UPS Toulouse, 118 route de Narbonne, 31062 Toulouse Cedex 4, France

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BRIAN WYVILL

Dept. of Computer Science, University of Calgary, 2500 University Dr. NW Calgary, Alberta, T2N 1N4, Canada

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, and

ERWIN DE GROOT

Dept. of Computer Science, University of Calgary, 2500 University Dr. NW Calgary, Alberta, T2N 1N4, Canada

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https://doi.org/10.1142/S021865430400064XCited by:26 (Source: Crossref)

Abstract

Potential functions allow the definition of both an implicit surface and its volume. In this representation, two categories can be distinguished: bounded and unbounded representations. Boolean composition operators are standard modelling tools allowing complex objects to be built by the combination of simple volume primitives. Though they are well defined for the second category, there is no clear definition of the properties that such operators should satisfy in order to provide bounded representation with both smooth and sharp transition. In this paper, we focus on bounded implicit representation. We first present fundamental properties to create adequate composition operators. From this theoretical framework, we derive a set of Boolean operators providing union, intersection and difference with or without smooth transition. Our new operators integrate accurate point-by-point control of smooth transitions and they generate G¹ continuous potential fields even when sharp transition operators are used.

Keywords:

AMSC: 22E46, 53C35, 57S20

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