Controllable Binary Csg Operators for "soft Objects"

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.