Controllable Binary CSG Operators for "Soft Objects"

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 denned 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 G 1 continuous potential fields even when sharp transition operators are used.

Adequate inner bound for geometric modeling with compact field functions

“…Hsu et al [13] improved the control of the blending size using adequate transfer functions modifying the slope of the composed field functions. Barthe et al [14] defined a set of constraints for the creation of binary composition operators on compact fields, focusing on the implicit surface and the outside bound of the field functions. Based on these constraints, a new blending operator with shape control and a clean-union operator (union with a smooth field everywhere except at the surface intersections) are proposed.…”

“…Following the previous constraints [14], Bernhardt et al [16] introduced locally restricted binary blending operators for compact field functions. They can interpolate between a cleanunion and a blend through a parameter used to restrict the blend where the combined implicit surfaces intersect only.…”

“…For instance, f c might come from skeleton-based soft-objects [4], convolution surfaces [23], or objects resulting from non conforming compositions [12,14]. To this end, we use the transfer function:…”

“…Outside this bound, the function f uniformly equals zero. Many different operators have been developed over the years, increasing their variety and improving their effectiveness [3,12,13,14,15]. While simple max-based composition functions may be enough to define n-ary Boolean operators with sharp transitions (i.e., union, intersection and difference), the most recent and advanced operators are restricted to the composition of only two fields at once [16,17].…”

“…As a consequence, since blending produces a smooth transition linking the combined objects in their outside volume part, little attention has been paid to definition of the part of the field function defining the inside of the volume. Thus only the following constraints have been considered in the design of operators on compact fields [14]:…”