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.

Texture mapping is an essential component for creating 3D models and is widely used in both the game and the movie industries. Creating texture maps has always been a complex task and existing methods carefully balance flexibility with ease of use. One difficulty in using texturing is the repeated placement of individual textures over larger areas. In this paper we propose a method which uses decals to place images onto a model. Our method allows the decals to compete for space and to deform as they are being pushed by other decals. A spherical field function is used to determine the position and the size of each decal and the deformation applied to fit the decals. The decals may span multiple objects with heterogeneous representations. Our method does not require an explicit parameterization of the model. As such, varieties of patterns including repeated patterns like rocks, tiles, and scales can be mapped. We have implemented the method using the GPU where placement, size, and orientation of thousands of decals are manipulated in real time.

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