International audienceMedial surfaces are well-known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. Many applications in computer graphics can benefit from their properties, if we use them as Shape Representation Models (SRMs). However, visualizing the shape described by a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh for any closed surface described by a medial surface. This method is based on the construction of an adaptive voxelisation from the geometry encoded with the medial surface. This discretization has the same topology as the described object, regardless its genus. Then, we mesh the boundary of this voxel-based representation to get a coarse approximation. Finally we refine this mesh using an original migration algorithm, in order to smooth the result and be as close as possible to the described object. An empirical study, on both CAO and laser scan models, shows the efficiency of our method in providing high quality surfaces with a reasonable computational complexity

We are presenting here a new reliable algorithm to trace curves using interval arithmetic. We give several computable criteria which guarantee the convergence of the correction step of the classical predictor-corrector method. Our method avoids, for instance, to jump from a component of the curve to another one; this kind of mistake typically causes inconsistencies in the topology of intersecting surfaces in geometric modelers.

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Blobs, developed by J.F. Blinn in 1982, are the implicit surfaces obtained by composition of a real numerical function and a distance function. Since, many authors (C. Murakami, H. Nishimura, G. Wyvill…) defined their own function of density, from these implicit surfaces are interesting from several points of view. In particular, their fusion makes it possible to easily obtain an implicit equation of resulting surface. However, these surfaces do not admit a parametric equation yet. In this article, we will establish the parametric equation of two blobs in fusion, defined by the function of density of C. Murakami, by using an algebraic method. Then, we will develop another method, based on the differential equations.

We propose studying the variations of volume of implicit objects during an animation according to several points of view: choice of the function of density, variations of parameters such as the iso-value and the radius of influence for a given function, variations of the parameters inherent in a particular function. Modification of parameters of the function of density must be carried out with care. There are no rules concerning these variations. To avoid the non-monotonous variations, it is necessary to choose a function of density beforehand and study the intervals of variation of its parameters. A new discretization makes it possible to locate these variations for a later use in a process of control of these variations.