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Shape design is often performed by starting from a basic surface and by refining it afterward by adding details. In order to construct this first approximation surface, we present in this article a method to generate a basic polyhedron from a volumic voxel-based skeleton. This approach preserves the topology described by the discrete skeleton in a 3D grid considering the 26-adjacency: if a cycle is sketched, then there is a hole in the resulting surface, and if a closed hull is designed, then the output has a cavity. We verify the same properties for connected components. This surrounding basic polyhedron is computed with simple geometrical rules, and it is a good starting point for 3D shape design from a discrete voxel skeleton. In order to add multiresolution features to our approach, we use this rough mesh as the control polyhedron of a subdivision surface, according to the Loop scheme dedicated to triangulated surfaces. We show that the resulting set of smooth refined meshes is well suited for further modifications in the frame of a 3D modeling software.

In this paper, we present a new approach to geometrical modeling which allows the user to easily characterize and control the shape defined to a closed surface. We will focus on dealing with the shape's topological, morphological and geometrical properties separately. To do this, we have based our work on the following observations concerning surfaces defined by control-points, and implicit surfaces with skeleton. They both provide complementary approaches to the surface's deformation, and both have specific advantages and limits. We thus attempted to conceive a model which integrates the local and geometrical characterization induced by the control points, as well as the representation of the morphology given by the skeleton. Knowing that the lattice of control points is close to the surface and that the skeleton is centered in the related shape, we thought of a 3-layer model. The transition layer separates the local geometrical considerations from those linked to the global morphology. We apply our model to shape design in order to modify an object in an interactive and ergonomic way, as well as to reconstruction which allows better shape understanding. To do so, we present the algorithms related to these processes.

A graphics package for generating the range data of 3-D objects is described, The simulating data generated by this package can be used for 3-D object recognition or related research. It is a useful tool for someone who wants to work on range data of 3-D objects, but does not have a good range finder…