An indirect method for meshing parametric surfaces conforming to a user-specifiable size map is presented. First, from this size specification, a Riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related Riemannian space (the so-called ‘unit mesh’). Then, based on the intrinsic properties of the surface, the Riemannian structure is induced into the parametric space. Finally, a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced Riemannian structure. This mesh is constructed using a combined advancing-front—Delaunay approach applied within a Riemannian context. The proposed method can be applied to mesh composite parametric surfaces. Several examples illustrate the efficiency of our approach. Copyright © 2000 John Wiley & Sons, Ltd.

Parametric surface meshing using a combined advancing-front generalized Delaunay approach

In this paper we describe how the use of B-Spline surfaces allows lissom movements of body and face. Our method is empirical, based on a parametrical animation. It can be combined with a muscles model for facial animation as we illustrated for the speech.

Animation of a B-Spline figure

Optimal matching of convex polygons

Some aspects of parametric surface meshing

A method is proposed for the determination of a progressive polyhedral approximation of 3-D digitized surfaces whose points are located on a regular lattice. It relies on an iterative and adaptative splitting of the triangular faces of an initial polyhedral surface. Assuming a bijection between the digitized surface and its approximation, a partition of the data base is operated. The algorithm allows for the measurement of the local quality of the approximation and avoids the generation of ill-defined triangles with sharp corners. Its low computational complexity permits the approximation of very large sets of points (hundreds of thousands).

Adaptative Polyhedral Approximation Of Digitized Surfaces

A simple, low cost, and universal automatic 3-D acquisition system was developped using active triangulation. Its main characteristics are: - its speed of acquisition (about 1 minute per object), - the density of its sampling (from 30,000 to 250,000 measures per object), - the structured lattice of the resulting data (distributed on parallel and meridian equidistant lines). From these data, it is possible to use several techniques of surface approximation to compress the information: some of them are presented here, with their respective performances (quality, compression rate, complexity of programming). They are divided into two main classes: - planar approximations, - spline function approximations. We also present several advantages of the resulting data base which is structured like a picture data base. We can take advantage of this structure to develop very fast processing techniques.

F. Schmitt

Papers

Acquisition And Representation Of Object Surface Data