Section: New Results

High order geometric modeling

Participants : Patrick Laug [correspondant] , Houman Borouchaki.

In the area of geometric modeling, major challenges are linked to the efficient visualization of CAD surfaces and to the generation of meshes adapted to numerical simulation. In this context, the elaboration and implementation of a discrete geometric model provides a simple and universal representation model, without the need for CAD. A first study has been carried out for a model of degree 1 (one) defined by a "triangulation" composed of quadrilaterals and triangles. The advantage of this model of degree 1 lies in its geometric simplicity. However, in the case of complex surfaces, it may require a very large number of elements, and besides it is not sufficiently rich to give certain essential characteristics like geometric curvatures. The main goal of this project is to extend this discrete model of degree 1 to higher degrees. These studies are conducted by “MODIS”, an Associate Team comprising members of research teams at Inria, UTT (France) and Polytechnique Montreal (Canada) from 2017 to 2019. This year (2018) has been mostly devoted to the software implementation of all the theoretical bases obtained last year. In particular, chapters 6 and 11 of a recent book [22] give data structures where a local numbering is recursively defined for any order of the elements.