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Meshing 3D Domains Bounded by Piecewise Smooth Surfaces

Rineau, Laurent and Mariette Yvinec

Proceedings, 16th International Meshing Roundtable, Springer-Verlag, pp.443-460, October 14-17 2007

IMR
PROCEEDINGS

16th International Meshing Roundtable
Seattle, Washington, U.S.A.
October 14-17, 2007

INRIA, BP 93 06902 Sophia Antipolis, France.
[email] Laurent.Rineau@sophia.inria.fr
[email] Mariette.Yvinec@sophia.inria.fr

Abstract
This paper proposes an algorithm to mesh 3D domains bounded by piecewise smooth surfaces. The algorithm may handle multivolume domains defined by non connected or non manifold surfaces. The boundary and subdivision surfaces are assumed to be described by a complex formed by surface patches stitched together along curve segments. The meshing algorithm is a Delaunay refinement and it uses the notion of restricted Delaunay triangulation to approximate the input curve segments and surface patches. The algorithm yields a mesh with good quality tetrahedra and offers a user control on the size of the tetrahedra. The vertices in the final mesh have a restricted Delaunay triangulation to any input feature which is a homeomorphic and accurate approximation of this feature. The algorithm also provides guarantee on the size and shape of the facets approximating the input surface patches. In its current state the algorithm suffers from a severe angular restriction on input constraints. It basically assumes that two linear subspaces that are tangent to non incident and non disjoint input features on a common point form an angle measuring at least 90 degrees.

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