S. Y. Oudot, L. Rineau, M. Yvinec. Meshing Volumes Bounded by Smooth Surfaces. Proc. 14th Internat. Meshing Roundtable, pp. 203-220, 2005. Full version in Engineering with Computers, 26(3):265-279, 2010 (pdf).


This paper introduces a three-dimensional mesh generation algorithm for domains bounded by smooth surfaces. The method combines a surface mesher with a volume mesher, both based on Delaunay refinement, to get a greedy algorithm that samples the interior and the boundary of the domain at once. The algorithm constructs provably-good meshes, it gives control on the size of the mesh elements through a user-defined sizing field, and it guarantees the accuracy of the approximation of the domain boundary. A noticeable feature is that the domain boundary has to be known only through an oracle that can tell whether a given point lies inside the object and whether a given line segment intersects the boundary. This makes the algorithm generic enough to be applied to a wide variety of objects, ranging from domains defined by implicit surfaces to domains defined by level-sets in 3D grey-scaled images or by point-set surfaces.


 author = {S. Y. Oudot and L. Rineau and M. Yvinec},
 title = {Meshing Volumes Bounded by Smooth Surfaces},
 booktitle = {Proc. 14th Internat. Meshing Roundtable},
 pages = {203--220},
 year = {2005}