Generation of three-dimensional Delaunay meshes from weakly structured and inconsistent data. (Russian, English) Zbl 1249.65041

Garanzha, V. A.; Kudryavtseva, L. N.

Zh. Vychisl. Mat. Mat. Fiz. 52, No. 3, 499-520 (2012); translation in Comput. Math. Math. Phys. 52, No. 3, 427-447 (2012).

Summary: A method is proposed for the generation of three-dimensional tetrahedral meshes from incomplete, weakly structured, and inconsistent data describing a geometric model. The method is based on the construction of a piecewise smooth scalar function defining the body so that its boundary is the zero isosurface of the function. Such implicit description of three-dimensional domains can be defined analytically or can be constructed from a cloud of points, a set of cross sections, or a “soup” of individual vertices, edges, and faces. By applying Boolean operations over domains, simple primitives can be combined with reconstruction results to produce complex geometric models without resorting to specialized software. Sharp edges and conical vertices on the domain boundary are reproduced automatically without using special algorithms.

MSC:

65D18	Numerical aspects of computer graphics, image analysis, and computational geometry
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Keywords:

tetrahedral meshes, Delaunay triangulation, radial base functions, variation method, reconstruction of surface; complex geometric models; algorithms

Software:

DistMesh