This review paper gives a detailed account of the development of mesh generation techniques on planar regions, over curved surfaces and within volumes for the past years. Emphasis will be on the generation of the unstructured meshes for purpose of complex industrial applications and adaptive refinement finite element analysis. Over planar domains and on curved surfaces, triangular and quadrilat...

This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe triangulations, we rely on a combinatorial hypermap specification framework we have been developing for years. We embed hypermaps in the plane by attaching coor...

The restricted Delaunay triangulation can be conceived as an operator that takes as input a k-manifold (typically smooth) embedded in R and a set of points sampled with sufficient density on that manifold, and produces as output a k-dimensional triangulation of the manifold, the input points serving as its vertices. What happens if we feed that triangulation back into the operator, replacing th...

This paper describes an algorithm for generating unstructured triangular meshes from a continuous two-dimensional object represented by an image. The algorithm uses squares as a background grid from which to build the quadrilateral elements that conform to the input contours. Then the triangulation is obtained by automatically choosing the diagonals that optimize the angles of the triangles. Th...

Volume calculation from 3D point cloud is widely used in engineering and applications. The existing methods either have large errors or are time-consuming. This paper focuses on the coal measurement. Based triangular mesh generated cloud, each triangle projected downward to base plane form a voxel. We derive formula of voxel by an integral method, which more efficient than method decomposing in...