期刊名称：ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences
印刷版ISSN：2194-9042
电子版ISSN：2194-9050
出版年度：2010
卷号：XXXVIII - 4/W15
页码：69-72
出版社：Copernicus Publications
摘要：The definition of a Delaunay tetrahedralization (DT) of a set S of points is well known: a DT is a tetrahedralization of S in whichevery simplex (tetrahedron, triangle, or edge) is Delaunay. A simplex is Delaunay if all of its vertices can be connected by acircumsphere that encloses no other vertex. An important remark made in virtually all papers on this topic is that “although anynumber of vertices is permitted on the sphere”, a Delaunay tetrahedralization is unique “only if the points are in general position,which is the absence of degeneracy (i.e., five or more vertices possible on the circumsphere)”.For applications in which the DT must be unique and invariant invariable under either geometrical rotation or the numbering of thepoints of set S, degenerated cases are expected to be resolved or at least indicated.This research, however, will direct to a method in which degenerated cases are not solved by a geometrically distorted set of inputdata using Steiner Points, nor is just one of the possible ‘unique’ DTs generated. To the contrary, an extra type of ‘non-geometrical’,flat, zero-volume ‘tetrahedra’ is purposely introduced in order to indicate the degenerated cases within the applied data structure ofthe tetrahedralization. The four vertices of these flat tetrahedra lie on the same circumsphere as the vertices of their neighboringtetrahedra.Once the set S of points is tetrahedralized, these flat tetrahedra provide a tool with which to discover other ‘unique’ DTs of the set Sof points. From this set of unique DTs, the one having a global optimum can be selected for a given purpose, e.g. to support datadependentapplications. Another benefit in creating flat tetrahedra is the ability to indicate nearly degenerated cases, eliminating theneed for exact arithmetic
