Automatic mesh generation is one of the most important parts in CIMS (Computer Integrated Manufacturing System). A method based on mesh grad-ing propagation which automatically produces a triangular mesh in a multiply...Automatic mesh generation is one of the most important parts in CIMS (Computer Integrated Manufacturing System). A method based on mesh grad-ing propagation which automatically produces a triangular mesh in a multiply connected planar region is presented in this paper. The method decomposes the planar region into convex subregions, using algorithms which run in linear time. For every subregion, an algorithm is used to generate shrinking polygons according to boundary gradings and form Delaunay triangulation between two adjacent shrinking polygons, both in linear time. It automatically propagates boundary gradings into the interior of the region and produces satisfactory quasi-uniform mesh.展开更多
The proof of the Jordan Curve Theorem (JCT) in this paper is focused on a graphic illustration and analysis ways so as to make the topological proof more understandable, and is based on the Tverberg’s method, which i...The proof of the Jordan Curve Theorem (JCT) in this paper is focused on a graphic illustration and analysis ways so as to make the topological proof more understandable, and is based on the Tverberg’s method, which is acknowledged as being quite esoteric with no graphic explanations. The preliminary constructs a parametrisation model for Jordan Polygons. It takes quite a length to introduce four lemmas since the proof by Jordan Polygon is the approach we want to concern about. Lemmas show that JCT holds for Jordan polygon and Jordan curve could be approximated uniformly by a sequence of Jordan polygons. Also, lemmas provide a certain metric description of Jordan polygons to help evaluate the limit. The final part is the proof of the theorem on the premise of introduced preliminary and lemmas.展开更多
An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of...An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.展开更多
文摘Automatic mesh generation is one of the most important parts in CIMS (Computer Integrated Manufacturing System). A method based on mesh grad-ing propagation which automatically produces a triangular mesh in a multiply connected planar region is presented in this paper. The method decomposes the planar region into convex subregions, using algorithms which run in linear time. For every subregion, an algorithm is used to generate shrinking polygons according to boundary gradings and form Delaunay triangulation between two adjacent shrinking polygons, both in linear time. It automatically propagates boundary gradings into the interior of the region and produces satisfactory quasi-uniform mesh.
文摘The proof of the Jordan Curve Theorem (JCT) in this paper is focused on a graphic illustration and analysis ways so as to make the topological proof more understandable, and is based on the Tverberg’s method, which is acknowledged as being quite esoteric with no graphic explanations. The preliminary constructs a parametrisation model for Jordan Polygons. It takes quite a length to introduce four lemmas since the proof by Jordan Polygon is the approach we want to concern about. Lemmas show that JCT holds for Jordan polygon and Jordan curve could be approximated uniformly by a sequence of Jordan polygons. Also, lemmas provide a certain metric description of Jordan polygons to help evaluate the limit. The final part is the proof of the theorem on the premise of introduced preliminary and lemmas.
文摘An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.
