Geometry Processing Method Based On Hexagonal Mesh

The article is a review of geometry processing method based on hexagonal mesh.Surface modeling is computer graphics and computer-aided geometric design of an important,mainly research in the computer system environment,said on the surface,design,display and analysis. Development of the theory of free-form surfaces through the application of the practice of long-term planning.As early as during the Second World War,Aircraft Industries has successfully created a set of aircraft and its main structural shape of the number of defined methods.60's Betsy and Coons has long been engaged in Egypt through the aircraft,vehicle design and processing,to a more perfect expression of a common form of curves and surfaces.In recent years,computer graphics display for the authenticity of interactive real-time requirements and increasing the target more and more a geometric design diversity,uniqueness and the complexity of topological structure,graphics,industrial and manufacturing industry towards globalization,integration of and network.With the three-dimensional scanning laser ranging data sampling techniques and the improvement of hardware devices,surface modeling in the past few years have enjoyed great development,mainly in the area of research,said the rapid expansion and innovation methods, especially worth mentioning dispersion modeling is the rapid development of ideas.With the traditional row modeling compared to the characteristics of the mesh is subdivided into discrete shapes much of the potential catch.First of all,this method of surface modeling features in vivid animation and sculptured surface design and processing in the home,has been widely used.After years of development,Discrete surface modeling has been developed,including a breakdown of the grid and the point cloud,such as the expression of a number of specific formats,as well as a variety of geometric approach.Discrete modeling CAGD thinking represents the development trend of the future will more and more in CAGD occupy an important position.Triangular mesh is the most basic,the most flexible form of the mesh,and the detailed study of the triangular network has greatly promoted the development of sub-methods,research in the grid to occupy the overwhelming superiority.At the same time,also widespread in nature hexagonal mesh,such as cellular,snow films and so is the oval or round hexagonal reasonable approximation,can be used for texture synthesis and mapping,Wavelet and finite element analysis.Not only that,if observed continuously seamlessly cover only two-dimensional plane of the regular polygon regular triangle,square and regular hexagon of these three,then to the importance of hexagonal mesh on the obvious.On the importance of hexagonal mesh,we are very concerned about the manner of their generation.To this end,we first take a look at a well-known shapes of discrete subdivision of the Doo-Sabin algorithm,which is encrypted grid operation and the operation of the dual structure of the synthesis.In general,the triangle mesh in the regular vertex connectivity case is 6,so its dual hexagonal mesh is the mesh.In this way,triangulation after using Dupin duality,we can form a special hexagonal mesh with a flat surface that is hexagonal space mesh.This article details how to get good hexagonal mesh(that is,non-self-intersection of the hexagonal mesh the way).And pointed out that:a good hexagonal mesh is a prerequisite for effective triangulation,For example,the practice of optimal Delaunay triangulation.Literature[1]provides a hexagonal grid to generate a three-step:1) Calculated on the surface of an effective triangulation T.2) Through the Dupin duality into a similar flat surface with a hexagonal mesh(?).3) Optimization(?) as a planar hexagonal mesh H.For the hexagonal mesh based on multi -resolution analysis,the main focus of this paper describes the thinking as well as a breakdown of the hexagonal mesh based on a breakdown.Segmentation of the origin of the cutting angle of the polygon to generate the discrete form of the method of curves.Its founder can be traced back to the 50's de Rahm.1974 Chaikin curve presents a quick way to intuitive,based on geometry,through the cutting angle to be a smooth line,which is the ideological breakdown of computer graphics in the first use of the system.Segmentation of much concern because it is an important and wavelet multi-resolution analysis theory and the close link between.Uniform node B-spline function can be regarded as a scaling function,which is constructed by B-spline wavelet.Frinklistein and Salesin study on the closed interval B-spline wavelet multi -resolution analysis theory,and for the first time to discuss the B-spline curves and tensor product surfaces that form the multi-resolution and its application in the edit.This article also describes a hexagonal mesh based on sub-format-cellular breakdown.That is,a method is different from the existing sub-sub-hexagon method.In sub-cellular,through transformation,and then the nature of the use of circulant matrices,eigenvalues can still accurate presentation,which parameters can be selected so that a breakdown of this new format to reach everywhere tangent plane continuous.Hexagonal mesh as a result of a breakdown of the many advantages,we have introduced on the basis of a breakdown of the relevant thoughts and multi -resolution analysis,and focus on its application in the Surveying and Mapping,described the multi-resolution discrete global mesh system Construction,such as plot discrete hexagonal mesh generation algorithm and based on the spherical-hexagonal mesh system of spatial information processing methods:Discrete spherical grid model is the management of an effective way to mass data,how to build a grid of spherical model is the basis of such issues:1 Discrete spherical mesh model is the management of an effective way to mass data,how to build a mesh of spherical model is the basis of such issues.Described in this paper,discrete global mesh system is mainly to study how the Earth(see oval) recursive subdivision for the area of the surface,yet how to distinguish the shape of the same series of hierarchical mesh.The use of Schneider(Snyder) plot,such as plane and spherical projection to establish the corresponding relationship between the hexagonal mesh used as the basic unit,built a multi-resolution global network management system[42].On the basis of the design of the plot,such as three spherical discrete hexagonal mesh generation algorithm[47].That is,C-Ⅰnetwork,C-Ⅱnetwork,C-Ⅰ/C-Ⅱnetwork.2 As a result of discrete spherical mesh system of spatial information management of the global mass is a general concern by the new ways,Therefore,[48]used the method proposed by Schneider, etc.First of all,the plot will be flat polyhedron projection multi-resolution hexagonal mesh is mapped to the spherical surface into a grid system constitutes a border point and then quaternion group of spherical hexagonal mesh of the spatial relationship between into a spherical triangle to deal with quad -tree,QTM expanding the use of coding schemes in the 3-axis coordinate system of discrete grid of latitude and longitude under the address code and unit conversion between;the end of the cell analysis and retrieval algorithms.The experimental results show that this method of data processing units directly address coding operate with high efficiency.3 Algorithm is based on the main ideas ISEA projection.ISEA projection that Icosahedron Schneider(Snyder) and other well-known product is the projection map projection of Jurists Schneider (Snyder) made a plot position,such as projection.Its definition is based Icosahedron the center of the face for the projection center, the use of spherical projection plot conditions,such as the product of their body surface Icosahedron.Based on the hexagonal mesh,the paper also described based on the spherical-hexagonal mesh system of spatial information processing methods and discrete spherical hexagonal plot,such as mesh generation algorithm and deformation analysis.Finally,for the hexagonal mesh theory,algorithms and applications,according to the author's own experience are given a number of summing up and made a hexagonal mesh on Some Thoughts on the future development.