Research On Adaptive Subdivision Surface Technology Based On Loop Scheme

Subdivision scheme is a new kind of discrete modeling technology which presents modeling surfaces by denning control meshes and subdivision rules. This technology not only preserves several advantages of traditional B-spline surfaces,especially the properties of localness and affine-invariance,but also has some special advantages such as the adaptability to arbitrary topology which the parameter surface technology does not have.These make subdivision sur-face one of the most powerful geometric modeling tools.Subdivision scheme is a discrete representation method based on grid re-finement,which can form smooth surfaces from arbitrary topology grids.The basic idea is as follows:for a given initial grid,define a subdivision rule,invert new vertexes,thus the grid is constantly refined to a grid sequence which con-verges to a smooth siirface in the limit.This method overcomes the difficulty parameter surfaces have to handle arbitrary topology grid and the difficulty of joining by carrying out special subdivision rules on irregular topology mesh-es.Its idea being simple and easy to perform,subdivision scheme has become an important part in Computer Aided Design and Computer Graphics.Adaptive subdivision is designed to segment less times in flat areas and more times in relatively complex areas for the purpose of reducing the number of meshes until meeting the given threshold criteria.It can inhibit the number of meshes from growing too fast while guaranteeing the surface quality.The article is based on triangular Loop adaptive subdivision scheme,aiming at improving its ability of modeling surfaces to provide more important appli- cations. Firstly,we introduce the history of subdivision scheme and its develop-ment at home and abroad.After describing the basic concepts and theories,we present the classification,characteristics,convergence and continuity analysis and so on.Then the details of several classic schemes such as Catmull-Clark, Doo-Sabin, Loop, Modified Butterfly,31/2,4-8are presented.After introducing adaptive subdivision and its necessity,a new definition about the flatness of a vertex is raised to control the number of times of adaptive subdivision until it meets users’requirements.At last,the algorithm is implemented in C++envi-ronment and by analyzing the figure as well as data results,we can come to the conclusion that the new definition and algorithm is reasonable and effectively reduce the number of meshes while guaranteeing the quality of subdivision surfaces.