Research For Theory Of Subdivision Surfaces And Critical Technology Of Its Applications

This paper studies the basic theory and application of the key issues of subdivision surfaces. First, comprehensive analysis and comparison of the current subdivision surface algorithms'theory and their own characteristics; The character of the subdivision surfaces is that the number of facets grows exponentially with the level of subdivision, so two adaptive subdivision surface algorithm will be proposed by this paper; And then studied and proposed a algorithm to solve the error and threshold selection for the adaptive subdivision algorithm; Finally, the requirements of high-quality rendering, the latest algorithms for wireframe model rendering to be proposed based on the current geometry shader (Shader Model 4.0), focus on solving the aliasing problem of the edge of the model.With the development of computer hardware, the modeling technology involving complex topology and characteristics of the three-dimensional model has become the hot spot research area of computer-aided design (CAD), computer-aided geometric design (CAGD) and computer graphics (CG), In a wide variety of geometric modeling techniques, surface modeling methods has a more concise form, relatively easy for collision detection, and providing scalable primitives and a more smooth and continuous higher surfaces with respect to the polygon modeling techniques. Common sophisticated surface modeling technologies include parametric surfaces modeling, implicit surface modeling, deformation of surface modeling, hybrid modeling and the the subdivision surface modeling techniques that will be researched in this paper. Compared to other technologies in terms of surface modeling, subdivision surface modeling technology is the bridge and connection between the polygons modeling methods and parametric surfaces modeling, that is, integration of the non-continuous mesh and continuous surfaces. Subdivision surface generates much denser patches from the original control mesh by using a specified algorithm. The original control mesh will converge a smooth resulting surface when repeatedly applying the subdivision generating procedure. The technique of subdivision modeling have more advantages such as arbitrary topology, multiresolution, numerical stability and code simplicity, so they can be used in CAD, computer animation, some business 3D modeling software like Maya and 3ds MAX. In recent years, theoretical research of the subdivision surface about the geometric properties of its limit surfaces have abundant results, the paper will be based on these studies, from a practical point of view, and propose some robust algorithms for soloving the bottleneck-problems. The main contents include the followings:1, briefly review the history of subdivision surfaces and subdivision surface modeling analysis related to the comprehensive analysis of research results, focusing on its application bottlenecks and propose solutions related to this overview.2, systematic introductions to the subdivision surface of the triangle mesh and quadrilateral mesh from the perspective of comprehensive exposition of the two types of subdivision methods. Comparative analysis of the main characteristics of the different subdivision algorithms and their application details, and gives the results of experimental comparison of various algorithms.3, the character of the subdivision surfaces is that the number of facets grows exponentially with the level of subdivision, in order to solve the higher requriments for computer hardware and easy for the real-time rendering, this paper proposes two universal adaptive subdivision surface algorithms. The two new algorithms can apply to different sub-base methods and different mesh primitives by comparing the curvature of the current use of adaptive criterions; we can fully display the advantages of the new algorithms.4, a comprehensive analysis of subdivision results in the theoretical calculation, combined with the widely used algorithm for Catmull-Clark subdivision calculations illustrate the idea of subdivision surfaces, theory and important results.5, subdivision surfaces and adaptive subdivision surface accuracy of research, mainly from the practical point of view, for the first time using Hausdorff distance algorithm to determine the effect of the approximations of the subdivision mesh or adaptive subdivision mesh relative to the various criterion, solve most of the other algorithms are from the perspective of experience and experimentation provide threshold, based on the lack of accuracy and criterion-related.6, given the current graphics processing unit (GPU), the rapid development of CG has become another research focus areas proposed in this paper based on the latest shader model 4.0-the geometry shader to draw three-dimensional model such as subdivision surface rendering of the wire-frame algorithm. Most algorithms are based on the traditional graphics processing pipeline, performance and effect is clearly lower than the graphics hardware-based algorithms, this paper based on the relevant algorithm, a focus on solving the model proposed anti-aliasing contour rendering algorithms. Experiments show that the algorithm that the rendering the wire-frame about a 3d model compared to other GPU-based graphics rendering algorithm has a better edge antialiasing.