The G~2 Processing Of Extraordinary Points In Subdivision Surface

This paper studies the1 G continuity and2 G continuity of the subdivision surface based on relevant theory of geometric modeling and reverse engineering in deep, especially for containing the extraordinary points surface in case.Firstly, this paper discusses three kinds of classical subdivision method, presents a shape adjustable subdivision algorithm, and gives geometric rules and topology rule of new algorithm.The new algorithm achieves the purpose of adjusting the shape by introducing subdivision shape adjustment parameter t( 0 ￡t ￡1).Secondly,for the1 G of extraordinary points, this paper presents a kind of spline surface reconstruction algorithm, scattered data points of arbitrary topological shape have three different parametric quadrilateral mesh obtained control.Then, it uses the bi-quadratic and bi-cubic tensor product spline to fit in regular point and extraordinary points.At last,obtain the1 G smooth surface. Using this method, B-spline surfaces naturally satisfy the tangent plane continuity. Compared with previous methods, this method can guarantee the1 G, using low order spline fitting, reduces the complexity of the algorithm and improves the efficiency of surface modeling.Thirdly,it discusses the2 G of extraordinary points.Using the continuity conditions, this paper constructs biseptic tensor product patches,At the same time, using the FTP transform to improve the efficiency of calculation complexity reduction.Then, given by using cyclic matrix and energy function optimization method with n-sided hole filling, Bezier control explicit point solutions, so that the surface and the Catmull-Clark subdivision surface splicing to achieve the overall2 G continuities. Compared with existing methods, the algorithm is not subject to the valences limit on the number of extraordinary vertices. To a given topology grid conditions, adjusting the position and shape of surfaces by introducing the parameter, making the surfaces adjustable. At last, the method improves the operation efficiency and reducing the complexity of the algorithm.Finally, this paper gives some algorithm process and data structure, validated for the algorithm presented in this paper and gives some examples. In addition, based on the summary of the full text research, for the future research work is prospected.