| Volumetric modeling has always been an important part in the field of 3D physical modeling and isogeometric analysis.and subdivision is a simple and effective model modeling technology in computer graphics.Subdivision technology has numerous advantages over modeling techniques.Subdivision technology is a method of converting a low-resolution mesh to a high-resolution mesh,and it has numerical stability by using subdivision methods to assist modeling,simple code,applying arbitrary topology easily and other advantages.According to the position relationship between the subdivision mesh and the initial mesh,the subdivision algorithm can be divided into approximating subdivision and interpolatory subdivision.Although approximating subdivision tends to produce better shapes,there are many specific cases where we need to use interpolatory subdivision because of shrinkage in the subdivision of model shapes during approximating subdivision.Therefore,how to combine the advantages of approximating subdivision and interpolatory subdivision is particularly important.Compared with surface interpolatory subdivision,the volumetric interpolatory subdivision has less research content,so two efficient and high-quality new volumetric interpolatory subdivision will be proposed in this thesis.1.In this thesis,based on conjugate gradient method,a new interpolatory volumetric subdivision is proposed,and a complete mathematical proof of its convergence is given,and it is proved that it takes at most n iterations to complete convergence for a mesh model of n vertexes.Then,under several fitting error,the effectiveness and efficiency of the algorithm are successfully verified by comparing the number of iterations and time overhead with PIA and W-PIA volumetric subdivision by comparing several model examples.2.Based on the intrinsic relationship between cubic B-spline curve refinement and the four-point interpolatory subdivision,a heuristically constructed interpolatory volumetric subdivision is proposed in this thesis.The core of this subdivision is that each type of new insertion vertex has corresponding operators according to the Catmull-Clark volumetric subdivision,and the original vertex position remains unchanged during the subdivision,which ensures the realization of the interpolation.Finally,several experimental examples are used to verify the continuity of the algorithm,and the effectiveness and advantages of the algorithm are verified by comparative analysis with other interpolatory subdivisions. |
