Application Of Subdivision And Optimization In CAGD

The method of combining subdivision with optimization in CAGD is a research focus during these years,which has a wide perspective in reverse engineering, data transmission and so on.The main idea of subdivision modeling is refining the control mesh recursively using subdivision rules, the new vertexes are computed by the average weighted sum of their neighbors from the old control net. The limit of the control net is either smooth curves or convergent and smooth surfaces. The efficiency of subdivision algorithms, which reduce the cost of modeling, their flexibility and simplicity, especially the adaptability of arbitary topology make them suitable for many interactive computer graphics applications.Optimization is another focused area whose main work is to find the best result of a target function with contrains. This problem is often converted to finding the extremum of a target function without constrains. In the real world, many researchers and engineers is absorbed by its simple expression and exact model reflection ability. With the progress of computer techniques, its computation precision and efficiency is promoted largely. By now, it has become a powerful mathematical tool to solve projections. In CAGD, a geometric modeling problem can be posed as a set of geometric modeling constraints, in which it has founded the connection between CAGD and optimization. Thus, the problem of finding the optimized gemotric model can be solved as an optimization problem.This issue summarizes and studies the basic conceptions and theories, modeling methods and classic computation methods of subdivision and optimization. Besides, in order to reduce the data generated by subdivision, a method combining subdivision with optimization which sample the model in the dispatcher and reconstruct it in the receiver is proposed here. The efficiency of data transmission is promoted. And it is also extended into curve approximation. Numerical experiments are also given to show that the algorithm is simple, fast and efficient.