四种逼近型细分算法对比研究及应用

Comparative Research and Application of Four Approximation Subdivision Algorithms

摘要: 曲面细分作为生成平滑表面的重要手段，已广泛应用于计算机图形学。在实体建模中，多边形网格虽然可以表示物体形状，但在实际采样中由于采样的不均匀性或物体的遮挡等导致获得的初始网格不够光滑，难以表达曲面的真实形状，而曲面细分可以有效解决网格光滑问题。近年来，有些逼近型细分算法，在经典算法的基础上通过改变细分规则，实现了某些效果或者控制了网格的数量，但是其应用的广泛性和普适性较低。本文选取了经典的逼近型Catmull-Clark细分法、Doo-Sabin细分法、Loop细分法和√3细分法进行了对比实验，并阐述了各细分算法的适用范围。此外，基于贪婪算法对采集到的真实数据进行重建，得到初始三角网格；然后，根据细分算法特点，采用Loop细分对初始三角网格进行细分，最后得到光顺的细分曲面。

Abstract: As an important means of generating smooth surfaces, surface subdivision has been widely used in computer graphics. In solid modeling, although the polygon mesh can represent the shape of the object, the initial mesh obtained in actual sampling is not smooth enough due to the unevenness of the sampling or the occlusion of the object, and it is difficult to express the true shape of the surface. Surface subdivision can effectively solve the problem of mesh smoothness. In recent years, some approximation subdivision algorithms have achieved certain specific effects or controlled the number of grids by changing subdivision rules on the basis of classic algorithms, but their application versatility and universality are low. This paper selects the classic approximation Catmull-Clark subdivision, Doo-Sabin subdivision, Loop subdivision and Sqrt3 subdivision for comparative experiments, and explains the applicable scope of each subdivision algorithm. In addition, based on the greedy algorithm, the collected real data is reconstructed to obtain the initial triangle mesh; then, according to the characteristics of the subdivision algorithm, the loop subdivision algorithm is used to subdivide the initial triangle mesh, and finally a smooth subdivision surface is obtained. As an important means of generating smooth surfaces, surface subdivision has been widely used in computer graphics.