具有特殊效果的混合细分方法

Hybrid Subdivision Algorithm with Special Effect

提出了基于三角形和四边形的混合控制网格的细分曲面尖锐特征、半尖锐特征生成和控制方法,避免了已有方法仅局限于初始控制网格为单一的三角形或单一的四边形网格的缺陷.通过局部修改混合细分规则,在光滑混合曲面上产生了刺、尖、折痕、角的尖锐特征效果,并对尖锐特征处局部细分矩阵进行了详细的特征分析,讨论了极限曲面的收敛性及光滑性.同时,用特征处的离散曲率来控制特征处的尖锐程度,实现了半尖锐的特征效果,并通过自适应细分方法,把尖锐特征、半尖锐特征的生成统一起来.该方法具有多分辨率表示能力强、局部性好、简单易操作的特点.实验结果表明,该算法效果好,成功地解决了混合曲面特殊效果生成问题.

Previous methods for generation of sharp features of subdivision surfaces were based on that initial control meshes are either triangle-only meshes or quadrangle-only meshes. However, in engineering surface modeling, general shapes designers often want to model certain regions with triangle and quadrangle hybrid patches structure. In order to overcome the defect in generation of sharp features utilizing traditional approaches, in this paper, we propose a method for creating sharp features and semi-sharp features on hybrid subdivision surfaces. By local modifying hybrid subdivision rules, sharp features such as dart, cusp, crease and corner are generated. We also give eigenanalysis of local subdivision matrices for the piecewise smooth subdivision rules that include sharp features, and the convergence and smoothness of the limit surface are discussed. Meanwhile, by controlling sharpness using discrete curvature at feature vertex, we realize semi-sharp features effect. Examples demonstrate explicit and efficiency of our method.