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基于B样条的细分曲面参数化

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四边形细分曲面参数化算法在游戏影视领域具有广泛应用,但现有算法无法兼顾参数化速度和质量。为此,提出一种基于B样条的细分曲面参数化算法,首先将细分曲面转化为分片B样条曲面,然后通过最优化几何扭曲对样条曲面逐片进行参数化;对于一些细分曲面分片较多的情况,文中通过拼接相邻面片,对合并曲面进行参数化。不同于定义在分片线性空间上的网格类参数化算法,文中以数量更少的控制网格为优化变量,得到的定义在样条空间上的参数化映射在分片内部具有C2连续性。与现有算法相比,收敛速度更快,参数化结果的扭曲更低,采取的合并策略能有效地减少割缝数量,提升参数化结果的质量。
B-Splines Based Subdivision Surfaces Parameterization
The quadrilateral subdivision surface parameterization algorithm is widely used in the gaming and film industry.However,current algorithms do not effectively balance the speed and quality of parameteriza-tion.To tackle this problem,a B-spline-based subdivision surface parameterization algorithm is proposed.In this algorithm,the input subdivision surface is first transformed into a piecewise B-spline surface.Then,the spline surface is parameterized section by section using optimized geometric distortion.In cases where the subdivision surface has numerous subdivisions,the algorithm utilizes patch concatenation to parameterize the merged surface.Unlike grid-based parameterization algorithms that are defined in the piecewise linear space,the proposed algorithm reduces the number of control grids used as optimization variables.This ap-proach results in a parameterization mapping defined in the spline space,ensuring C2 continuity within each patch.Compared to existing algorithms,the algorithm demonstrates faster convergence,lower overall dis-tortion in parameterization results,effective reduction of seam count through merging strategies,and im-proved quality of the parameterization outcomes.

subdivision surfacesB-splinesmesh parameterizationcomputer graphicsquadrilateral mesh

王智巍、陈仁杰

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中国科学技术大学数学科学学院 合肥 230022

细分曲面 B样条函数 网格参数化 计算机图形学 四边形网格

2024

计算机辅助设计与图形学学报
中国计算机学会

计算机辅助设计与图形学学报

CSTPCD北大核心
影响因子:0.892
ISSN:1003-9775
年,卷(期):2024.36(11)