六面体插值体细分方法研究与应用

Research and Application of the Interpolatory Volumetric Subdivision Scheme over Hexahedral Lattice

细分方法是一种非常有效的表示曲线、曲面和三维体甚至高维数据的手段 ,针对细分方法新的研究热点问题———体细分实体造型 ,提出了一种新的基于六面体拓扑网格结构的插值型体细分方法 ,使用多元情形下生成函数的性质进行了收敛性证明 ,给出了计算实例 ;结合离散动力学方程 ,对细分方法初始控制网格赋予一定的物理属性和运动约束 ,建立动态细分体变形算法 。

Volumetric subdivision modeling and its application is currently one of the active research topics in the domain of computer graphics and animation A new interpolatory volumetric subdivision scheme over the regular hexahedral lattice is proposed and its convergence is proved using the multivariate generating function associated with the volumetric subdivision The volumetric mass spring is also introduced based on the regular hexahedral lattice, and controlled by the discrete Lagrangian equation to realize dynamic deformation of the subdivision volume Meanwhile, this scheme is applied to the functional garment CAD to dynamically calculate the elastic human body's deformation under constraint of tight cloth and hierarchically visualize the human body after volumetric subdivision