基于顶点变形梯度的点云曲面形状插值  

Shape interpolation for point set surface based on vertex deformation gradient

作　　者：谭光华[1] 张引[1] 陈志杨[2] 吴双卿[1] 张三元[1] 

机构地区：[1]浙江大学CAD＆CG国家重点实验室,浙江杭州310027 [2]浙江工业大学软件学院,浙江杭州200030

出　　处：《浙江大学学报（工学版）》2008年第10期1681-1686,共6页Journal of Zhejiang University：Engineering Science

基　　金：国家“863”高技术研究发展计划资助项目(2007AA01Z311,2007AA04Z1A5)

摘　　要：为了重用现有模型,减少动画设计的工作量,需在点云曲面关键帧之间进行形状插值.给出了点云曲面顶点变形梯度的计算方法,顶点变形梯度由其k邻近点决定,并从二次能量优化的角度给出了一个闭合解.基于该变形梯度以及移动最小二乘方法建立了源点云与目标点云之间的对应关系;将变形梯度进行矩阵极分解,对分解后的各分量分别进行插值,再通过一个全局的二次能量优化实现点云曲面的形状插值.该方法直接在点云上进行,无需类似网格的拓扑结构,也不要求源点云与目标点云具有相同的采样点数和一致的对应关系.实验表明,该方法能有效地实现源点云与目标点云之间的形状插值.Shape interpolation between the key frames of point set surfaces was considered to reuse the existing models and reduce the workload of animation design. An approach was proposed to compute the vertex deformation gradient of each point for point set surface. The vertex deformation gradient was defined by its k nearest neighbor points and a closed form solution was presented from the view of quadric energy optimization. The correspondence between two point set surfaces was established based on the deformation gradient and the moving least square method. The deformation gradient was decomposed into a rotation and a stretching component with the matrix polar factorization. Then each component was interpolated individually over the time. Shape interpolation was implemented through a global quadric energy optimization. The approach applies on point set surface directly. The approach does not need the topology information of the vertices and the compatible triangulation between the two surfaces in contrast to the interpolation between triangular meshes, i Numerous examples show that the approach is effective to fulfill the shape interpolation between two point set surfaces.

关 键 词：顶点变形梯度 形状插值 点云曲面 极分解 移动最小二乘法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]