邻域表示的形状刚性操作实现方法  

Implementation of as-rigid-as-possible shape manipulation based on neighborhood representation

作　　者：雷闻宇[1] 高博宇 雷开彬[3] 

机构地区：[1]中国科学技术大学数学科学学院,合肥230026 [2]建国大学网络多媒体系 [3]西南民族大学计算机科学与技术学院,成都610041

出　　处：《计算机工程与应用》2012年第31期186-190,共5页Computer Engineering and Applications

基　　金：国家民委重点资助项目(No.08XN05);西南民族大学自然科学重点项目(No.07N016)

摘　　要：角色动画编辑的核心技术之一,是形状既能实现刚性变形,又能实现实时操作。在形状刚性操作计算中,通过定义三角网格顶点的面邻域和点邻域的平方差度量,简化自由顶点与约束顶点的坐标分离。这种表示法,在整体拟合中使得x坐标与y坐标能够独立求解。在算法实现中,设计恰当的系数矩阵和常数项向量的链表结构,采用矩阵索引存储和共轭梯度求解,减少数据的重复计算。实验表明,在普通的PC机上能够实现约1000个顶点的网格实时交互变形操作。One of the key technology of character animation editing is not only to achieve as-rigid-as-possible shape deformation, but also real-time operations. Computing in the shape manipulation, by defining the square difference metric of vertex neighborhood and face neighborhood on mesh, coordinates separation of free and constrain vertex is simplified. This algorithm can solve x and y coordinates independently in general fitting. In the implementing, the design of appropriate chain structure of coefficient matrix and constant vector. Duplication of data computing is reduced by indexed storage of sparse matrix and conjugate gradient method. Experiments show that in the ordinary personal computer to about 1000 mesh vertexes can be deformed in real-time interaction.

关 键 词：形状刚性操作 点邻域平方差 坐标分离 稀疏线性方程组 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]