中文摘要：

为保持三维模型表面细节和模型体积，提高模型变形的真实感效果，提出一种基于能量最小化的近刚性保体变形方法．首先对模型进行Laplacian变形，在此基础上，通过极分解求解曲面局部区域三角形的旋转变形，构建模型刚性变形能；然后通过模型体积积分离散化将模型体积变形约束转化为模型曲面变形约束，构建体积变形能；再通过衡量约束点的位置变形误差构建约束变形能．在最小二乘意义下最小化上述加权变形能，获得模型变形结果．实例结果表明，文中方法能够在线性的算法效率下获得近刚性保体变形效果，为模型的真实感变形提供了一条有效的途径．

英文摘要：

Surface detail preservation and model volume preservation are two important aspects for 3D model realistic deformation. A large number of methods for preserving both of the above two aspects have been developed in the past few years. However neither sole detail preserved method nor sole volume preserved method can well preserve them. In this paper, a 3D quasi-rigid deformation integrated with volume preservation approach is proposed. Model deformation is achieved by iteratively minimizing a combined deformation energy, the surface rigidity energy measures the deviation degree of the local surface deformation from its ideal rigid deformation and is computed by polar decomposing the Laplacian surface deformation result~ the volume deformation energy measures the volume changing during deformation and is expressed through discretizing the model surface volumetric integration~ the constraint energy measures how well the customer＇s interactive constraints being met. Experimental results show that our approach can obtain quasi-rigid and volume-preserved model deformation results within linear algorithm complexity.