A robust and efficient algorithm is presented to build mulitiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.%提出了一个健壮有效的网格模型多分辨分析方法. 该方法面向任意网格模型且不需要具有子分连通性, 通过删除边和拆分点操作进行网格模型的向下采样和向上采样, 将网格模型表示为由一个低分辨率的网格和一系列修改操作组成的多分辨模型. 该算法在向下采样时, 重点考虑了简化误差对模型精度的影响, 在生成网格多分辨模型时, 将细化操作分解为对网格模型的几何修改信息和各细化操作之间的关系信息, 确保了多分辨网格模型的健壮性. 实验结果证明了本算法的有效性.
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机译：A robust and efficient algorithm is presented to build mulitiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.%提出了一个健壮有效的网格模型多分辨分析方法. 该方法面向任意网格模型且不需要具有子分连通性, 通过删除边和拆分点操作进行网格模型的向下采样和向上采样, 将网格模型表示为由一个低分辨率的网格和一系列修改操作组成的多分辨模型. 该算法在向下采样时, 重点考虑了简化误差对模型精度的影响, 在生成网格多分辨模型时, 将细化操作分解为对网格模型的几何修改信息和各细化操作之间的关系信息, 确保了多分辨网格模型的健壮性. 实验结果证明了本算法的有效性.
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