Abstract: In this paper, the level set method is introduced to mesh simplification of the three-dimensional model. Construct a signed distance function, the zero set of which define the surface. Introduce a energy functional and minimize it to derive a second order Geometric Partial Differential Equation（GPDE） in the level-set formulation. The mesh simplification process is transferred into volumetric diffusion process of an implicit model. This method is used for simplification of digitized of large scene and relics in cultural heritage. The level-set mesh simplification algorithm are compared and analyzed with mesh simplification algorithm based on point-collapse on the visual quality and geometric error. The experiments show that it can be applied any topology of mesh. After model is large-scale simplified, it is still able to maintain a considerable number of important geometric features and better overall visual effect while maintaining a low error level.

Key words: mesh simplification, level-Set method, volumetric diffusion, digitization of cultural heritage

摘要： 将水平集方法引入到三维模型网格简化中，构造符号距离函数，函数的零集定义为初始曲面；引入一个能量泛涵，通过对其极小化诱导出一个水平集形式的二阶几何偏微分方程，从而将网格简化过程转化为隐式模型的体素扩散过程。该方法目前已经用于文化遗产数字化的大场景和文物的模型简化中。对水平集网格简化算法和现常用的基于点对收缩的网格简化算法在视觉质量和几何误差方面做了比较和分析，实验表明该方法适用于任意拓扑形状的网格模型，使得模型大规模简化后，在保持较低误差的同时，仍然能够保持相当多的重要几何特征和较好的整体视觉效果。

关键词: 网格简化, 水平集方法, 体素扩散, 文化遗产数字化