中文摘要：

提出了一种基于体积平方度量的三角形折叠网格简化新方法．新方法通过极小化误差目标函数简化三角形网格．简化误差定义为三角形简化后产生的网格模型平方体积变化，并以三角形几何形状因子和法向因子作为约束．简化误差的表示形式为一个二次目标函数，因此，每次简化后三角形网格的新顶点是一个线性问题的解．与目前简化效率最好的QEM方法相比，新方法不增加算法复杂度．如果被简化的三角形是强特征三角形，则用其高斯曲率最大的顶点作为新顶点，以保持原始模型的细节特征；对于非强特征三角形，新顶点用极小化折叠误差确定．对于边界三角形，新顶点的位置由不同于内部三角形的方法进行计算，保持了网格的边界特征．最后用实例说明新方法的有效性．

英文摘要：

A new algorithm for mesh simplification with triangle collapse based on square volume measure is presented in this paper. Models can be simplified by minimizing error objective function. Square volume error, shape factor and normal constraint factor of triangles are combined together to define the simplification error, which can be described as a quadratic objective function. New vertices replaced collapsed triangles can be determined linearly. Comparing with the QEM method which is the most effective method so far, computation complexity will not be increased. Gaussian curvature factor is computed for each collapsed triangle and used to identify strong feature triangle. For non-strong feature triangle, new vertex position is determined by minimizing the error objective function. For strong feature triangle, new vertex is taken the strong feature vertex of the three triangle vertices for preserving the model feature. Each collapsed triangle is processed as inner triangle or boundary triangle to keep the boundary feature. Experiments for the efficiency of the new algorithm are included.