面向移动端的渐进网格简化算法

针对现有渐进网格（PM）简化算法在网格高度简化时无法保持模型关键特征、简化速度慢、无法适应多种模型等问题，提出一种以可变参数结合二次误差和类曲率特征度的边折叠算法（QFVP），用于构建面向移动端的渐进网格。首先，该算法通过设置可变参数w，调整二次误差和类曲率特征度在边折叠误差中的相对大小，提升了算法的简化质量，扩大了算法的适用范围；其次，训练了一个误差反向传播（BP）神经网络，用于确定模型w值；再次，提出了边折叠过程中法向量线性估算法，提高算法简化速度，与Gouraud估算法相比，平均缩短网格简化时间23.7%。对比实验显示，QFVP简化生成渐进网格的基网格整体误差小于二次误差度量（QEM）算法和Melax算法；简化时间比QEM算法平均延长7.3%，比Melax算法平均缩短54.7%。

Progressive mesh simplification algorithm for mobile devices

To solve the problems that existing Progressive Mesh (PM) simplification algorithms are facing, such as, loosing key features when meshes are highly simplified, low simplification speed and limited applicability for various models, an edge-collapsing mesh simplification algorithm combining Quadric Error Metric （QEM） and curvature-like Feature value with Variable Parameter (QFVP) was proposed to build progressive meshes for mobile devices. Firstly, the variable parameter w was set to control the relative magnitude of quadratic error and curvature-like value in edge-collapsing error, improving the simplification quality of the algorithm and making the algorithm more applicable. Secondly, an error Back Propagation (BP) neural network was trained to determine the w value of the model. Thirdly, the normal vector linear estimation method in the edge-collapse process was proposed, which shortens the mesh simplification time by 23.7% on average compared to Gouraud estimation method. In the comparison experiments, the PM’s basic meshes generated by QFVP have smaller global error (measured by Hausdorff distance) than those generated by QEM algorithm or Melax algorithm. And QFVP has simplification time about 7.3% longer than QEM algorithm and 54.7% shorter than Melax algorithm.