基于二次误差度量的网格简化算法

Mesh Simplification Based on Quadric Error Metrics

网格简化是提高计算机处理复杂模型速度的有效方法 ,要求算法时间和空间复杂性低、简化质量高且简化结果中三角形紧致性好 .给出一种简化三角形网格表示的三维模型的算法 .算法采用边折叠为基本操作 ,以点到相关直线的距离的平方为误差度量 .为降低算法的空间复杂性 ,简化过程中每个点只保留一个浮点数的历史记录 .实验结果表明 ,在 P 上 ,算法可在 12 s内简化含 7万个三角形的模型 ,简化结果中三角形紧致性大于 0 .9的三角形数为 56%

Mesh simplification can efficiently improve the processing speed of complex 3D models by computer. Mesh simplification requires low time and space complexity, high quality and triangularity compactness. A new algorithm to simplify dense meshes is presented. The algorithm uses edge collapse and error metrics based on squared distances from vertex to associated lines. To reduce the memory consumption, it keeps one float number for each vertex as the history record of the simplification. Examples running on a PⅢ machine show that the algorithm can simplify a model containing 7×10\+4 triangles in 12 s, and the number of triangles whose compactnesses are greater than 0 9 in simplified models is 56%.