隐式曲面的快速适应性多边形化算法

通过将隐式曲面多边形化过程分为“构造”和“适应性采样”两个阶段，实现了隐式曲面多边形逼近网格的适应性构造．通过基于空间延展的Marching Cubes方法得到隐式曲面较为粗糙的均匀多边形化逼近，根据曲面上的局部曲率分布，运用适应性细分规则对粗糙网格进行细分迭代，并利用梯度下降法将细分出的新顶点定位到隐式曲面上；最终得到的多边形网格是适应性的单纯复形网格，其在保持规定逼近精度的前提下，减少了冗余三角形的产生，网格质量有明显改善．该算法可用于隐式曲面的交互式可视化过程．

Rapid Polygonization of Implicit Surface Based on Adaptive Subdivision

This paper describes an adaptive and efficient algorithm for polygonization of implicit surfaces The algorithm covers two steps: initial polygonization and adaptive refinement In the first step, an initial coarse triangular mesh is created from the implicit surface using a variation of the traditional Marching Cubes Algorithm And then in the second step, the triangles in the coarse mesh are recursively subdivided by employing a sampling rate that varies spatially according to local complexity of the surface The vertices newly created in the refined mesh are projected onto the implicit surface by gradient-descending method Consequently, the algorithm produces the minimum number of polygons required to approximate the surface with a desired precision and the final mesh is simplicial complex Our algorithm can be used in the real-time environment of visualization to implicit surfaces