保证拓扑正确的高精度等值面提取技术

TOPOLOGICAL CORRECT AND HIGH RESOLUTION TECHNIQUE FOR THREE-DIMENSIONAL REVERSE

基于体数据的等值面提取是反求工程的重要组成部分。针对传统移动立方体算法存在二义性和提取精度较低等缺陷,新算法首先在立方体内采用三线性方法构造出精确等值面,然后引入面肩点、体肩点和变形点作为等值面的关键点,并对其几何属性进行分析,提出了一种自动保持拓扑正确的高精度等值面三角化算法。不同于以往的移动立方体算法,新算法无需事先生成多边形的基本构形列表,也不必进行旋转和互补等操作。对于任一给定的立方体配置,一旦计算出相应的变形点,新算法自动地对等值面进行三角化。最后给出的实例显示了新算法的有效性。

Isosurface extraction from volumetric data plays an important role in the field of visualization in scientific computing. To solve the ambiguity that the classical marching cube algorithm often suffers from and improve the extraction precision, first, accurate isosurface in the interior of cube is constructed by using the trilinear interpolant method. The face shoulder points, body shoulder points and inflection point are computed as the critical points located on the isosurface. The geometrical characteristics of those critical points are analyzed. Based on these preliminary results, a robust and high resolution triangulation algorithm for constructing a triangular mesh approximation to isosurface for data given on a 3D rectilinear grid is presented. Unlike the past work on marching cube algorithm, the new solution presented produces a robust representation of the surface in the interior of each grid cell without using look-up-table and complementary and rotation operations. For arbitrary cube configuration, once the corresponding inflection points have been computed, the new approach is intelligent to triangulate the isosurface. Finally, some examples are given to show the performance of the new algorithm.