面向二阶六面体生成的保证几何拓扑特征的等值面抽取方法

An Isosurface Extraction Method Guaranteed Topological Characteristics From Second-order Hexahedron

针对二阶多节点多面体可视化过程中存在的等值面准确拓扑及绘制、传输代价等问题,提出一种面向二阶20节点六面体生成的保证几何拓扑特征的等值面抽取方法.为反映网格单元内部等值面片真实凹凸性质、克服拓扑二义性,对二阶20节点六面体单元等参插值函数进行研究及特征分析,在网格单元棱边计算等值面片轮廓等值点,在表面及体内提取可以表现等值面几何特征的关键点;根据三类插值关键点间的逻辑关系制定了令拓扑准确唯一的等值面片三角化规则及修复策略,同时设计了基于关键点的三角面片压缩索引结构.实验结果证明,该方法可准确计算并描述二阶20节点六面体网格单元内部等值面的几何拓扑结构,具备对不同精度要求的适应性,并有效降低了绘制与传输代价.

In order to solve the problems in the visualization process of second-order multi-node polyhedrons, such as isosurface topolo- gy, drawing and transmission cost, an isosurface extraction method which can guarantee the geometric topology characteristics in sec- ond-order hexahedron is proposed. To reflect the real bump properties of the isosurface and overcome the topology ambiguity, it analy- zes the characteristics of second-order hexahedral parameter interpolation function, calculates accurate contour points in edge, extracts the surface critical points and mesh critical points which can performance the geometric features of isosurface in second-order 20-node hexahedron ; On the basis of the logical relationship among the three types of interpolation critical points, it develops the rules of isosur- face triangulation and repair strategies,which makes topology accurately and uniquely. At the same time, it designs the compressed in- dex structures of triangles based on the critical points. The results of experiments show that the method can calculate and describe the isosurface geometry topology accurately within the second-order 20-node hexahedron, it has the adaptation on different accuracy re- quirements, and reduces the drawing and transmission cost dramatically.