移动立方体算法面二义性问题研究

Research on Ambiguous Cases of Marching Cubes Algorithm

在三维表面建模技术中,Marching Cubes算法是应用最为广泛的方法之一。该算法简单高效,但是也存在一定的不足之处,比如面的二义性问题。构造等值面时,在特定情况下对相同的等值点可以采取不同的连接方式,就会产生二义性,这将使得生成的等值面拓扑结构不一致,导致物体表面模型有孔洞。针对这一问题,本文提出了一种基于插值点连线交点的解决方法,通过计算插值点连线交点的场函数值,唯一确定二义性面上等值线的连接方式,解决了面二义性,保证了等值面拓扑结构的一致。

In the3D surface modeling technology,Marching Cubes is one of the most widely used algorithms.Thealgorithm is simple and efficient,but there are also some shortcomings,such as the ambiguous cases.When constructing theisosurface,if different connection methods are applied on the same equivalent point in the specific case,ambiguity will beproduced,which will cause the inconsistency of the generated isosurface topological structure,and eventually produce holeson the object surface.To solve this problem,this paper proposes a solution based on the intersection of interpolation points.By calculating the field function values of the intersection of interpolation points,the connection method of the isolines canbe uniquely determined,which solves the ambiguity problem and guarantees the consistency of the isosurface topologicalstructure.