An elaborate ambiguity detection method for constructing isosurfaces within tetrahedral meshes

• Published in: Computers & graphics 1995-05, Vol.19 (3), p.355-364
• Main Authors: Zhou, Yong, Chen, Weihai, Tang, Zesheng
• Format: Article
• Language: English
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Exact sciences and technology; Pattern recognition. Digital image processing. Computational geometry
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/0097-8493(95)00006-X

The algorithm for constructing isosurfaces within tetrahedral meshes has been considered as one approach to solving the ambiguity problem in the marching cubes method and has attracted extensive attention. In this paper, it is pointed out that the ambiguity problem still exists even if isosurfaces are generated through tetrahedral meshes. Then, based on the assumption that the function value distribution along the edges of a cube is linear, the criterion for testing the intersection between an isosurface and a tetrahedron edge is given, followed by the intersection points calcuclation method. The connection of intersection points in tetrahedra to construct polygons and the triangularization of polygons are discussed in detail. A comparison between the marching cubes method, the existing marching tetrahedra method and the new marching tetrahedra method is presented. It is shown that the isosurfaces generated by our method are independent of the subdivision modes of the tetrahedra from cubes. Finally, two isosurface images generated by our method are shown.