六面体自動生成の原理と双対輪体の自己交差解消方法の提案  [in Japanese] The Principle of Automatic Hexahedral Mesh Generation and the Proposal of the Method for Getting Rid of Self-intersections of Dual Cycles  [in Japanese]

In all approaches of automatic generation of hexahedral meshes, there are some methods utilizing dual cycles of the quadrilateral mesh on the surface of the object based on STC theory. This paper points out the defect and its cause of those methods, in particular dual cycle elimination method and whisker weaving method. Both methods start with a quadrilateral surface mesh without self-intersections of dual cycles. But this condition is not a necessary one. This paper also makes clear the relation of self-intersections of dual cycles and possibility of hexahedral mesh generation and describes the necessary and sufficient condition that surface meshes have to satisfy for hexahedral mesh generation. Finally, the new canceling methods of self-intersecting dual cycles are proposed.