シェル形状モデリングのオイラーモデルに関する研究

抄録

The paper represents the shell geometric modelling for sheet metal products and shell structured products. A modelling method for the shell geometry objects adopts the Euler topology based model firstly developed by Baumgart for the solid geometric modelling. The Euler characteristic equation for the shell geometric modelling is derived in the general form as ν-e+f-a=s-h and the Euler operations are introduced by the. use of the derived equation. The newly developed Euler equation makes it possible to deal with holes and flaps within faces, which are not homeomorphic to the 2-dimensional simplex. Verification to the derived equation is discussed from the view point of the graph theory as well. Some examples show that the new equation is applicable to a variety of shell geometries with the holes and flaps. Furthermore, a surface orientability is discussed and a recognition algorithm is offered to get rid of unoriented surface geometries. This algorithm also makes a difference between inner edges and boundary edges in the shell.