微分幾何学に基づく展開可能な曲面の設計支援

抄録

A method to design a developable surface and its developed shape is proposed. A developable surface, which is generated by sweeping a straight line along a three-dimensional curve, can be seen every product such as shipping, architecture, cloth, and so on. Although it is important to design the surface in case that designers give some constraints, its design process is not automated because of the difficulty of its modeling. Especially, cloth products are required to design not only its three-dimensional shape but also its developed shape. Therefore, we aim to propose a method to design the surface satisfying some constraints and its developed shape. As an example, we assume that some constraints are related to the control points of a curve in a developable surface. In this paper, it is revealed that the direction of a generatrix can be determined geometrically when a pair of three-dimensional curves is given. And this design process can be converted to the optimization problem. It is verified that we can calculate different surfaces and developed shapes using this method when different constraints are given.