Design of developable surfaces using the given data points

Abstract

Many products such as ships, buildings, and clothes contain developable surfaces generated by sweeping a straight line along a three-dimensional curve. An automated design process does not exist due to difficulties satisfying the conditions of a developable surface. This study proposes a method to design a developable surface from the intended data points using the design process of a two-piece brassiere cup as an example. Here, we model a developable surface based on the differential geometry, which converts the design to its boundary curves. Then we formulate the error between the developable surface and the data points from the geometry condition and the optimization problem in the design process. Our method is verified by applying it to three examples: a shape composed of two developable surfaces, a sphere, which is a non-developable surface, and a realistic breast shape.