Modeling Developable Mesh Surface by Lofting

Abstract

In the metal building and garment industries, product model is required to be or closed to be developable surface (can be flattened onto planar patterns without any distortion, tear or stretch).Current work mainly focuses on interpolating only two curves with a narrow developable strip, and lose the generality of applications in industries, which often require N (N>2) curves to determine the final shape feature, and seek one interpolated developable surface. In this paper, a new developability degree criterion is introduced first and a novel lofting algorithm is proposed to model a quasi-developable mesh surface for the given characteristic curves. The curves are first adaptively sampled and then planar triangles are tiled to interpolate all sampling points. The optimal triangulation in terms of given criterion is mapped as one shortest-path finding graph problem, which can be solved by using well-known Dijkstra’s algorithm.