A Shape-preserved Method To Improve The Developability Of Mesh

Developability is one of the most important intrinsic properties of surface, which is applied widely in practice. For instance, the modeling of ship needs bending some plane materials, while the materials can not afford tensioning and bending infinitely, so the surface of the ship should be developable or approximatively developable. Another example is the design and manufacture of clothes and shoes. Thereby the study on developability of surface is necessary.In the last few decades, much work has been done on the developability of two classes of surfaces: parametric surfaces and meshes. But most Mesh-based methods mainly discuss the approach to develop a mesh or to deform it with developability preserved, while seldom prior research on improving the developabihty of a mesh has been found in literature. Since subdivision is an important method for modeling complex objects, to improve the developabihty of subdivision surface becomes a valuable topic. This paper has discussed how to improve the developability of subdivision surface. It is formulated as a constrained optimization problem, which can preserve the shape of the mesh simultaneously.In the third chapter of this paper, numerical experiments illustrate its feasibility. We still found that for a fine mesh, the developability will be improved through Loop subdivision, while this does not necessary hold for a relatively coarse mesh. Therefor, the relationship between subdivision and the developability of a mesh should be studied in the future.