A Novel Surface Flattening Method Based on Mesh Edges

This paper proposes a novel optimal method based on mesh edges for flattening complex surfaces. In the optimal flattening model, the edge-lengths of the original surface´s mesh are selected as optimization variables, and the error of the edge-lengths between the original mesh and the optimal mesh is selected as objective function, and each internal point of the mesh being developable is selected as optimization constrain. By Newton´s Method and matrix calculating technologies, the optimization problem can be resolved, and a developable surface which has the minimum error of the edge-lengths can be constructed. Finally, a ripple-style flattening method is used to flatten the optimal developable surface, thus the flattening result of the original surface is obtained. Numerical experimental results show that the method can flatten all kinds of complex surfaces stably, quickly and accurately, and the flattening operation can be finished more simply.