Towards flattenable mesh surfaces

In many industries, products are constructed by assembled surface patches in 3, where each patch is expected to have an isometric map to a corresponding region in 2. The widely investigated developable surfaces in differential geometry show this property. However, the method to model a piecewise-linear surface with this characteristic is still under research. To distinguish from the continuous developable surface, we name them as flattenable mesh surfaces since a polygonal mesh has the isometric mapping property if it can be flattened into a two-dimensional sheet without stretching. In this paper, a novel flattenable mesh surface (Flattenable Laplacian mesh) is introduced and the relevant modelling tool is formulated. Moreover, for a given triangular mesh which is almost flattenable, a local perturbation approach is developed to improve its flattenability. The interference between the meshes under process and their nearby objects has been prevented in this local flattenable perturbati...

• Type: Journal
• Year: 2008
• Where: CAD
• Authors: Charlie C. L. Wang
• Keywords: CAD 2008, Continuous Developable Surface, Flattenable Mesh, Mesh, Theoretical Computer Science