Flattenable Mesh Processing by Controllable Laplacian Evolution

Models represented by polygonal meshes have been more and more widely used in CAD/CAM systems. In sheet manufacturing industries, the flattenability of a model is very important. Prior methods for processing the flattenability of a mesh surface usually employ a constrained optimization framework, which takes the positions of all its non-boundary vertices as variables in computation. For a mesh surface with hundred thousands of vertices, solving such an optimization is very time-consuming, and may exceed the capacity of main memory. In this paper, we develop a controllable evolution method to process the flattenability of a given mesh patch. It decouples the global optimization problem into a sequence of local controllable evolution steps, each of which has only one variable. Therefore, mesh surfaces with large number of vertices can be processed.