Mesh Editing with Curvature Flow Laplacian

Differential coordinates are essentially vectors encoded in the global coordinate system. Since the local features on a mesh are deformed and rotated during editing, the differential coordinates must somehow be transformed to match the desired new orientations, otherwise distortion like shearing and stretching will occur. This transformation problem is basically a chicken-and-egg problem: the reconstruction of the deformed surface requires properly oriented differential coordinates, while the reorientation of these coordinates depend on the unknown deformed mesh. We present an iterative Laplacian-based editing framework to solve this transformation problem. The only user input required are the positions of the handles, not their local frames. Thus our system supports simple point handle editing. Our iterative updating process nds the best orientations of local features, including the orientations at the point handles.