Reduce the stretch in surface flattening by finding cutting paths to the surface boundary

This paper presents a method for finding cutting paths on a 3D triangular mesh surface to reduce the stretch in the flattened surface. The cutting paths link the surface boundary and the nodes where the Gaussian curvature is high, and their total length is minimized. First, a linear algorithm for computing an approximate boundary geodesic distance map is introduced; the map encapsulates the undirected geodesic distance from every triangular node to the surface boundary approximately. This is followed by determining the undirected shortest paths passing through all the nodes where the Gaussian curvature is larger than a threshold. The cutting paths walk along the triangular edges of the given surface. Compared with other similar approaches, our method reaches a faster speed, and can deal with surfaces with widely distributed curvatures.