Least squares quasi-developable mesh approximation

Surface developability is a key feature in many industrial product designs. In this paper, based on a measure defined in an extended Gaussian image, an efficient least squares solution is proposed to achieve an optimal quasi-developable mesh patch. For a free-form mesh model assembled by a set of patches, each patch can be deformed using the least squares solution to obtain the best developability within a user-specified tolerance while the patch boundary remains continuous with neighboring patches. The proposed least squares scheme formulates the quasi-developable mesh approximation problem as a large sparse linear system with its coefficient matrix independent of the mesh verticesʼ new positions. We show that this linear system can be efficiently solved by a least squares direct matrix solver. Experimental results and applications are provided to demonstrate the controllability of shape change as well as the effectiveness of mesh developability improvement provided by the proposed solution.