A least-norm approach to flattenable mesh surface processing

Following the definition of developable surface in differential geometry, the flattenable mesh surface, a special type of piecewise- linear surface, inherits the good property of developable surface about having an isometric map from its 3D shape to a corresponding planar region. Different from the developable surfaces, a flattenable mesh surface is more flexible to model objects with complex shapes (e.g., cramped paper or warped leather with wrinkles). Modelling a flattenable mesh from a given input mesh surface can be completed under a constrained nonlinear optimization framework. In this paper, we reformulate the problem in terms of estimation error. Therefore, the shape of a flattenable mesh can be computed by the least-norm solutions faster. Moreover, the method for adding shape constraints to the modelling of flattenable mesh surfaces has been exploited. We show that the proposed method can compute flattenable mesh surfaces from input piecewise linear surfaces successfully and efficiently.