2D Shape Deformation Using Nonlinear Least Squares Optimization

This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: Laplacian coordinates of the boundary curve and local area of the shape interior, which are together represented in a non-quadric energy function. An iterative Gauss-Newton method is used to minimize this nonlinear energy function. The result is an interactive shape deformation system that can achieve physically plausible results that are hard to achieve with previous linear least squares methods. Besides preserving local shape properties, we also introduce a scheme to preserve the global area of the shape which is useful for deforming incompressible objects.