A New Constrained Shape Deformation Operator With Applications in Footwear Design Available to Purchase

In this paper, we address a problem that arises in several engineering applications: the deformation of a curve with constraints on its length. Since length is an integral property, typically computed by numerical methods, therefore implementing such shape change operations is non trivial. Recently some researchers have attempted to solve such problems for multi-resolution representations of curves. However, we take a differential geometric approach. The modification problem is formulated as constrained optimization problem, which is subsequently converted to an unconstrained min-max problem using Lagrangian multipliers. This problem is solved using the Uzawa method. The approach is implemented in MATLAB™, and some examples are presented in the paper.