Curve and surface design using multiresolution constraints

Abstract

The paper presents a method of designing curves and surfaces by solving the constraints imposed on the shapes at multiresolution levels. In this method, the curves and surfaces are represented by endpoint interpolating B splines and their corresponding wavelets. At each resolution level, the shape is determined by minimizing the energy function subject to the deformation of the shape while preserving the given constraints. Constraints at a low resolution level are converted to those at a high resolution level using wavelet transforms in order to associate all the constraints with the common basis functions. The constraints at multiresolution levels are then solved recursively from low to high resolution levels. Design examples are also presented.