Detail-preserving variational design of B-spline curves and surfaces

Multiresolution models provide a powerful tool for complex shape multiresolution editing. However, it is still hard and not intuitive to modify, the overall shape of a model while preserving its details by manipulating its control points at lower resolution levels. A better control of deformations and a more intuitive interface should allow the user to control the deformation of a model by manipulating the model directly. This can be achieved by using variational modeling techniques. This paper presents a variational framework for multiresolution model design. The modeled shape is represented as a multiresolution B-spline curve or surface, which can be interactively deformed by direct user inputs. The focus of this paper is on handling multiresolution constraints and preserving surface details throughout the deformation process. To avoid smoothing out the details of the shape in variational modeling, we optimize the deformation energy alone instead of the total energy of the deformed shape. To accelerate the convergence of the iterative energy minimization process, a wavelet-based iterative method is used to compute the solution in a hierarchical fashion.