Detail-Preserving Variational Design of B-Spline Curves and Surfaces

Multiresolution models provide a powerful tool forcomplex shape multiresolution editing. However, it is stillhard and not intuitive to modify the overall shape of amodel while preserving its details by manipulating itscontrol points at lower resolution levels. A better controlof deformations and a more intuitive interface shouldallow the user to control the deformation of a model bymanipulating the model directly. This can be achieved byusing variational modeling techniques. This paperpresents a variational framework for multiresolutionmodel design. The modeled shape is represented as amultiresolution B-spline curve or surface, which can beinteractively deformed by direct user inputs. The focus ofthis paper is on handling multiresolution constraints andpreserving surface details throughout the deformationprocess. To avoid smoothing out the details of the shape invariational modeling, we optimize the deformation energyalone instead of the total energy of the deformed shape.To accelerate the convergence of the iterative energyminimization process, a wavelet-based iterative method isused to compute the solution in a hierarchical fashion.