Detail-preserving variational surface design with multiresolution constraints

where I and II are the first and second fundamental forms of the surface S and ||.| | is a suitably chosen matrix norm. It is often the case, however, that the input model has high-frequency geometric detail across multiple resolutions which needs to be preserved during global deformations of its shape. Fairing techniques like the one just described tend to smooth out not only the global shape of the object, but the high-frequency detail as well (see Figure 2). To avoid this problem, multi-band decomposition schemes have been proposed [13], in which a multiresolution modeling operation and the associated fairing step are applied within one frequency band. Subsequently, the higher frequency detail is reconstructed using a displacement map. This implies computing and storing the displacement map prior to editing and restoring it afterwards. We opt for an alternative approach that avoids the computation of the displacement map and the overhead associated with saving and restoring high-frequency information by considering the deformations applied to the initial shape as a vector field defined over the input model. Instead of optimizing the energy of the deformed shape, we optimize the energy of the deformations and we apply the resulting smooth vector field to the original shape to obtain the deformed one. Using this approach, the input model becomes the rest shape to which the optimization converges in the absence of constraints. In the language of elastic body deformations, this is equivainria-00544740

Detail-preserving variational surface design with multiresolution constraints

International audienceWe present a variational framework for rapid shape prototyping. The modeled shape is represented as a Catmull-Clark multiresolution subdivision surface which is interactively deformed by direct user input. Free-form design goals are formulated as constraints on the shape and the modeling problem is cast into a constrained optimization one. The focus of this paper is on handling multiresolution constraints of different kinds and on preserving surface details throughout the deformation process. Our approach eliminates the need for an explicit decomposition of the input model into frequency bands and the overhead associated with saving and restoring high-frequency detail after global shape fairing. Instead, we define a deformation vector field over the model and we optimize its energy. Surface details are considered as part of the rest shape and are preserved during free-form model editing. We explore approximating the solution of the optimization problem to various degrees to balance trade-offs between interactivity and accuracy of the results

Detail-preserving variational surface design with multiresolution constraints

We present a variational framework for rapid shape prototyping. The modeled shape is represented as a Catmull-Clark multiresolution subdivision surface which is interactively deformed by direct user input. Free-form design goals are formulated as constraints on the shape and the modeling problem is cast into a constrained optimization one. The focus of this paper is on handling multiresolution constraints of different kinds and on preserving surface details throughout the deformation process. Our approach eliminates the need for an explicit decomposition of the input model into frequency bands and the overhead associated with saving and restoring high frequency detail after global shape fairing. Instead, we define a deformation vector field over the model and we optimize its energy. Surface details are considered as part of the rest shape and are preserved during free-form model editing. We explore approximating the solution of the optimization problem to various degrees to balance trade-offs between interactivity and accuracy of the results

Detail-preserving variational surface design with multiresolution constraints

We present a variational framework for rapid shape prototyping. The modeled shape is represented as a Catmull-Clark multiresolution subdivision surface which is interactively deformed by direct user input. Free-form design goals are formulated as constraints on the shape and the modeling problem is cast into a constrained optimization one. The focus of this paper is on handling multiresolution constraints of different kinds and on preserving surface details throughout the deformation process. Our approach eliminates the need for an explicit decomposition of the input model into frequency bands and the overhead associated with saving and restoring high frequency detail after global shape fairing. Instead, we define a deformation vector field over the model and we optimize its energy. Surface details are considered as part of the rest shape and are preserved during free-form model editing. We explore approximating the solution of the optimization problem to various degrees to balance trade-offs between interactivity and accuracy of the results