دانلود رایگان مقاله سطوح freeform تطبیقی

Abstract

The conformality of freeform surfaces highly affects their rendering and tessellation results. To improve the conformality of freeform surfaces, a novel freeform surface representation named hierarchical freeform surfaces is presented in this paper. The conformality energy of hierarchical freeform surfaces is first formulated and its numerical approximation is then constructed using the composite Simpson’s rule. By constructing the parameterization of the initial freeform transformation using the Ricci flow method, the optimal freeform transformation is obtained by the Levenberg–Marquardt method, which is further interleaved with the freeform refinement procedure to generate a hierarchical freeform surface with bounded conformality deviations. Examples are given to show the performance of our algorithm for rendering and tessellation applications.

5. Conclusions

In order to improve conformality of given NURBS surfaces, an optimization algorithm is presented in this paper based on freeform transformations (hierarchical freeform surfaces). A nonlinear energy measuring the conformality deviations and its numerical approximation are formulated. To minimize the discretized version of the conformal energy, the initial freeform transformation is first obtained by approximating the conformal mapping of the 3D discretized mesh, which is computed using Ricci flow method. To further improve the conformality of the initial freeform transformation, the nonlinear conformality optimization and the transformation refinement interleave until the conformality deviation is reduced to the user specified tolerance. Several examples are given to show the performance of our algorithm for rendering and tessellation applications.