Fast volume-preserving free-form deformation using multi-level optimization

We present a fast algorithm for preserving the total volume of a solid undergoing free-form deformation using level-of-detail representations. Given the boundary representation of a solid and user-specified deformation, the algorithm computes the new node positions of the deformation lattice, while minimizing the elastic energy subject to the volume-preserving criterion. During each iteration, a non-linear optimizer computes the volume deviation and its derivatives based on a triangular approximation, which requires a finely tessellated mesh to achieve the desired accuracy. To reduce the computational cost, we exploit the multi-resolution representations of the boundary surfaces to greatly accelerate the performance of the non-linear optimizer. This technique also provides interactive response by progressively refining the solution. Furthermore, it is generally applicable to lattice-based free-form deformation and its variants. Our implementation has been applied to several complex solids. We have been able to achieve an order of magnitude performance improvement over the conventional methods. (C) 2000 Elsevier Science Ltd. All rights reserved.