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SAVOYE, Y. 2017. Stokes coordinates. In Proceedings of the 33rd computer graphics spring conference, 15-17 May 2017, Mikulov, Czech Republic. New York: ACM [online], article no. 5. Available from: https://doi.org/10.1145/3154353.3154354
Cage-based structures are reduced subspace deformers enabling non-isometric stretching deformations induced by clothing or muscle bulging. In this paper, we reformulate the cage-based rigging as an incompressible Stokes problem in the vorticity space. The key to our approach is a compact stencil allowing the expression of fluid-inspired high-order coordinates. Thus, our cage-based coordinates are obtained by vorticity transport as the numerical solution of the linearized Stokes equations. Then, we turn the incompressible creeping Newtonian flow into Stokes equations, and we devise a second-order compact approximation with center differencing for solving the vorticity-stream function. To the best of our knowledge, our work is the first to devise a vorticity-stream function formulation as a computational model for cage-based weighting functions. Finally, we demonstrate the effectiveness of our new techniques for a collection of cage-based shapes and applications.