\[r=\sqrt{1+\alpha\cos2\theta}.\] All these curves enclose the same area.

The quality of a Fourier approximation of a closed curve \(\gamma:\mathbb S^1\to\mathbb R^2\) depends heavily on its parametrization. Below: a square approximated with 1, 2, and 3 nonzero Fourier modes.

2. A simple incompressible fluid solver that dramatically reduces the energy loss associated with advection-projection algorithms. This paper was a lot of fun to write; big props to my coauthors Jonas Zehnder and Bernhard Thomaszewski at the U de Montréal.
jzehnder.me/publications/advec

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1. A method to simulate cloth with accurate frictional contact, using an adaptive refinement strategy and an implicit formulation for exact Coulomb friction. Most of the credit goes to lead author Jie Li and to our INRIA collaborators Gilles Daviet and Florence Bertails-Descoubes.
www-users.cselabs.umn.edu/~lix

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