Interpolation of liquids' height inside a mesh

This short paper details an approach to simulate liquids inside a mesh with an approximate but fast method. Only height is computed, and is used for rendering. One of the benefits of our approach is that height is obtained in a continuous way, by interpolating accurately pre-computed heights. The algorithm presented here uses a two-dimensional Lagrange interpolation. Variables used for interpolation are: desired volume and rotation of the object. Interpolation is improved by using zeros of Chebyshev polynomials, to avoid Runge's phenomenon. Interpolating pre-computed data generates a 2D formula which, at runtime, costs negligible computational time. Results show a very small difference between interpolated height and pre-computed height (mean error <0.1%).