Differentiable Curl-Noise: Boundary-Respecting Procedural Incompressible Flows Without Discontinuities

We present Differentiable Curl-Noise, a C1 procedural method to animate strictly incompressible fluid flows in two dimensions. While both the original Curl-Noise method of Bridson et al. [2007] and a recent modification by Chang et al. [2022] have been used to design incompressible flow fields, they often suffer from non-smoothness in their handling of obstacles, owing in part to properties of the underlying Euclidean distance function or closest point function. We therefore propose a differentiable scheme that modulates the background potential in a manner that respects arbitrary solid simple polygonal objects placed at any location, without introducing discontinuities. We demonstrate that our new method yields improved flow fields in a set of two dimensional examples, including when obstacles are in close proximity or possess concavities.