Large, 3D ice formations such as icicles exhibit a high degree of geometric and optical complexity. Modeling these features by hand can be a daunting task, so we present a novel physically-based algorithm for simulating this phenomenon. Solidification is usually posed as a so-called `Stefan problem', but the problem in its classic form is inappropriate for simulating the ice typically found in a winter scene. We instead use the `thin-film' variant of the Stefan problem to derive velocity equations for a level set simulation. However, due to the scales involved in the problem, even an adaptive grid level set solver is still insufficient to track the tip of an icicle. Therefore, we derive an analytical solution for the icicle tip and use it to correct the level set simulation. The results appear to be in agreement with experimental data. We also present a physically-based technique for modeling ripples along the ice surface that alleviates the need to explicitly track small-scale geometry. To our knowledge, our approach is the most complete model available, and produces complex visual phenomena that no previous method has been able to capture.

Full Paper:	To appear in 2006 ACM/Eurographics Symposium on Computer Animation [2.3 MB PDF]
Videos:	Icicles growing on a fountain [5.8 MB MOV] Icicles forming on a rooftop [5.4 MB MOV] Simulated Andy Goldsworthy sculpture [8.2 MB MOV]
Links:	The original Andy Goldsworthy sculpture: