Keyframe Control of Smoke Simulations
Adrien Treuille, Antoine McNamara, Zoran Popović, Jos Stam
ACM Transactions on Graphics / SIGGRAPH (2003)

We describe a method for controlling smoke simulations through user-specified keyframes. To achieve the desired behavior, a continuous quasi-Newton optimization solves for appropriate "wind" forces to be applied to the underlying velocity field throughout the simulation. The cornerstone of our approach is a method to efficiently compute exact derivatives through the steps of a fluid simulation. We formulate an objective function corresponding to how well a simulation matches the user's keyframes, and use the derivatives to solve for force parameters that minimize this function. For animations with several keyframes, we present a novel multiple-shooting approach. By splitting large problems into smaller overlapping subproblems, we greatly speed up the optimization process while avoiding certain local minima.

Adrien Treuille, Antoine McNamara, Zoran Popović, Jos Stam (2003). Keyframe Control of Smoke Simulations. ACM Transactions on Graphics / SIGGRAPH, 22(3), 716--723.

author = "Adrien Treuille and Antoine McNamara and Zoran
Popovi\'{c} and Jos Stam",
title = "Keyframe Control of Smoke Simulations",
year = "2003",
month = jul,
journal = "ACM Transactions on Graphics / SIGGRAPH",
volume = "22",
number = "3",
pages = "716--723",
links = {},