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Controllable Smoke Animation With Guiding Objects LIN SHI and YIZHOU YU University of Illinois at Urbana-Champaign This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target implicit function, a shape transformation is generated between an initial smoke region and the target object. In order to match the smoke surface with the target surface, we impose carefully designed velocity constraints on the smoke boundary during a dynamic ?uid simulation. The velocity constraints are derived from an iterative functional minimization procedure for shape matching. The dynamics of the smoke is formulated using a novel compressible ?uid model which can effectively absorb the discontinuities in the velocity ?eld caused by imposed velocity constraints while reproducing realistic smoke appearances. As a result, a smoke region can evolve into a regular object and follow the motion of the object, while maintaining its smoke appearance. Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation; I.6.8 [Simulation and Modeling]: Types of Simulation—Animation General Terms: Algorithms, Experimentation, Theory Additional Key Words and Phrases: Constrained animation, ?uid simulation, implicit functions, level sets, shape matching, shape transformations, velocity constraints 1. INTRODUCTION Amorphous but elegantly moving matters, such as clouds, fog, and smoke, give people plenty of space for imagination. We are excited when a cloud in the sunset sky assumes the approximate shape of an animal or some other real object. It is indeed an exhilarating event because of its rareness. For the same