The simulation of deformable objects has received much attention, thanks to a wide range of applications in animation and shape modeling. A challenging issue is how to maintain the volume of objects such as soft tissues during deformation, which is often the key to physical realism. Irving and his coauthors provide a simple yet elegant solution to this problem by treating objects as incompressible fluids and applying fluid simulation techniques to maintain volume both globally and locally. In addition, they incorporate object contact and self-contact into the system of constraints, which allows conflicting constraints to be handled in a more systematic fashion.

One of the key ideas behind their success is to enforce incompressibility at the one-ring of each node rather than at each tetrahedron. This approach alleviates the problem caused by an overly constrained system, which typically leads to local minima. The authors also solve position and velocity separately when correcting volumes, which reduces oscillations often associated with volume recovery.

The proposed solution is simple, flexible, and elegant. Researchers and users of fluid and solid simulations, as well as shape manipulation, can all potentially benefit from learning the details of this work. On the other hand, an open question remains: What is the most proper representation for the purpose of shape deformation, especially when interactivity is highly desired? While volume preservation is important, it usually requires treating shapes as solids rather than their boundary surfaces. The jury still seems to be undecided on this issue.