Collision detection and the physically based modeling of deformable objects have been extensively researched. These processes need to be carried out in real time for interactive applications. To ensure real-time rates throughout the simulation, it is desirable to use time-critical systems that can interrupt the collision detection process or the object deformation simulations to fit a time budget. The authors of this paper tackle this important problem, and present an interruptible approach for collision detection and the animation of deformable solids.

The authors’ physical model is a stiffness warping formulation of linear finite element methods. They seem to be using vertex warping instead of element warping, which may yield inaccurate results due to ghost forces. These ghost forces appear since node warping does not guarantee that the sum of elastic forces is null. The model lies in a hexahedral mesh, with elements of different sizes leading to situations where a hexahedron may have four (or more) smaller neighbor hexahedrons, and hence vertices in the middle of the edges, known as virtual nodes. This creates T-junctions that are not advisable for visually realistic simulations. To handle this, the authors detect the virtual nodes, and use projection constraints to correct the position of the virtual node and put it on the edge of the neighbor hexahedron. The authors do not give details of how projection constraints are computed; they don’t specify if they move only the location of the node, or compute a force to place it in the desired position. If the node has been simply relocated without a force constraint, then this might increase the ghost forces already existing in the model.

Time-critical deformable object simulation was achieved by means of a multiresolution approach. The authors used a mechanism to predict a required number of on-the-fly simplifications or subdivisions. The prediction is based on the error given by the difference between the current and desired simulation cost of the considered simulation step. Hence, highly deformed parts are refined, and less deformed parts are simplified. Changing the topology to make subdivisions or simplifications may introduce some artifacts in the underlying physical model. The authors give a short and insufficient explanation on this subject. Additionally, it would have been desirable to describe in detail how the cost functions were computed.

To carry out interruptible collision detection, the authors used sphere tree hierarchies, but they don’t explain how the sphere tree is generated and adapted after topology modifications. I tend to think that they used an octree to generate the sphere tree, since it is also used to update the hierarchy tree. The authors update the hierarchies using a combination of existing techniques, however the way they interrupt the collision detection process is not clear.

Most of the work in this paper is based on a clever combination of existing techniques. However, in some parts of the paper, there is a need for further explanations of important aspects, including how the cost functions are computed, how the collision detection is interrupted, and which sphere-tree generator was used.