Geometric Contact Potential

New York University
ACM Transactions on Graphics (Siggraph 2025)
Interpolate start reference image.

Our method (right) elliminates the spurious collision forces in IPC (left).

Abstract

Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding intersections, which are the cause of most robustness problems in complex deformation simulation with contact. However, existing barrier-potential methods may lead to spurious forces and imperfect satisfaction of the geometric constraints. They may have strong resolution dependence, requiring careful adaptation of the potential parameters to the object discretizations.

We present a systematic derivation of a continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence on shape, and absence of forces in rest configurations. Our potential is formulated independently of surface discretization and addresses the shortcomings of existing potential-based methods while retaining their advantages.

We present a discretization of our potential that is a drop-in replacement for the potential used in IPC, and compare its behavior to other potential formulations, demonstrating that it has the expected behavior. The presented formulation connects existing barrier approaches, as all recent existing methods can be viewed as a variation of the presented potential, and lays a foundation for developing alternative (e.g., higher-order) versions.

Results

Challenging scenes

Our method is able to simulate challenging examples in the IPC without any intersection.

Large dhat

Our method (middle and right) allows much larger dhat compared with IPC (left).
dhat-distribution-epsilon.png

Shape optimization

Our simulator is naturally differentiable and allows shape optimizations. Large dhat allows our method to make progress in cases where IPC cannot.
plier.png

Less spurious forces

Our method does not have the horizontal spurious force in IPC that causes the block to rotate.

IPC

Ours

The collision force of our method is more concentrated at places where the force is necessary compared with IPC and convergent IPC.
plier.png

Friction forces

Our method naturally supports the IPC style friction.

IPC

Ours


Convergence

Thanks to the ability of using a large dhat, our method converges faster, thus takes less time to simulate.

IPC

Ours