Filter Line Search*

The Incremental Potential Contact (IPC) method effectively maintains non-interpenetration constraints within solid simulations. This method models a constitutive relationship that directly correlates contact forces with their respective distances, thus converting the constrained problem into an unconstrained one. By using appropriately small time steps, the IPC allows for robust and accurate solid simulations free from obstacle interpenetration within an optimization-based time integration framework.

However, challenges arise when using larger time steps, which can introduce multiple local minima in the Incremental Potential. This condition can lead to tunneling issues, where solids might unexpectedly pass through obstacles due to overly large search directions. To mitigate this risk, we introduce a filter line search strategy supplemented by continuous collision detection (CCD). This approach is designed to prevent tunneling by continuously adjusting the trajectory of solids in response to potential collisions.

To illustrate these concepts, we will examine a case study where an elastic square falls onto the ground. This example will demonstrate the effectiveness of the IPC method along with the filter line search and CCD in managing the dynamics of solid bodies and ensuring accurate, interpenetration-free simulations.