Minimal distance segment to segment with Karush-Kuhn-Tucker conditions



The module minDist2segments_KKT returns the minimal distance between two line segments. It uses the Karush-Kuhn-Tucker conditions (KKT) for the minimization under constraints.

Practical application

We use the present module to avoid topology violations in an entangled polymer system. To preserve the topology in a system of entangled polymers we need to determine the minimal distance between two bonds. Once done we can apply either a soft or hard core potential to avoid the crossing of two bonds. Here, we propose to determine the minimal distance between two segments with the help of the Karush-Kuhn-Tucker conditions.

This module is a part of an E-CAM pilot project at the ENS Lyon, focused on the implementation of contact joint to resolve excluded volume constraints

Background information

A detailed derivation of the minimal distance between two segments using the Karush-Kuhn-Tucker conditions is available at

This module is used by other ongoing work, such as module velocities_resolve_EV, that resolves the excluded volume constraint  with a velocity formulation.

Source code

The source code and more information can be found at minDist2segments_KKT GitLab repository.