Video shows the results of a solver I'm working on to allow my tank simulator's skinned-mesh-based tank tracks to have realistic catenary sag in the direction of gravity, without needing any physics simulation.
The solver is given two wheels and a fixed length of tank track pinned at the ends to the two wheels, and solves for the catenary curve that is tangent to both wheels and satisfies the constraint that the total length of the track sections (the free-hanging catenary section plus the length of each circular-arc** section in contact with the wheels) must equal the length of track provided.
** Due to the discrete nature of the track having a fixed number of hinged links, and the drive sprocket having a set number of teeth, what I'm calling circular wheels are in truth N-gons.
![](https://s2.save4k.ru/pic/gs8tIMGOJrQ/maxresdefault.jpg)