“Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections.”
Every point on the curve pushes against every other point, so it can never pass through itself. That turns knot untangling, cable routing and 3D layout into one optimization problem. The paper compared 19 alternative methods and its scheme beat them. The code is open, the math is hard, and the results look like art.