Swarm Systems Lab

Paper accepted in Applied Mathematics and Computation!

← All news Four plots comparing a polygonal chain with its conventional and directional smoothings, and the error of each.

Paper accepted in Applied Mathematics and Computation!

Our paper titled Directional Mollification for Knot-Preserving C∞ Smoothing of Polygonal Chains with Explicit Curvature Bounds, by Alfredo González-Calvin, Juan F. Jiménez and Hector, has been accepted in Applied Mathematics and Computation.

We introduce a directional mollification operator that turns a polygonal chain into a C∞ curve that stays arbitrarily close to the original one while passing exactly through its vertices. The smoothing is local, so changing one segment only affects the curve in a controllable neighborhood, and the curvature comes with closed-form bounds. This is useful for generating smooth paths for robots, computer graphics and CNC machining.

A 3D polygonal chain inside a cube with its smoothed curves, next to a plot of curvature and its upper bounds.
A polygonal chain in 3D with both smoothings, and their curvature together with the closed-form curvature bounds.

The paper

  1. [J30]

    Directional Mollification for Knot-Preserving C∞ Smoothing of Polygonal Chains with Explicit Curvature Bounds

    A. González-Calvin, J. F. Jiménez, HG de Marina · Applied Mathematics and Computation

    Journal DOI PDF