Distributional radius of curvature
We show that any continuous plane path that turns to the left has a well-defined distribution that corresponds to the radius of curvature of smooth paths. We show that the distributional radius of curvature determines the path uniquely except for a translation. We show that Dirac delta contributions in the radius of curvature correspond to facets, that is, flat sections of the path, and show how a path can be deformed into a facet by letting the radius of curvature approach a delta function. Copyright © 2005 John Wiley & Sons, Ltd.
Publication Source (Journal or Book title)
Mathematical Methods in the Applied Sciences
Estrada, R. (2006). Distributional radius of curvature. Mathematical Methods in the Applied Sciences, 29 (4), 427-444. https://doi.org/10.1002/mma.692