Convex hulls of bounded curvature

Jean-Daniel Boissonnat (1) , Sylvain Lazard (1)

1 PRISME - Geometry, Algorithms and Robotics

In this paper, we consider the problem of computing a convex hull of bounded curvature of a set S of points in the plane, i.e., a set containing S and whose boundary is a curve of bounded curvature of minimal length. We prove that, if the radius of the smallest disk that contains S is greater than 1, such a hull is unique. We show that the computation of a convex hull of bounded curvature reduces to convex programming or to solving a set of algebraic systems.

Domaines: Géométrie algorithmique [cs.CG]

Jean-Daniel Boissonnat, Sylvain Lazard. Convex hulls of bounded curvature. Canadian Conference on Computational Geometry (CCCG'96), 1996, Ottawa, Canada. pp.14-19. ⟨inria-00442802⟩