A Measure of Non-convexity in the Plane and the Minkowski Sum

  • Authors:

  • R. N. Karasev

  • Affiliations:

  • Moscow Institute of Physics and Technology, Dept. of Mathematics, Institutskiy per. 9, 141700, Dolgoprudny, Russia

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2010

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Abstract

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for “not far from convex” regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no “holes”.