Area, perimeter and derivatives of a skin curve

  • Authors:

  • Ho-Lun Cheng;Herbert Edelsbrunner

  • Affiliations:

  • Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL;Department of Computer Science, Duke University, Durham, and Raindrop Geomagic, Research Triangle Park, NC

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2003

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Abstract

The body defined by a finite collection of disks is a subset of the plane bounded by a tangent continuous curve, which we call the skin. We give analytic formulas for the area, the perimeter, the area derivative, and the perimeter derivative of the body. Given the filtrations of the Delaunay triangulation and the Voronoi diagram of the disks, all formulas can be evaluated in time proportional to the number of disks.