3D ball skinning using PDEs for generation of smooth tubular surfaces

Greg Slabaugh*, Brian Whited, Jarek Rossignac, Tong Fang, Gozde Unal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C1 continuous, and for each ball, it is tangent to the ball along a circle of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's surface area, mean curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations.

Original languageEnglish
Pages (from-to)18-26
Number of pages9
JournalCAD Computer Aided Design
Issue number1
Publication statusPublished - Jan 2010
Externally publishedYes


  • Minimal surfaces
  • Partial differential equations
  • Skinning
  • Splines
  • Variational methods


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