Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces

Helmut Pottmann*, Karsten Opitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Visualization of a scalar-valued function f{hook} defined on Euclidean n-space En is often based on its graph-hypersurface Γ(f{hook}) ⊂ Rn+1. Particularly for curvature interrogation, it is natural to equip Rn-1 with a so-called isotropic metric and use isotropic measures of the graph instead of Euclidean invariants. The ideas are extended to functions defined on surfaces in E3. We present the central formulae for a curvature analysis of functions defined on surfaces. It is shown how to use them for visualization purposes and as a mathematical basis for the construction of interpolating or approximating functions on surfaces.

Original languageEnglish (US)
Pages (from-to)655-674
Number of pages20
JournalComputer Aided Geometric Design
Issue number6
StatePublished - Dec 1994
Externally publishedYes


  • Curvature analysis
  • Differential geometry
  • Functions on surfaces
  • Isotropic geometry
  • Scattered data interpolation and approximation
  • Scientific visualization

ASJC Scopus subject areas

  • Modeling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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