Applications of Laguerre geometry in CAGD

Helmut Pottmann*, Martin Peternell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

90 Scopus citations

Abstract

We briefly introduce to the basics of Laguerre geometry and then show that this classical sphere geometry can be applied to solve various problems in geometric design. In the present part, we focus on applications of the cyclographic model of Laguerre geometry and the cyclographic map. It relates the medial axis and Voronoi curves/surfaces to special surface/surface intersections and the corresponding trimming procedures to hidden line removal. Rational canal surfaces are treated as cyclographic images of rational curves in ℝ4. This leads to a simple control structure for rational canal surfaces. Its practical use is demonstrated at hand of modeling techniques with Dupin cyclides.

Original languageEnglish (US)
Pages (from-to)165-186
Number of pages22
JournalComputer Aided Geometric Design
Volume15
Issue number2
DOIs
StatePublished - Jan 1 1998

Keywords

  • Blending
  • Canal surface
  • Dupin cyclide
  • Geometrical optics
  • Laguerre geometry
  • Medial axis
  • NC milling
  • Rational curve
  • Rational surface
  • Voronoi curve
  • Voronoi surface

ASJC Scopus subject areas

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

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