Geometric design of motions constrained by a contacting surface pair

Michael Hofer*, Helmut Pottmann, Bahram Ravani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We discuss the following problem which arises in robot motion planning, NC machining and computer animation: Given are a fixed surface Ψ and N positions Φ i of a moving surface Φ such that the Φ i are in point contact with Ψ. Compute a smooth and fair Euclidean gliding motion Φ(t) of the surface Φ on the surface Ψ which interpolates (or approximates) the given positions Φ i at time instances t i . First we generalize interpolatory variational subdivision algorithms for curves to curves on surfaces. Second we study an unconstraint motion design algorithm which we then extend to the main contribution of this paper, an algorithm for the design of a motion constraint by a contacting surface pair. Both motion design algorithms use a feature point representation of the moving surface, subdivision algorithms for curves, instantaneous kinematics, and ideas from line geometry. Geometric methods are used for the numerical solution of the arising optimization problems.

Original languageEnglish (US)
Pages (from-to)523-547
Number of pages25
JournalComputer Aided Geometric Design
Volume20
Issue number8-9
DOIs
StatePublished - Jan 1 2003

Keywords

  • Gliding motion
  • Kinematics
  • Line geometry
  • Motion design
  • Variational subdivision

ASJC Scopus subject areas

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

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