A Theory of Geometric Contact for Computer Aided Geometric Design of Parametric Curves

  • Chih Lee
  • Bahram Ravani
  • An Tzu Yang
Conference paper

Abstract

This paper develops a theory of contact for piecewise parametric curves based on the differential geometry of evolutes, polar curves and binormal indicatrices. This theory is completely geometric, independent of parametrization and generalizes to any order. Two sets of dimensionless characteristic numbers describing the local geometry of a curve up to the nth order are defined. These characteristic numbers can be used to describe conditions for higher order contacts in an algebraic fashion. The same characteristic numbers can also be used to interpret contact conditions of up to nth order in terms of the geometry of higher evolutes and binormal indicatrices. The resulting geometric contact conditions are used to design piecewise parametric curves for Computer Aided Geometric Design (CAGD) applications.

Key words

Geometric Contact Principal Evolute Polar Curve Binormal Indicatrix Geometric Continuity 
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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Chih Lee
    • 1
  • Bahram Ravani
    • 2
  • An Tzu Yang
    • 2
  1. 1.A74/124 IBM, MCAE IntegrationSan JoseUSA
  2. 2.Department of Mechanical EngineeringUniversity of CaliforniaDavisUSA

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