Rational continuity: parametric, geometric, and Frenet frame continuity of rational curves

ABSTRACT

The parametric, geometric, or Frenet frame continuity of a rational curve has often been ensured by requiring the homogeneous polynomial curve associated with the rational curve to possess either parametric, geometric, or Frenet frame continuity, respectively. In this paper, we show that this approach is overly restrictive and derive the constraints on the associated homogeneous curve that are both necessary and sufficient to ensure that the rational curve is either parametrically, geometrically, or Frenet frame continuous.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation
          Subjects: Spline and piecewise polynomial interpolation; Smoothing

  J. Computer Applications
  J.6 COMPUTER-AIDED ENGINEERING
      Subjects: Computer-aided design (CAD)

General Terms:
Algorithms, Design, Theory