An investigation of curvature variations over recursively generated B-spline surfaces

ABSTRACT

The continuity properties of recursively generated B-spline surfaces over an arbitrary topology have been related to the eigenproperties of the local subdivision tranformation, and conditions have been established on the subdivision weightings for tangent plane continuity at extraordinary points. In this paper, curves through an extradordinary point, which align in both the tagent and binormal direction, are identified, and their curvatures are compared either side of the point. Further restrictions on the subdivision weightings are derived to optimize the curvature properties of the surface. In general continuity of curvature is not attained.

REFERENCES

• 1: A A Ball , D J T Storry, A matrix approach to the analysis of recursively generated B-spline surfaces, Computer-Aided Design, v.18 n.10, p.437-442, Oct. 1986
• 2: A. A. Ball , D. J. T. Storry, Conditions for tangent plane continuity over recursively generated B-spline surfaces, ACM Transactions on Graphics (TOG), v.7 n.2, p.83-102, April 1988 [doi>10.1145/42458.42459]
• 3: BALL, A. A., AND STORRY, D. J. T. Recursively generated B-spline surfaces. In CAD84 (Brighton, Sussex, U.K., April 3-5, 1984), Butterworths, 1984, 112-119.
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INDEX TERMS

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

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Eigenvalues and eigenvectors (direct and iterative methods)

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Geometric algorithms, languages, and systems

General Terms:
Algorithms, Design, Theory

Keywords:
discrete Fourier transform, non-rectangular topologies