Helix splines as an example of affine Tchebycheffian splines

Helmut Pottmann*, Michael G. Wagner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


The present paper summarizes the theory of affine Tchebycheffian splines and presents an interesting affine Tchebycheffian free-form scheme, the "helix scheme". The curve scheme provides exact representations of straight lines, circles and helix curves in an arc length parameterization. The corresponding tensor product surfaces contain helicoidal surfaces, surfaces of revolution and patches on all types of quadrics. We also show an application to the construction of planar C 2 motions interpolating a given set of positions. Because the spline curve segments are calculated using a subdivision algorithm, many algorithms, which are of fundamental importance in the B-spline technique, can be applied to helix splines as well. This paper should demonstrate how to create an affine free-form scheme fitting to certain special applications.

Original languageEnglish (US)
Pages (from-to)123-142
Number of pages20
JournalAdvances in Computational Mathematics
Issue number1
StatePublished - Jan 1994
Externally publishedYes


  • B-spline
  • Free-form curve
  • Tchebycheffian spline
  • blossoming
  • helicoidal surface
  • helix
  • motion design
  • quadric surface
  • screw motion
  • tensor product surface

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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