A recursive evaluation algorithm for a class of Catmull-Rom splines

Phillip J. Barry, Ronald N. Goldman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

It is known that certain Catmulb-Rom splines [7] interpolate their control vertices and share many properties such as affine invariance, global smoothness, and local control with B-spline curves; they are therefore of possible interest to computer aided design. It is shown here that another property a class of Catmull-Rom splines shares with B-spline curves is that both schemes possess a simple recursive evaluation algorithm. The Catmulb-Rom evaluation algorithm is constructed by combining the de Boor algorithm for evaluating B-spline curves with Neville's algorithm for evaluating Lagrange polynomials. The recursive evaluation algorithm for Catmull-Rom curves allows rapid evaluation of these curves by pipellning with specially designed hardware. Furthermore it facilitates the development of new, related curve schemes which may have useful shape parameters for altering the shape of the curve without moving the control vertices. It may also be used for constructing transformations to B-sier and B-spline form.

Original languageEnglish (US)
Title of host publicationProceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988
EditorsRichard J. Beach
PublisherAssociation for Computing Machinery, Inc
Pages199-204
Number of pages6
ISBN (Electronic)0897912756, 9780897912754
StatePublished - Aug 1 1988
Event15th International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988 - Atlanta, United States
Duration: Aug 1 1988Aug 5 1988

Publication series

NameProceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988

Other

Other15th International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988
CountryUnited States
CityAtlanta
Period8/1/888/5/88

Keywords

  • B-spline
  • Catmull-Rom spline
  • De Boor algorithm
  • Lagrange polynomial
  • Neville's algorithm
  • Recursive evaluation algorithm

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