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

Phillip J. Barry; Ronald N. Goldman

doi:10.1145/54852.378511

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

Phillip J. Barry, Ronald N. Goldman

Computer Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988
Editors	Richard J. Beach
Publisher	Association for Computing Machinery, Inc
Pages	199-204
Number of pages	6
ISBN (Electronic)	0897912756, 9780897912754
DOIs	https://doi.org/10.1145/54852.378511
State	Published - Aug 1 1988
Event	15th International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988 - Atlanta, United States Duration: Aug 1 1988 → Aug 5 1988

Publication series

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

Other

Other	15th International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988
Country/Territory	United States
City	Atlanta
Period	8/1/88 → 8/5/88

Bibliographical note

Publisher Copyright:
© 1988 ACM.

Keywords

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

Access

10.1145/54852.378511

Cite this

Barry, P. J., & Goldman, R. N. (1988). A recursive evaluation algorithm for a class of Catmull-Rom splines. In R. J. Beach (Ed.), Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988 (pp. 199-204). (Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988). Association for Computing Machinery, Inc. https://doi.org/10.1145/54852.378511

A recursive evaluation algorithm for a class of Catmull-Rom splines. / Barry, Phillip J.; Goldman, Ronald N.

Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988. ed. / Richard J. Beach. Association for Computing Machinery, Inc, 1988. p. 199-204 (Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Barry, PJ & Goldman, RN 1988, A recursive evaluation algorithm for a class of Catmull-Rom splines. in RJ Beach (ed.), Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988. Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988, Association for Computing Machinery, Inc, pp. 199-204, 15th International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988, Atlanta, United States, 8/1/88. https://doi.org/10.1145/54852.378511

Barry PJ, Goldman RN. A recursive evaluation algorithm for a class of Catmull-Rom splines. In Beach RJ, editor, Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988. Association for Computing Machinery, Inc. 1988. p. 199-204. (Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988). https://doi.org/10.1145/54852.378511

Barry, Phillip J. ; Goldman, Ronald N. / A recursive evaluation algorithm for a class of Catmull-Rom splines. Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988. editor / Richard J. Beach. Association for Computing Machinery, Inc, 1988. pp. 199-204 (Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1988).

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AB - 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.

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

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