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Author Goldman, Ronald N. ♦ Barry, Phillip J.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Recursive evaluation algorithm ♦ Neville's algorithm ♦ De boor algorithm ♦ Lagrange polynomial ♦ Catmull-rom spline ♦ B-spline
Abstract It is known that certain Catmull-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 Catmull-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 pipelining 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 Bézier and B-spline form.
Description Affiliation: Computer Graphics Laboratory, Computer Science Dept., Univ. of Waterloo, Waterloo, Ontario, Canada N2L 3G1 (Barry, Phillip J.; Goldman, Ronald N.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1988-08-01
Publisher Place New York
Journal ACM SIGGRAPH Computer Graphics (COMG)
Volume Number 22
Issue Number 4
Page Count 6
Starting Page 199
Ending Page 204


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Source: ACM Digital Library