Keywords
approximation theory, computational geometry, polynomials, solid modelling, approximation errors, canonical representation
Abstract
The interval Bezier curve, which, unlike other curve and surface approximation schemes, can transfer a complete description of approximation errors between diverse CAD/CAM systems that impose fundamentally incompatible constraints on their canonical representation schemes, is described. Interval arithmetic, which offers an essentially infallible way to monitor error propagation in numerical algorithms that use floating-point arithmetic is reviewed. Affine maps, the computations of which are key operations in the de Casteljau subdivision and degree-elevation algorithms for Bezier curves, the floating-point error propagation in such computations, approximation by interval polynomials, and approximation by interval Bezier curves are discussed.
Original Publication Citation
Sederberg, T. W., and R. T. Farouki. "Approximation by Interval Bezier Curves." Computer Graphics and Applications, IEEE 12.5 (1992): 87-95.
BYU ScholarsArchive Citation
Sederberg, Thomas W. and Farouki, Rida T., "Approximation by interval Bezier curves" (1992). Faculty Publications. 714.
https://scholarsarchive.byu.edu/facpub/714
Document Type
Peer-Reviewed Article
Publication Date
1992-09-01
Permanent URL
http://hdl.lib.byu.edu/1877/1249
Publisher
IEEE
Language
English
College
Physical and Mathematical Sciences
Department
Computer Science
Copyright Status
© 1992 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Copyright Use Information
http://lib.byu.edu/about/copyright/