The conversion of a dynamic B-spline curve into piecewise polynomials in power form
- Authors
- Kim, DS; Ryu, J; Lee, HC; Shin, H
- Issue Date
- Apr-2002
- Publisher
- ELSEVIER SCI LTD
- Keywords
- dynamic curve; B-spline; polynomial; power form; basis conversion; Taylor expansion
- Citation
- COMPUTER-AIDED DESIGN, v.34, no.4, pp.337 - 345
- Journal Title
- COMPUTER-AIDED DESIGN
- Volume
- 34
- Number
- 4
- Start Page
- 337
- End Page
- 345
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/26843
- DOI
- 10.1016/S0010-4485(01)00090-2
- ISSN
- 0010-4485
- Abstract
- The evaluation of points and the computations of inflection points or cusps on a curve are often necessary in CAGD applications. When a curve is represented in a B-spline form, such computations can be made easier once it is transformed into a set of piecewise polynomial curves in power form. The usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in power form is done either by a knot refinement followed by basis conversions, or by applying a Taylor expansion on each knot span of a B-spline curve. Presented in this paper is a new algorithm to convert a B-spline curve into a set of piecewise polynomial curves in power form. Experiment shows that the proposed algorithm significantly outperforms the conventional approach when one or more control points of a B-spline curve are continuously moving. (C) 2002 Elsevier Science Ltd. All rights reserved.
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