NDLI: Representing conics by low degree rational DP curves

Content Provider	Springer Nature Link
Author	Hu, Qian qian Wang, Guo jin
Copyright Year	2010
Abstract	A DP curve is a new kind of parametric curve defined by Delgado and Peña (2003); it has very good properties when used in both geometry and algebra, i.e., it is shape preserving and has a linear time complexity for evaluation. It overcomes the disadvantage of some generalized Ball curves that are fast for evaluation but cannot preserve shape, and the disadvantage of the Bézier curve that is shape preserving but slow for evaluation. It also has potential applications in computer-aided design and manufacturing (CAD/CAM) systems. As conic section is often used in shape design, this paper deduces the necessary and sufficient conditions for rational cubic or quartic DP representation of conics to expand the application area of DP curves. The main idea is based on the transformation relationship between low degree DP basis and Bernstein basis, and the representation theory of conics in rational low degree Bézier form. The results can identify whether a rational low degree DP curve is a conic section and also express a given conic section in rational low degree DP form, i.e., give positions of the control points and values of the weights of rational cubic or quartic DP conics. Finally, several numerical examples are presented to validate the effectiveness of the method.
Starting Page	278
Ending Page	289
Page Count	12
File Format	PDF
ISSN	18691951
Journal	Journal of Zhejiang University SCIENCE C
Volume Number	11
Issue Number	4
e-ISSN	1869196X
Language	English
Publisher	SP Zhejiang University Press
Publisher Date	2010-04-17
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Conic sections Bernstein basis DP basis Rational low degree Bézier curves Rational low degree DP curves Communications Engineering, Networks Electronics and Microelectronics, Instrumentation Computer Systems Organization and Communication Networks Computer Hardware Electrical Engineering Computer Science
Content Type	Text
Resource Type	Article
Subject	Engineering

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