Application of a metric for complex polynomials to bounded modification of planar Pythagorean-hodograph curves

Farouki, Rida A. M. T. (author), Knez, Marjetka (author), Vitrih, Vito (author), Žagar, Emil (author)

By interpreting planar polynomial curves as complex-valued functions of a real parameter, an inner product, norm, metric function, and the notion of orthogonality may be defined for such curves. This approach is applied to the complex pre-image polynomials that generate planar Pythagorean-hodograph (PH) curves, to facilitate the implementation of bounded modifications of them that preserve their PH nature. The problems of bounded modifications under the constraint of fixed curve end points and end tangent directions, and of increasing the arc length of a PH curve by a prescribed amount, are also addressed.

• Language: English
• Keywords: complex polynomials, inner product, norm, metric, Pythagorean-hodograph curves, bounded modification
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 16 str.
• Numbering: Vol. 456, art. 116235
• PID: 20.500.12556/RUL-160684
• UDC: 519.6
• ISSN on article: 0377-0427
• DOI: 10.1016/j.cam.2024.116235
• COBISS.SI-ID: 206109955
• Publication date in RUL: 03.09.2024

Record is a part of a journal

• Title: Journal of computational and applied mathematics
• Shortened title: J. comput. appl. math.
• Publisher: Elsevier
• ISSN: 0377-0427
• COBISS.SI-ID: 27496960

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• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
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