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Arc length preserving approximation of circular arcs by Pythagorean-hodograph curves of degree seven

2022/01/19 by Emil Žagar, Žagar, Emil
Computer Science · Engineering · #65D05 #65D07 #65D17 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Image and Object Detection Techniques #Numerical Analysis (math.NA) #Tribology and Lubrication Engineering

paper · pdf · doi:10.48550/arxiv.2201.07445

openalex publication_date 2022/01/19 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper interpolation of two planar points, corresponding tangent directions and curvatures with Pythagorean-hodograph (PH) curves of degree seven preserving an arc length is considered. A general approach using complex representation of PH curves is presented and a detailed analysis of the problem for data arising from a circular arc is provided. In the case of several solutions some criteria for the selection of the most appropriate one are described and an asymptotic analysis is given. Several numerical examples are included which confirm theoretical results.

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