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Title:C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs
Authors:ID Bastl, Bohumír (Author)
ID Bizzarri, Michal (Author)
ID Knez, Marjetka (Author)
ID Lávička, Miroslav (Author)
ID Michálkova, Kristýna (Author)
ID Šír, Zbiněk (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author)
Files:URL http://dx.doi.org/10.1016/j.cam.2013.08.007
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:In this paper the C1 Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates C1 data at one point and they are then joined together with a C1 continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally C1 continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.
Keywords:mathematics, parametric curve, PH curve, Pythagorean-hodograph, Hermite interpolation, biarc, cubic curve
Year of publishing:2014
Number of pages:str. 65-78
Numbering:Vol. 257
PID:20.500.12556/RUP-7739 This link opens in a new window
ISSN:0377-0427
UDC:519.65
COBISS.SI-ID:16726361 This link opens in a new window
Publication date in RUP:03.04.2017
Views:2672
Downloads:43
Metadata:XML DC-XML DC-RDF
:
BASTL, Bohumír, BIZZARRI, Michal, KNEZ, Marjetka, LÁVIČKA, Miroslav, MICHÁLKOVA, Kristýna, ŠÍR, Zbiněk, VITRIH, Vito and ŽAGAR, Emil, 2014, C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs. [online]. 2014. Vol. 257, p. 65–78. [Accessed 3 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.cam.2013.08.007
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Secondary language

Language:English
Abstract:V članku je obravnavana C1 Hermiteova interpolacija s prostorskimi loki, katerih hodograf je pitagorejski. Opisan je splošen algoritem za njihovo konstrukcijo. Vsak segment loka, ki je sestavljen iz dveh delov, interpolira pozicijo in tangento v robni točki. Segmeta sta v sredini spojena C1 gladko. Dobljen lok je podan v zaključeni obliki s tremi prostimi parametri. Dva sta izbrana na podlagi asimptotične analize, tretjega pa izberemo tako, da minimiziramo dolžino loka ali elastično napetostno energijo. Končni rezultat je interpolacijski zlepek, ki ga je mogoče konstruirati lokalno in obstaja za poljubno konfiguracijo podatkov Hermiteovega tipa.
Keywords:matematika, parametrična krivulja, PH krivulja, pitagorejski hodograh, Hermiteova interpolacija, lok, kubična prostorska krivulja


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