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Title:Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves
Authors:ID Jaklič, Gašper (Author)
ID Kozak, Jernej (Author)
ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author)
Files:URL http://dx.doi.org/10.1016/j.cagd.2008.07.006
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:In this paper, the geometric Lagrange interpolation of four points by planar cubic Pythagorean-hodograph (PH) curves is studied. It is shown that such an interpolatory curve exists provided that the data polygon, formed by the interpolation points, is convex, and satisfies an additional restriction on its angles. The approximation order is $4$. This gives rise to a conjecture that a PH curve of degree ▫$n$▫ can, under some natural restrictions on data points, interpolate up to ▫$n+1$▫ points.
Keywords:numerical analysis, planar curve, PH curve, geometric interpolation, Lagrange interpolation
Year of publishing:2008
Number of pages:str. 720-728
Numbering:Vol. 25, no. 9
PID:20.500.12556/RUP-7727 This link opens in a new window
ISSN:0167-8396
UDC:519.651
DOI:10.1016/j.cagd.2008.07.006 This link opens in a new window
COBISS.SI-ID:14898777 This link opens in a new window
Publication date in RUP:03.04.2017
Views:2155
Downloads:131
Metadata:XML RDF-CHPDL DC-XML DC-RDF
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Secondary language

Language:Slovenian
Title:Geometrijska Lagrangeova interpolacija z ravninskimi kubičnimi krivuljami s Pitagorejskim hodografom
Abstract:V članku je obravnavana geometrijska Lagrangeova interpolacija štirih točk z ravninskimi kubičnimi krivuljami s Pitagorejskim hodografom. Dokazano je, da taka interpolacijska krivulja obstaja, če je podatkovni poligon, ki ga sestavljajo interpolacijske točke, konveksen, in njegovi koti zadoščajo dodatnim omejitvam. Red aproksimacije je 4. Tako dobimo domnevo, da lahko PH krivulja stopnje ▫$n$▫ interpolira do ▫$n+1$▫ točk pri nekaterih naravnih pogojih na podatke.
Keywords:numerična analiza, ravninska krivulja, PH krivulja, geometrijska interpolacija, Lagrangeova interpolacija


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