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Title:Lagrange geometric interpolation by rational spatial cubic Bézier curves
Authors:ID Jaklič, Gašper (Author)
ID Kozak, Jernej (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author)
Files:URL http://dx.doi.org/10.1016/j.cagd.2012.01.002
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:V članku obravnavamo Lagrangeovo geometrijsko interpolacijo s prostorskimi racionalnimi kubičnimi Bézierovimi krivuljami. Pokažemo, da pod določenimi naravnimi omejitvami obstaja enolična rešitev problema. še več, rešitev je podana v preprosti zaključeni obliki in je zato zanimiva za praktične aplikacije. Asimptotična analiza potrdi pričakovani red aproksimacije, namreč 6. Numerični primeri nakažejo možnost uporabe te metode pri obetavni geometrijski nelinearni subdivizijski shemi.
Keywords:numerična analiza, geometrijska Lagrageova interpolacija, racionalna Bézierova krivulja, prostorska krivulja, asimptotična analiza, subdivizija, numerical analysis, geometric Lagrange interpolation, rational Bézier curve, spatial curve, asymptotic analysis, subdivision
Year of publishing:2012
Number of pages:str. 175-188
Numbering:Vol. 29, iss. 3-4
PID:20.500.12556/RUP-7735 This link opens in a new window
ISSN:0167-8396
UDC:519.651
COBISS.SI-ID:16207449 This link opens in a new window
Publication date in RUP:03.04.2017
Views:3078
Downloads:89
Metadata:XML DC-XML DC-RDF
:
JAKLIČ, Gašper, KOZAK, Jernej, VITRIH, Vito and ŽAGAR, Emil, 2012, Lagrange geometric interpolation by rational spatial cubic Bézier curves. [online]. 2012. Vol. 29, no. 3–4, p. 175–188. [Accessed 3 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.cagd.2012.01.002
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Secondary language

Language:English
Title:Lagrangeova geometrijska interpolacija z racionalnimi prostorskimi kubičnimi Bezierovimi krivuljami
Abstract:In the paper, the Lagrange geometric interpolation by spatial rational cubic Bézier curves is studied. It is shown that under some natural conditions the solution of the interpolation problem exists and is unique. Furthermore, it is given in a simple closed form which makes it attractive for practical applications. Asymptotic analysis confirms the expected approximation order, i.e., order six. Numerical examples pave the way for a promising nonlinear geometric subdivision scheme.


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