| Title: | Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves |
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| Authors: | ID Jaklič, Gašper (Author)
ID Kozak, Jernej (Author)
ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author)
ID Žagar, Emil (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.cagd.2008.07.006
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| 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. |
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| Keywords: | numerical analysis, planar curve, PH curve, geometric interpolation, Lagrange interpolation |
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| Year of publishing: | 2008 |
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| Number of pages: | str. 720-728 |
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| Numbering: | Vol. 25, no. 9 |
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| PID: | 20.500.12556/RUP-7727  |
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| ISSN: | 0167-8396 |
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| UDC: | 519.651 |
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| DOI: | 10.1016/j.cagd.2008.07.006 |
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| COBISS.SI-ID: | 14898777 |
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| Publication date in RUP: | 02.04.2017 |
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| Views: | 2510 |
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| Downloads: | 132 |
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