| Title: | Parametric curves with Pythagorean binormals |
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| Authors: | ID Kozak, Jernej (Author)
ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author) |
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| Files: |  http://download.springer.com/static/pdf/237/art%253A10.1007%252Fs10444-014-9387-7.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs10444-014-9387-7&token2=exp=1443686327~acl=%2Fstatic%2Fpdf%2F237%2Fart%25253A10.1007%25252Fs10444-014-9387-7.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs10444-014-9387-7*~hmac=be8b3293d4d0115e847f9d5731a8f88c9cefeed18ace668ef1899ffa70905302
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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, a class of rational spatial curves that have a rational binormal is introduced . Such curves (called PB curves) play an important role in the derivation of rational rotation-minimizing osculating frames. The PB curve construction proposed is based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials. The construction significantly simplifies if the curve is a polynomial one. Further, polynomial PB curves of the degree % 7 and rational PB curves of the degree % 6 that possess rational rotation-minimizing osculating frames are derived, and it is shown that no lower degree curves, constructed from quadratic quaternion polynomials, with such a property exist. |
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| Keywords: | pitagorejski hodograf, pitagorejska binormala, racionalna krivulja, dualne koordinate, rotacijsko minimizirajoče ogrodje, pitagorejska binormala, racionalna krivulja, dualne koordinate, rotacijsko minimizirajoče ogrodje, Pythagorean-hodograph, Pythagorean-binormal, rational curve, dual coordinates, rotation-minimizing frame, osculating frame |
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| Year of publishing: | 2015 |
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| Number of pages: | str. 1-20 |
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| Numbering: | Vol. , no. |
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| PID: | 20.500.12556/RUP-7158  |
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| ISSN: | 1019-7168 |
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| UDC: | 519.65 |
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| DOI: | 10.1007/s10444-014-9387-7 |
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| COBISS.SI-ID: | 1537835204 |
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| Publication date in RUP: | 15.10.2015 |
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| Views: | 3899 |
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| Downloads: | 143 |
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| Metadata: |    |
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