Parametric curves with Pythagorean binormals

Kozak, Jernej; Knez, Marjetka; Vitrih, Vito

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Title:	Parametric curves with Pythagorean binormals
Authors:	ID Kozak, Jernej (Author) ID Knez, Marjetka (Author) ID Vitrih, Vito (Author)
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
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
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.
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
Year of publishing:	2015
Number of pages:	str. 1-20
Numbering:	Vol. , no.
PID:	20.500.12556/RUP-7158
ISSN:	1019-7168
UDC:	519.65
DOI:	10.1007/s10444-014-9387-7
COBISS.SI-ID:	1537835204
Publication date in RUP:	15.10.2015
Views:	3256
Downloads:	130
Metadata:
:	KOZAK, Jernej, KNEZ, Marjetka and VITRIH, Vito, 2015, Parametric curves with Pythagorean binormals. [online]. 2015. P. 1–20. [Accessed 5 April 2025]. DOI 10.1007/s10444-014-9387-7. Retrieved from: 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 Copy citation

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