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On the classification of rational second-order Bézier curves. / Grigor'ev, M. I.; Malozemov, V. N.; Sergeev, A. N.

In: Vestnik St. Petersburg University: Mathematics, Vol. 41, No. 2, 06.2008, p. 176-181.

Research output: Contribution to journal › Article › peer-review

Harvard

Grigor'ev, MI, Malozemov, VN & Sergeev, AN 2008, 'On the classification of rational second-order Bézier curves', Vestnik St. Petersburg University: Mathematics, vol. 41, no. 2, pp. 176-181. https://doi.org/10.3103/S106345410802012X

APA

Grigor'ev, M. I., Malozemov, V. N., & Sergeev, A. N. (2008). On the classification of rational second-order Bézier curves. Vestnik St. Petersburg University: Mathematics, 41(2), 176-181. https://doi.org/10.3103/S106345410802012X

Vancouver

Grigor'ev MI, Malozemov VN, Sergeev AN. On the classification of rational second-order Bézier curves. Vestnik St. Petersburg University: Mathematics. 2008 Jun;41(2):176-181. https://doi.org/10.3103/S106345410802012X

Author

Grigor'ev, M. I. ; Malozemov, V. N. ; Sergeev, A. N. / On the classification of rational second-order Bézier curves. In: Vestnik St. Petersburg University: Mathematics. 2008 ; Vol. 41, No. 2. pp. 176-181.

BibTeX

@article{c158d7b11db9482faad5684e3dc76539,
title = "On the classification of rational second-order B{\'e}zier curves",
abstract = "Each rational (projective) B{\'e}zier curve is determined by three points in the plane and by positive weights assigned to these points. As is known, any such curve is an arc of either a parabola, an ellipse, or a hyperbola. An equation for a projective B{\'e}zier curve in barycentric coordinates is derived. This equation depends on a parameter. A complete classification of the curves under consideration in terms of parameter values is suggested.",
author = "Grigor'ev, {M. I.} and Malozemov, {V. N.} and Sergeev, {A. N.}",
note = "Copyright: Copyright 2012 Elsevier B.V., All rights reserved.",
year = "2008",
month = jun,
doi = "10.3103/S106345410802012X",
language = "English",
volume = "41",
pages = "176--181",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - On the classification of rational second-order Bézier curves

AU - Grigor'ev, M. I.

AU - Malozemov, V. N.

AU - Sergeev, A. N.

N1 - Copyright: Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2008/6

Y1 - 2008/6

N2 - Each rational (projective) Bézier curve is determined by three points in the plane and by positive weights assigned to these points. As is known, any such curve is an arc of either a parabola, an ellipse, or a hyperbola. An equation for a projective Bézier curve in barycentric coordinates is derived. This equation depends on a parameter. A complete classification of the curves under consideration in terms of parameter values is suggested.

AB - Each rational (projective) Bézier curve is determined by three points in the plane and by positive weights assigned to these points. As is known, any such curve is an arc of either a parabola, an ellipse, or a hyperbola. An equation for a projective Bézier curve in barycentric coordinates is derived. This equation depends on a parameter. A complete classification of the curves under consideration in terms of parameter values is suggested.

UR - http://www.scopus.com/inward/record.url?scp=84859705003&partnerID=8YFLogxK

U2 - 10.3103/S106345410802012X

DO - 10.3103/S106345410802012X

M3 - Article

AN - SCOPUS:84859705003

VL - 41

SP - 176

EP - 181

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 73934653