Mapping rational rotation-minimizing frames from polynomial curves on to rational curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423267" target="_blank" >RIV/00216208:11320/20:10423267 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nQMwE9HF1P" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nQMwE9HF1P</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2020.101833" target="_blank" >10.1016/j.cagd.2020.101833</a>

Result language
angličtina
Original language name
Mapping rational rotation-minimizing frames from polynomial curves on to rational curves
Original language description
Given a polynomial space curve that has a rational rotation-minimizing frame (an RRMF curve), a methodology is developed to construct families of rational space curves with the same rotation-minimizing frame as at corresponding points. The construction employs the dual form of a rational space curve, interpreted as the edge of regression of the envelope of a family of osculating planes, having normals in the direction and distances from the origin specified in terms of a rational function as . An explicit characterization of the rational curves generated by a given RRMF curve in this manner is developed, and the problem of matching initial and final points and frames is shown to impose only linear conditions on the coefficients of , obviating the non-linear equations (and existence questions) that arise in addressing this problem with the RRMF curve . Criteria for identifying low-degree instances of the curves are identified, by a cancellation of factors common to their numerators and denominators, and the methodology is illustrated by a number of computed examples.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA20-11473S" target="_blank" >GA20-11473S: Symmetry and invariance in analysis, geometric modelling and control theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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