Determining surfaces of revolution from their implicit equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43925446" target="_blank" >RIV/49777513:23520/15:43925446 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.cam.2015.05.006" target="_blank" >http://dx.doi.org/10.1016/j.cam.2015.05.006</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2015.05.006" target="_blank" >10.1016/j.cam.2015.05.006</a>

Result language
angličtina
Original language name
Determining surfaces of revolution from their implicit equations
Original language description
Results of number of geometric operations are in many cases surfaces described implicitly. Then it is a challenging task to recognize the type of the obtained surface, find its characteristics and for the rational surfaces compute also their parameterizations. In this contribution we will focus on surfaces of revolution. These objects, widely used in geometric modelling, are generated by rotating a generatrix around a given axis. If the generatrix is an algebraic curve then so is also the resulting surface, described uniquely by a polynomial which can be found by some well-established implicitation technique. However, starting from a polynomial it is not known how to decide if the corresponding algebraic surface is rotational or not. Motivated by this,our goal is to formulate a simple and efficient algorithm whose input is a polynomial with the coefficients from some subfield of RR and the output is the answer whether the shape is a surface of revolution. In the affirmative case we al
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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