Recognizing implicitly given rational canal surfaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43926966" target="_blank" >RIV/49777513:23520/16:43926966 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0747717115000760" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0747717115000760</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jsc.2015.08.003" target="_blank" >10.1016/j.jsc.2015.08.003</a>

Result language
angličtina
Original language name
Recognizing implicitly given rational canal surfaces
Original language description
It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In this paper we will investigate in more detail the case of canal surfaces that are often used in geometric modelling, Computer-Aided Design and technical practice (e.g. as blending surfaces smoothly joining two parts with circular ends). It is known that if the squared medial axis transform is a rational curve then so is also the corresponding surface. However, starting from a polynomial it is not known how to decide if the corresponding algebraic surface is a rational canal surface or not. 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 surface is a rational canal surface. In the affirmative case we also compute a rational parameterization of the squared medial axis transform which can be then used for finding a rational parameterization of the corresponding implicitly given canal surface.
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
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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