Rational Pythagorean-hodograph space curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104794" target="_blank" >RIV/00216208:11320/11:10104794 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0167839611000033" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0167839611000033</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2011.01.002" target="_blank" >10.1016/j.cagd.2011.01.002</a>

Result language
angličtina
Original language name
Rational Pythagorean-hodograph space curves
Original language description
A method for constructing rational Pythagorean-hoclograph (PH) curves in R(3) is proposed, based on prescribing a field of rational unit tangent vectors. This tangent field, together with its first derivative, defines the orientation of the curve osculating planes. Augmenting this orientation information with a rational support function, that specifies the distance of each osculating plane from the origin, then completely defines a one-parameter family of oscillating planes, whose envelope is a developable ruled surface. The rational PH space curve is identified as the edge of regression (or cuspidal edge) of this developable surface. Such curves have rational parametric speed, and also rational adapted frames that satisfy the same conditions as polynomial PH curves in order to be rotation-minimizing with respect to the tangent. The key properties of such rational PH space curves are derived and illustrated by examples, and simple algorithms for their practical construction by geometri
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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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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