G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F12%3A43898297" target="_blank" >RIV/49777513:23520/12:43898297 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-642-27413-8_9" target="_blank" >http://dx.doi.org/10.1007/978-3-642-27413-8_9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-27413-8_9" target="_blank" >10.1007/978-3-642-27413-8_9</a>

Result language
angličtina
Original language name
G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions
Original language description
It was recently proved in that all rational hypocycloids and epicycloids are Pythagorean hodograph curves, i.e., rational curves with rational offsets. In this paper, we extend the discussion to a more general class of curves represented by trigonometricpolynomial support functions. We show that these curves are offsets to translated convolutions of scaled and rotated hypocycloids and epicycloids. Using this result, we formulate a new and very simple G2 Hermite interpolation algorithm based on solvinga small system of linear equations. The efficiency of the designed method is then presented on several examples. In particular, we show how to approximate general trochoids, which, as we prove, are not Pythagorean hodograph curves in general.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)