PH krivulje in njihove posplošitve / PH curves and their generalizations
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Naziv Tittle |
PH krivulje in njihove posplošitve / PH curves and their generalizations |
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Akronim Acronim |
Z7-4052 |
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Opis Description |
(SI) Cilj predlaganega projekta je priti do novih ugotovitev v povezavi s PH krivuljami in njihovimi posplošitvami. Sprva bodo raziskave osredotočene na nekatere pomembne odprte probleme, ki se nanašajo na (prostorske) polinomske PH krivulje, predvsem na nekatere pomembne interpolacijske sheme, ki še niso bile analizirane. V nadaljevanju bodo obravnavana posebna racionalna ogrodja PH krivulj, ki so posebej pomembna za konstrukcijo gibanj togih teles, kar je pomembno področje znotraj robotike. Natančneje, analizirane bodo sheme za interpolacijo G1 podatkov za gibanje z ERF in RRMF ogrodji prostorskih PH krivulj (stopenj 5 in 7). Nato bodo obravnavane tudi razne posplošitve polinomskih PH krivulj. Sprva bo pozornost namenjena nekaterim interpolacijskim shemam z ravninskimi racionalnimi PH krivuljami, nato pa shemam z ravninskimi cikloidnimi krivuljami s pitagorejskim hodografom (PHC krivuljami). Nazadnje bo raziskava s krivulj prenešena še na t.i. PN ploskve, ki veljajo za posplošitev PH krivulj na ploskve. Ti rezultati se bodo lahko neposredno aplicirali v konkretno proizvodno okolje. Imeli bodo pomembno vlogo v robotiki, CNC aplikacijah, proizvodnih tehnologijah in sistemih, CAD/CAM sistemih ter drugih modernih računalniško podprtih aplikacijah. (EN) The aim of the proposed project is to obtain some new results on PH curves and their generalizations. Initially, research will be focused on some open problems concerning (spatial) polynomial PH curves, in particular, some important interpolation schemes, that have not been analysed yet, will be considered. Then particular rational adapted frames of spatial polynomial PH curves will be considered. They play an important role in motion design applications, which is an important field in robotics. More precisely, a scheme for interpolation of G1 Hermite motion data with ERF and RRMF frames of spatial PH curves (of degree 5 and 7) will be analysed. Furthermore, some generalizations of polynomial PH curves will be considered. First, some interpolation schemes with planar rational PH curves will be studied, and secondly, interpolation by planar cycloidal PH curves (PHC curves) will be considered. Finally, some PN surfaces, as a generalization of PH curves to surfaces, will be discussed. These results can all be applied to robotics, CNC machines, manufacturing technologies and systems, CAD/CAM systems and many other modern computer-supported applications. |
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Vrsta projekta Project Type |
Podoktorski projekt |
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Trajanje Duration |
01/07/2011 - 30/06/2013 |
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URL URL |
https://www.sicris.si/public/jqm/prj.aspx?lang=slv&opdescr=search&opt=2&subopt=400&code1=cmn&code2=auto&psize=10&hits=1&page=1&count=&search_term=Z7-4052&id=7152&slng=&order_by= |
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Vodja projekta Project Leader |
Vito Vitrih |
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Sodelujoče organizacije Participating organizations |
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Oddelek Department |
Oddelek za matematiko IAM |