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  • Current geometric modelling (Computer Aided Geometric Design) uses several operations defined over algebraic varieties whose output are again algebraic varieties (e.g. offsetting, operation of convolution, bisectors). Nevertheless, an uncomfortable feature of these constructions is the fact that the output variety may be, in some sense, more complicated than the input varieties ? e.g. its algebraic degree is often higher, it consists of more components and mainly it does not have to be rational although the both input objects are rational. From this reason, it is necessary to leave the rational world of CAGD and use the techniques of algebraic geometry which work over the field of complex numbers and thus give global and more general results. Especially, we discuss an unifying approach based on the so called incidence varieties.
  • Current geometric modelling (Computer Aided Geometric Design) uses several operations defined over algebraic varieties whose output are again algebraic varieties (e.g. offsetting, operation of convolution, bisectors). Nevertheless, an uncomfortable feature of these constructions is the fact that the output variety may be, in some sense, more complicated than the input varieties ? e.g. its algebraic degree is often higher, it consists of more components and mainly it does not have to be rational although the both input objects are rational. From this reason, it is necessary to leave the rational world of CAGD and use the techniques of algebraic geometry which work over the field of complex numbers and thus give global and more general results. Especially, we discuss an unifying approach based on the so called incidence varieties. (en)
Title
  • Study Of Algebraic Operations Used In CAGD Through Incidence Varieties
  • Study Of Algebraic Operations Used In CAGD Through Incidence Varieties (en)
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  • Study Of Algebraic Operations Used In CAGD Through Incidence Varieties
  • Study Of Algebraic Operations Used In CAGD Through Incidence Varieties (en)
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  • RIV/49777513:23520/11:43898296!RIV12-MSM-23520___
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  • S, Z(MSM4977751301)
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  • 233027
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  • RIV/49777513:23520/11:43898296
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  • Algebraic varieties, incidence variety, convolutions, offsets, bisectors, conchoids, genus (en)
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  • [986DD82D662D]
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  • Bratislava
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  • Bratislava
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  • Aplimat 2011
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  • Lávička, Miroslav
  • Vršek, Jan
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  • Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava
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  • 978-80-89313-51-8
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  • 23520
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