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001-es BibID:	BIBFORM041940
Első szerző:	Kunkli Roland (matematika, informatika, ábrázoló geometria szakos tanár)
Cím:	Isoptics of Bézier curves / Kunkli Roland, Papp Ildikó, Hoffmann Miklós
Dátum:	2013
ISSN:	0167-8396
Megjegyzések:	Given a planar curve s(t), the locus of those points from which the curve can be seen under a fixed angle is called isoptic curve of s(t).Isoptics are well-known and widely studied, especially for some classical curves such as e.g. conics (Loria, 1911). They can theoretically be computed for a large class of parametric curves by the help of their support functions or by direct computation based on the definition, but unfortunately these computations are extremely complicated even for simple curves.Our purpose is to describe the isoptics of those curves which are still frequently used in geometric modeling ? the Bézier curves. It turns out that for low degree Bézier curves the direct computation is possible, but already for degree 4 or 5 the formulas are getting too complicated even for computer algebra systems. Thus we provide a new way to solve the problem, proving some geometric relations of the curve and their isoptics, and computing the isoptics as the envelope of envelopes of families of isoptic circles over the chords of the curve.
Tárgyszavak:	Műszaki tudományok Informatikai tudományok idegen nyelvű folyóiratközlemény külföldi lapban Bézier curves isoptics computer aided geometric design envelope
Megjelenés:	Computer Aided Geometric Design. - 30 : 1 (2013), p. 78-84. -
További szerzők:	Papp Ildikó (1971-) (matematika, informatika, ábrázoló geometria szakos tanár) Hoffmann Miklós (1966-) (matematikus, informatikus)
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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