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Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles

Barbora Pokorná ; Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic
Pavel Chalmovianský ; Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic

Puni tekst: engleski, pdf (485 KB) str. 5-16 preuzimanja: 152* citiraj
APA 6th Edition
Pokorná, B. i Chalmovianský, P. (2015). Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles. KoG, 19. (19.), 5-16. Preuzeto s https://hrcak.srce.hr/151328
MLA 8th Edition
Pokorná, Barbora i Pavel Chalmovianský. "Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles." KoG, vol. 19., br. 19., 2015, str. 5-16. https://hrcak.srce.hr/151328. Citirano 25.01.2020.
Chicago 17th Edition
Pokorná, Barbora i Pavel Chalmovianský. "Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles." KoG 19., br. 19. (2015): 5-16. https://hrcak.srce.hr/151328
Harvard
Pokorná, B., i Chalmovianský, P. (2015). 'Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles', KoG, 19.(19.), str. 5-16. Preuzeto s: https://hrcak.srce.hr/151328 (Datum pristupa: 25.01.2020.)
Vancouver
Pokorná B, Chalmovianský P. Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles. KoG [Internet]. 2015 [pristupljeno 25.01.2020.];19.(19.):5-16. Dostupno na: https://hrcak.srce.hr/151328
IEEE
B. Pokorná i P. Chalmovianský, "Collision-free Piecewise Quadratic Spline with Regular Quadratic Obstacles", KoG, vol.19., br. 19., str. 5-16, 2015. [Online]. Dostupno na: https://hrcak.srce.hr/151328. [Citirano: 25.01.2020.]

Sažetak
We classify mutual position of a quadratic Bézier curve and a regular quadric in three dimensional Euclidean space. For given fi rst and last control point, we find the set of all quadratic Bezier curves having no common point with a regular quadric. This system of such quadratic Bézier curves is represented by the set of their admissible middle control points. The spatial problem is reduced to a planar problem where the regular quadric is represented by a conic section. Then, the set of all middle control points is found for each type of conic section separately. The key issue is to fi nd the boundary of this set. It is formed from the middle control points of the Bézier curves touching the given conic section. Our results are applicable in collision-free paths computation for virtual agents where the obstacles are represented or bounded by regular quadrics. Another application can be found in searching for pointwise space-like curves in Minkowski space.

Ključne riječi
Bézier quadratic curve; regular quadric; intersection; collision-free paths

Hrčak ID: 151328

URI
https://hrcak.srce.hr/151328

[hrvatski]

Posjeta: 272 *