Original scientific paper

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

Abstract

We classify mutual position of a quadratic Bézier curve and a regular quadric in three dimensional Euclidean space. For given first 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 find 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.

Keywords

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

Hrčak ID:

151328

URI

https://hrcak.srce.hr/151328

Publication date:

19.1.2016.

Article data in other languages: croatian

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