Bishop curves and orthogonal trajectories

Approximate Hotspots of Orthogonal Trajectories

In this paper we study the problem of finding hotspots, i.e. regions in which a moving entity has spent a significant amount of time, for polygonal trajectories. The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals (2013) finds an axis-parallel square hotspot of fixed side length in O(n). Limiting ourselves to the case in which the entity moves in a direction parallel eith...

Note on the Curvature of Orthogonal Trajectories of Level Curves of Green's Function.

Indexing Spatio-Temporal Trajectories with Orthogonal Polynomials

—In this paper we consider d-dimensional spatiotemporal data (d 1) and ways to approximate and index it. We focus on indexing such data for similarity matching using orthogonal polynomial approximations. There are many ways to choose an approximation scheme for d-dimensional spatiotemporal trajectories. Some of them have been studied before. In this paper we extend the approach proposed in [6] ...

ASSOCIATED CURVES OF THE SPACELIKE CURVE VIA THE BISHOP FRAME OF TYPE-2 IN E₁³

The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obta...

Isometry Groups with Surface-Orthogonal Trajectories

Im allgemeinen Fall 4= 0 4= p) sind bisher keine physikalisch brauchbaren Lösungen angegeben worden, Lösungen also, die zu einer räumlich begrenzten Massenverteilung gehören. Das interessanteste, zweifellos schwierige Problem dürfte sein, eine innere Lösung zu finden, die sich an das von K E R R angegebene Außenfeld anschließt. Auf der Grenzfläche p = 0, die zugleich eine Fläche U = const ist, ...