Results 71 to 80 of about 824,488 (198)
, 2008 This educational Demonstration, primarily for vector calculus students, shows the moving Frenet frame (or TNB frame, for tangent, normal, and binormal).
Bykov, Nick
core
Development of Frenet-Serret Frame and the Apollonian Window [PDF]
, 2020 The present study focuses on developing a Frenet-Serret frame and the Apollonian Window. In the first part of the study Apollonian disks are generated for first four generations by developing visual basic codes in excel. For the second part of the study,
Karimushan, Syeda Fareeza
core
Inextensible Curve Flows in Dual Space
AxiomsThis paper develops a comprehensive quasi-frame theory for inextensible curve flows in the dual space D3. While the Frenet frame has been the traditional tool for studying curve evolution, it encounters singularities when curvature vanishes. We introduce
Ayman Elsharkawy +4 more
doaj +1 more source
IET Intelligent Transport Systems, Volume 20, Issue 1, January/December 2026.This article presents a metro‐based cross‐station delivery system utilizing autonomous delivery vehicles (ADVs) in the Shenzhen Metro, validated through simulation and real‐world deployment across five stations. The system integrates multi‐sensor fusion, YOLOv11s object detection and Voronoi‐guided A* path planning with PID–MPC control to enable robust
Wenbin Cao +4 more
wiley +1 more source
IET Intelligent Transport Systems, Volume 20, Issue 1, January/December 2026.This paper proposes an overtaking trajectory planning framework based on spatio‐temporal topology and reachable set analysis. It introduces topological classes to describe trajectories representing different overtaking behaviours. This method improves planning efficiency and guarantees kinematic feasibility by simplifying the problem through decoupling
Wule Mao +4 more
wiley +1 more source
ON NULL CURVES ON SURFACES AND NULL VECTORS IN LORENTZ SPACE
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2009 : In this work, we compare the Darboux frame and the Frenet frame of a null curve lying on a spacelike surface in the three-dimensional Lorentz space, and we show that the normal curvature of the curve is a constant.
A. Ceylan ÇÖKEN
doaj
On Frenet frames of complex submanifolds in complex projective spaces
Duke Mathematical Journal, 1984 The main results of this paper concern the curvature of a certain osculating bundle of complex projective manifolds. The author obtains a formula which generalizes a formula by Weyl for holomorphic curves - a so-called unintegrated Plücker formula. As a corollary he obtains the following characterization: The Veronese surfaces is the only surface in \({
openaire +2 more sources
TUBULAR SURFACES WITH DARBOUX FRAME IN GALILEAN 3-SPACE [PDF]
, 2019 In this paper, we define tubular surface by using a Darboux frame instead of a Frenet frame. Subsequently, we compute the Gaussian curvature and the mean curvature of the tubular surface with a Darboux frame.
Dede, Mustafa +6 more
core +1 more source
Quasi-position vector curves in Galilean 4-space
Frontiers in PhysicsThe Frenet frame is not suitable for describing the behavior of the curve in the Galilean space since it is not defined everywhere. In this study, an alternative frame, the so-called quasi-frame, is investigated in Galilean 4-space.
Ayman Elsharkawy, Noha Elsharkawy
doaj +1 more source
Parallel Transport Frame for Fiber Shape Sensing
IEEE Photonics Journal, 2018 This paper reports a reconstruction method to determine a 3-D space curve from the distributed strain by using the parallel transport frame. Parallel transport frame can efficiently eliminate the singularities and discontinuous point which appear in ...
Jiwen Cui +3 more
doaj +1 more source