Relation between Darboux and type-2 Bishop frames in Euclidean space

2016 ◽  
Vol 13 (07) ◽  
pp. 1650101 ◽  
Author(s):  
Amine Yilmaz ◽  
Emin Özyilmaz
Keyword(s):  
Euclidean Space ◽  
Transition Matrix ◽  
Geodesic Curvature ◽  
Spherical Image ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Spherical Images

In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.

scholarly journals Spherical Images of W-Direction Curves in Euclidean 3-Space

2020 ◽  
Vol 12 (3) ◽  
pp. 39
Author(s):  
Ìlkay Arslan Güven ◽  
Semra Kaya Nurkan ◽  
Ìpek Agaoglu Tor
Keyword(s):  
Vector Field ◽  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Darboux Vector ◽  
Slant Helix ◽  
Spherical Images

In this paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve. We obtain the Frenet apparatus of these spherical indicatrices and the characterizations of being general helix and slant helix. Moreover we give some properties between the spherical indicatrices and their associated curves.

scholarly journals Cusps of Bishop Spherical Indicatrixes and Their Visualizations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Haiming Liu ◽  
Donghe Pei
Keyword(s):  
Space Curve ◽  
Singular Points ◽  
Bishop Frame ◽  
Spherical Images

The main result of this paper is using Bishop Frame and “Type-2 Bishop Frame” to study the cusps of Bishop spherical images and type-2 Bishop spherical images which are deeply related to a space curve and to make them visualized by computer. We find that the singular points of the Bishop spherical images and type-2 Bishop spherical images correspond to the point where Bishop curvatures and type-2 Bishop curvatures vanished and their derivatives are not equal to zero. As applications and illustration of the main results, two examples are given.

scholarly journals SYSTEMATIC CALIBRATION FOR A BACKPACKED SPHERICAL PHOTOGRAMMETRY IMAGING SYSTEM

2016 ◽  
Vol XLI-B1 ◽  
pp. 695-702 ◽  
Author(s):  
J. Y. Rau ◽  
B. W. Su ◽  
K. W. Hsiao ◽  
J. P. Jhan
Keyword(s):  
Imaging System ◽  
Relative Orientation ◽  
Lens Distortion ◽  
Stereo Pair ◽  
3D Measurement ◽  
Spherical Image ◽  
Mobile Mapping ◽  
Mobile Mapping System ◽  
Spherical Images ◽  
Spherical Camera

A spherical camera can observe the environment for almost 720 degrees’ field of view in one shoot, which is useful for augmented reality, environment documentation, or mobile mapping applications. This paper aims to develop a spherical photogrammetry imaging system for the purpose of 3D measurement through a backpacked mobile mapping system (MMS). The used equipment contains a Ladybug-5 spherical camera, a tactical grade positioning and orientation system (POS), i.e. SPAN-CPT, and an odometer, etc. This research aims to directly apply photogrammetric space intersection technique for 3D mapping from a spherical image stereo-pair. For this purpose, several systematic calibration procedures are required, including lens distortion calibration, relative orientation calibration, boresight calibration for direct georeferencing, and spherical image calibration. The lens distortion is serious on the ladybug-5 camera’s original 6 images. Meanwhile, for spherical image mosaicking from these original 6 images, we propose the use of their relative orientation and correct their lens distortion at the same time. However, the constructed spherical image still contains systematic error, which will reduce the 3D measurement accuracy. Later for direct georeferencing purpose, we need to establish a ground control field for boresight/lever-arm calibration. Then, we can apply the calibrated parameters to obtain the exterior orientation parameters (EOPs) of all spherical images. In the end, the 3D positioning accuracy after space intersection will be evaluated, including EOPs obtained by structure from motion method.

scholarly journals Prediction of prevalence of type 2 diabetes in Rwanda using the metropolis-hasting sampling

2021 ◽  
Vol 21 (2) ◽  
pp. 702-709
Author(s):  
Angelique Dukunde ◽  
Jean Marie Ntaganda ◽  
Juma Kasozi ◽  
Joseph Nzabanita
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Type 2 Diabetes ◽  
Monte Carlo ◽  
Transition Matrix ◽  
Decision Makers ◽  
World Health ◽  
Health Decision ◽  
The Masses

In this work, we predict the prevalence of type 2 diabetes among adult Rwandan people. We used the Metropolis-Hasting method that involved calculating the metropolis ratio. The data are those reported by World Health Organiation in 2015. Considering Suffering from diabetes, Overweight, Obesity, Dead and other subject as states of mathematical model, the transition matrix whose elements are probabilities is generated using Metropolis-Hasting sampling. The numerical results show that the prevalence of type 2 diabetes increases from 2.8% in 2015 to reach 12.65% in 2020 and to 22.59% in 2025. Therefore, this indicates the urgent need of prevention by Rwandan health decision makers who have to play their crucial role in encouraging for example physical activity, regular checkups and sensitization of the masses. Keywords: Non communicable diseases; type 2 diabetes; Markov Chain Monte Carlo method; Metropolis-Hasting method; Transition probabilities.rds: 

scholarly journals Integral equations of biharmonic constant π₁-slope curves according to type-2 Bishop frame in the SOL space

2013 ◽  
Vol 31 (2) ◽  
pp. 205 ◽  
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Integral Equations ◽  
Bishop Frame ◽  
Sol Space

In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.

The ruled surfaces according to type-2 Bishop frame in E^3

2017 ◽  
Vol 12 ◽  
pp. 133-143
Author(s):  
Esra Damar ◽  
Nural Yuksel ◽  
Aysel Turgut Vanli
Keyword(s):  
Ruled Surfaces ◽  
Bishop Frame
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