Extracting road centrelines from binary road images by optimizing geodesic lines

2015 ◽  
Author(s):  
Shaoguang Zhou ◽  
Guojun Lu ◽  
Shyh Wei Teng ◽  
Dengsheng Zhang
Keyword(s):  
Geodesic Lines

Visualization of Enneper’s surface by line graphics

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 387-405 ◽  
Author(s):  
Vesna Velickovic
Keyword(s):  
Minimal Surface ◽  
Graphical Representations ◽  
Lines Of Curvature ◽  
Geodesic Lines

Here we study Enneper?s minimal surface and some of its properties. We compute and visualize the lines of self-intersection, lines of intersections with planes, lines of curvature, asymptotic and geodesic lines of Enneper?s surface. For the graphical representations of all the results we use our own software for line graphics.

scholarly journals Min-max embedded geodesic lines in asymptotically conical surfaces

2019 ◽  
Vol 112 (3) ◽  
pp. 411-445 ◽  
Author(s):  
Alessandro Carlotto ◽  
Camillo De Lellis
Keyword(s):  
Geodesic Lines ◽  
Conical Surfaces

SINGULARITIES OF GEODESIC FLOWS AND GEODESIC LINES IN PSEUDO-FINSLER SPACES. I

2016 ◽  
Vol 21 (1) ◽  
pp. 66-75
Author(s):  
A.N. Kurbatskiy ◽  
◽  
N.G. Pavlova ◽  
A.O. Remizov ◽  
◽  
...  
Keyword(s):  
Geodesic Flows ◽  
Finsler Spaces ◽  
Geodesic Lines

scholarly journals Random motions at finite velocity in a non-Euclidean space

2007 ◽  
Vol 39 (02) ◽  
pp. 588-611
Author(s):  
E. Orsingher ◽  
A. De Gregorio
Keyword(s):  
Half Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Finite Velocity ◽  
Geodesic Lines ◽  
Random Motions ◽  
Hyperbolic Brownian Motion ◽  
Stochastic Representations ◽  
Poincaré Disk ◽  
Limiting Case

In this paper telegraph processes on geodesic lines of the Poincaré half-space and Poincaré disk are introduced and the behavior of their hyperbolic distances examined. Explicit distributions of the processes are obtained and the related governing equations derived. By means of the processes on geodesic lines, planar random motions (with independent components) in the Poincaré half-space and disk are defined and their hyperbolic random distances studied. The limiting case of one-dimensional and planar motions together with their hyperbolic distances is discussed with the aim of establishing connections with the well-known stochastic representations of hyperbolic Brownian motion. Extensions of motions with finite velocity to the three-dimensional space are also hinted at, in the final section.

scholarly journals Derivation of Field Equations in Space with the Geometric Structure Generated by Metric and Torsion

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Nikolay Yaremenko
Keyword(s):  
Curvature Tensor ◽  
Geometric Structure ◽  
Jacobi Identity ◽  
Torsion Tensor ◽  
Variation Principle ◽  
Field Equations ◽  
Metric Tensor ◽  
Fundamental Tensor ◽  
Geodesic Lines ◽  
General Field

This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space generated jointly and agreed on by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor we obtained analog Ricci-Jacobi identity and evaluated the gap that occurs at the transition from the original to the image and vice versa, in the case of infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor παβ which is similar to the second fundamental tensor of hypersurfaces Yn-1, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational).

The Bubble Hall: Bamboo Reticular Geodesic Structure with the Shape of a Soap Bubble

2014 ◽  
Vol 600 ◽  
pp. 78-86
Author(s):  
João Victor Correia de Melo ◽  
Lucas Alves Ripper ◽  
José Luiz Mendes Ripper ◽  
Walter dos Santos Teixeira Filho
Keyword(s):  
Soap Bubble ◽  
Lightweight Structures ◽  
Constructive Methods ◽  
Geodesic Lines ◽  
Reticular Structure ◽  
Geodesic Structure ◽  
The One ◽  
The Way

This article aims to disclose some aspects of the research and constructive methods on lightweight structures made of tied-up bamboos developed by the Laboratory for Investigation in Living Design, LILD, from PUC-Rio. In this paper, we demonstrate the way of obtaining a shape similar to the one of a soap bubble when blown and manipulated by the researcher, according to previously established parameters. The approximation of such a geometry is achieved through a variety of interactive experiments between the states of a model electronic, manufactured /miniature, and in use that follow the logics of geodesic lines, obtained by means of a grid when inflated. Finally, we present results of initial observations of the assemblage of the bamboo reticular structure in the in use state, that we call The Bubble Hall.

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