A 3D proposal for the visualization of speed in railway networks

Alberto Almech; Eugenio Roanes-Lozan; Alberto Almech; Eugenio Roanes-Lozan

doi:10.3934/math.2020479

AIMS Mathematics

2020, Volume 5, Issue 6: 7480-7499. doi: 10.3934/math.2020479

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A 3D proposal for the visualization of speed in railway networks

Alberto Almech ¹,
Eugenio Roanes-Lozan ^{2
,
,}

1.
Universidad Complutense de Madrid, Madrid, Spain
2.
Instituto de Matemática Interdisciplinar & Departamento de Didáctica de las Ciencias Experimentales, Sociales y Matemáticas, Facultad de Educación, Universidad Complutense de Madrid, Spain

Received: 31 July 2020 Accepted: 14 September 2020 Published: 22 September 2020
MSC : 00A66, 05C62, 05C90, 90C35

This article deals with a proposal for visualizing the speed of the different sections of the lines of a railway network that has been implemented in the computer algebra system Maple. The idea is to organize the data (the speed in the different sections of the railway network) as a weighted graph. The endpoints of the sections considered are the vertices of the graph and the edges are the sections of the railway lines of the network. The weights of the edges reflect the different speeds in the sections of the network. The vertices of the graph are drawn in the xy plane according to their geographical coordinates. The edges are represented by segments in the xy plane. Vertical rectangles are lifted from these segments according to the weights of the edges (as a kind of wrinkled histogram). Two different methods are proposed to compute the height of the rectangles: one directly considers the difference of speeds with respect to the maximum average speed and the other calculates the height so that the area of the rectangle represents the time required to traverse the section. This way the speeds of the different sections of the lines can be easily visualized (in 3D). The underlying mathematics is elementary, but the implementation is complex and makes extensive use of the possibilities of Maple's plot package.
- graph theory,
- railway networks,
- visualization,
- real world applications,
- computer algebra systems
Citation: Alberto Almech, Eugenio Roanes-Lozan. A 3D proposal for the visualization of speed in railway networks[J]. AIMS Mathematics, 2020, 5(6): 7480-7499. doi: 10.3934/math.2020479

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Abstract

This article deals with a proposal for visualizing the speed of the different sections of the lines of a railway network that has been implemented in the computer algebra system Maple. The idea is to organize the data (the speed in the different sections of the railway network) as a weighted graph. The endpoints of the sections considered are the vertices of the graph and the edges are the sections of the railway lines of the network. The weights of the edges reflect the different speeds in the sections of the network. The vertices of the graph are drawn in the xy plane according to their geographical coordinates. The edges are represented by segments in the xy plane. Vertical rectangles are lifted from these segments according to the weights of the edges (as a kind of wrinkled histogram). Two different methods are proposed to compute the height of the rectangles: one directly considers the difference of speeds with respect to the maximum average speed and the other calculates the height so that the area of the rectangle represents the time required to traverse the section. This way the speeds of the different sections of the lines can be easily visualized (in 3D). The underlying mathematics is elementary, but the implementation is complex and makes extensive use of the possibilities of Maple's plot package.

References

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