Version 1
: Received: 27 August 2024 / Approved: 19 September 2024 / Online: 20 September 2024 (02:47:48 CEST)
How to cite:
James, D. Determining the Principal Azimuths of Valles Marineris: A Comparative Analysis of Bezier Spline and GIS Techniques. Preprints2024, 2024091514. https://doi.org/10.20944/preprints202409.1514.v1
James, D. Determining the Principal Azimuths of Valles Marineris: A Comparative Analysis of Bezier Spline and GIS Techniques. Preprints 2024, 2024091514. https://doi.org/10.20944/preprints202409.1514.v1
James, D. Determining the Principal Azimuths of Valles Marineris: A Comparative Analysis of Bezier Spline and GIS Techniques. Preprints2024, 2024091514. https://doi.org/10.20944/preprints202409.1514.v1
APA Style
James, D. (2024). Determining the Principal Azimuths of Valles Marineris: A Comparative Analysis of Bezier Spline and GIS Techniques. Preprints. https://doi.org/10.20944/preprints202409.1514.v1
Chicago/Turabian Style
James, D. 2024 "Determining the Principal Azimuths of Valles Marineris: A Comparative Analysis of Bezier Spline and GIS Techniques" Preprints. https://doi.org/10.20944/preprints202409.1514.v1
Abstract
Valles Marineris (VM), the most prominent example of a Martian Valley Network, has been extensively studied for over 50 years, yet no detailed examination of the principal azimuths of the system exists. To address this, two methods are presented to precisely calculate the principal azimuths, a Bezier Spline analysis, and a GIS technique. The medial axis of the main canyon of VM was determined analytically from cubic polynomial splines fitted to 93 coordinate points along both north and south edges of the canyon. These splines were optimized, and medial axis points were calculated through numerical techniques that ensured orthogonality between the tangents of each spline and their connecting normal lines. 1,000 Medial Axis points were extracted, and various regression models constructed, including fitting to sinusoidal and cubic polynomial curves, achieving accuracies with R² values of 0.98 and 0.99, respectively. Principal azimuths were obtained using the sinusoidal equation with the slope of the tangent at any point x simply determined by the derivative of the curve’s equation. This analytic approach was cross-validated by a GIS method (using QGIS software), where a vector medial axis was obtained which produced principal azimuths that agreed with values from the analytic study with a correlation coefficient of 1.00, and a p value of 6.43e-65. The findings suggest that a deterministic process plays a significant role in the structural geometry of VM, highlighting its potential importance in the canyon’s formation.
Keywords
valles marineris; cubic polynomial splines; multidimensional optimization; medial axis; valley network; mars; principal azimuths; GIS
Subject
Environmental and Earth Sciences, Space and Planetary Science
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
