TY - GEN
T1 - Calculation and Geometric Interpretation of the Curvatures of Implicit Curves and Surfaces with Mathematica
AU - Ipanaqué-Silva, Rolando E.
AU - Eche-Antón, Jhonny W.
AU - Contreras, Elmer P.Díaz
AU - Velezmoro-León, Ricardo
AU - Ipanaqué-Chero, Robert
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - In this paper, based on the formulas proposed by Ronald Goldman, new functions are defined and encoded in the Wolfram Language using the Mathematica symbolic calculation system. With the coded functions, the curvature of implicit plane curves, the curvature and twist of implicit space curves, and the Gaussian and mean curvatures of implicit surfaces can be calculated. All of these functions are included in a Mathematica package. Finally, the package’s functionality is shown by solving several exciting examples. The application of this package allows users to explore and understand the geometry of the analyzed implicit curves and surfaces. This results in a helpful computer tool of great value for educational purposes and to improve the visualization of these concepts.
AB - In this paper, based on the formulas proposed by Ronald Goldman, new functions are defined and encoded in the Wolfram Language using the Mathematica symbolic calculation system. With the coded functions, the curvature of implicit plane curves, the curvature and twist of implicit space curves, and the Gaussian and mean curvatures of implicit surfaces can be calculated. All of these functions are included in a Mathematica package. Finally, the package’s functionality is shown by solving several exciting examples. The application of this package allows users to explore and understand the geometry of the analyzed implicit curves and surfaces. This results in a helpful computer tool of great value for educational purposes and to improve the visualization of these concepts.
KW - Curvature
KW - Wolfram Language
KW - implicit curves
KW - implicit surfaces
UR - http://www.scopus.com/inward/record.url?scp=85200996616&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-65154-0_18
DO - 10.1007/978-3-031-65154-0_18
M3 - Conference contribution
AN - SCOPUS:85200996616
SN - 9783031651533
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 285
EP - 301
BT - Computational Science and Its Applications – ICCSA 2024 Workshops, Proceedings
A2 - Gervasi, Osvaldo
A2 - Murgante, Beniamino
A2 - Garau, Chiara
A2 - Taniar, David
A2 - C. Rocha, Ana Maria A.
A2 - Faginas Lago, Maria Noelia
PB - Springer Science and Business Media Deutschland GmbH
T2 - 24th International Conference on Computational Science and Its Applications, ICCSA 2024
Y2 - 1 July 2024 through 4 July 2024
ER -