TY - GEN
T1 - Calculation of the Differential Geometry of the Intersection of Implicit Hypersurfaces in with Mathematica
AU - Jiménez-Vilcherrez, Judith Keren
AU - Velezmoro-León, Ricardo
AU - Ipanaqué-Chero, Robert
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - In geometry, knowing the differential properties of a curve at a point is very important, as it would help us understand its behavior around that point; even more so when said curve is generated by the intersection of hypersurfaces in. This paper describes a new Mathematica package, Frenet4D, that allows to visualize and calculate the Frenet frame of the curve given by the transversal intersection of three implicit hypersurfaces in thus like the visualization of the respective hypersurfaces. The output obtained is consistent with Mathematica’s notation and results. To show the performance of the package, several illustrative and interesting examples are described.
AB - In geometry, knowing the differential properties of a curve at a point is very important, as it would help us understand its behavior around that point; even more so when said curve is generated by the intersection of hypersurfaces in. This paper describes a new Mathematica package, Frenet4D, that allows to visualize and calculate the Frenet frame of the curve given by the transversal intersection of three implicit hypersurfaces in thus like the visualization of the respective hypersurfaces. The output obtained is consistent with Mathematica’s notation and results. To show the performance of the package, several illustrative and interesting examples are described.
KW - Implicit hypersurface
KW - Implicit–implicit–implicit intersection
KW - Transversal intersection
UR - http://www.scopus.com/inward/record.url?scp=85115732448&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-86976-2_4
DO - 10.1007/978-3-030-86976-2_4
M3 - Conference contribution
AN - SCOPUS:85115732448
SN - 9783030869755
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 46
EP - 59
BT - Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings
A2 - Gervasi, Osvaldo
A2 - Murgante, Beniamino
A2 - Misra, Sanjay
A2 - Garau, Chiara
A2 - Blečić, Ivan
A2 - Taniar, David
A2 - Apduhan, Bernady O.
A2 - Rocha, Ana Maria
A2 - Tarantino, Eufemia
A2 - Torre, Carmelo Maria
PB - Springer Science and Business Media Deutschland GmbH
T2 - 21st International Conference on Computational Science and Its Applications, ICCSA 2021
Y2 - 13 September 2021 through 16 September 2021
ER -