RT info:eu-repo/semantics/article
T1 Efficient detection of symmetries polynomially parametrized curves
A1 Alcázar Arribas, Juan Gerardo
K1 Polynomial parametrization
K1 Symmetry
K1 Mirror symmetry
K1 Central symmetry
K1 Symmetry axes
K1 Symmetry center
K1 Ciencia
K1 Matemáticas
K1 Science
K1 Mathematics
AB We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on an algebraic relationship between proper parametrizations of a same curve, which leads to a triangular polynomial system that can be solved in a very fast way; in particular, curves parametrized by polynomials of serious degrees/coefficients can be analyzed in a few seconds. In our analysis we provide a good number of theoretical results on symmetries of polynomial curves, algorithms for detecting rotation and mirror symmetry, and closed formulae to determine the symmetry center and the symmetry axis, when they exist. Some observations and empiric results for the case of polynomial parametrizations with floating point coefficients are also reported.
PB Elsevier
SN 0377-0427
YR 2014
FD 2014
LK http://hdl.handle.net/10017/20446
UL http://hdl.handle.net/10017/20446
LA eng
NO Ministerio de Ciencia e Innovación
DS MINDS@UW
RD 25-abr-2024