Trabajo Fin de Grado
Curvas alabeadas con hodógrafo pitagórico
Autor/es | Gómez Guisado, Manuel |
Director | Márquez García, María del Carmen |
Departamento | Universidad de Sevilla. Departamento de Geometría y Topología |
Fecha de publicación | 2022-06-19 |
Fecha de depósito | 2023-02-21 |
Titulación | Universidad de Sevilla. Grado en Matemáticas |
Resumen | In this work, we investigate the properties of polynomial space curves r(t) = (x(t), y(t), z(t))
whose hodographs, r
0
(t) = (x
0
(t), y0
(t), z0
(t)), satisfy x
02
(t) + y
02
(t) + z
02
(t) ≡ σ
2
(t)
for ... In this work, we investigate the properties of polynomial space curves r(t) = (x(t), y(t), z(t)) whose hodographs, r 0 (t) = (x 0 (t), y0 (t), z0 (t)), satisfy x 02 (t) + y 02 (t) + z 02 (t) ≡ σ 2 (t) for some real polynomial σ(t). We give a characterization for all cubic Pythagoreanhodograph space curve and show that such curves correspond geometrically to a family of non-circular helices. Pythagorean-hodograph space curves of higher degree exhibit greater shape flexibility. We focus on the curves of degree 5, that admits a constructive representation. Pythagorean-hodograph space curves have two geometrically attractive attributes: (i) the arc length of any segment can be determined exactly without numerical aproximation; and (ii) the canal surfaces based on such curves as spines have precise rational parametrizations. |
Cita | Gómez Guisado, M. (2022). Curvas alabeadas con hodógrafo pitagórico. (Trabajo Fin de Grado Inédito). Universidad de Sevilla, Sevilla. |
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