Algebraic-trigonometric Pythagorean-hodograph curves and their use for Hermite interpolation - Archive ouverte HAL Access content directly
Journal Articles Advances in Computational Mathematics Year : 2014

Algebraic-trigonometric Pythagorean-hodograph curves and their use for Hermite interpolation

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Abstract

In this article we define a new class of Pythagorean-Hodograph curves built-upon a six-dimensional mixed algebraic-trigonometric space, we show their fundamental properties and compare them with their well-known quintic polynomial counterpart. A complex representation for these curves is introduced and constructive approaches are provided to solve different application problems, such as interpolating C 1 Hermite data and constructing spirals as G 2 transition elements between a line segment and a circle, as well as between a pair of external circles.
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Dates and versions

hal-03151851 , version 1 (04-07-2022)

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Lucia Romani, Laura Saini, Gudrun Albrecht. Algebraic-trigonometric Pythagorean-hodograph curves and their use for Hermite interpolation. Advances in Computational Mathematics, 2014, 40 (5-6), pp.977-1010. ⟨10.1007/s10444-013-9338-8⟩. ⟨hal-03151851⟩
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