Algebraic-Trigonometric Pythagorean-Hodograph space curves
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We introduce a new class of Pythagorean-Hodograph (PH) space curves - called Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) space curves - that are defined over a six-dimensional space mixing algebraic and trigonometric polynomials. After providing a general definition for this new class of curves, their quaternion representation is introduced and the fundamental properties are discussed. Then, as previously done with their quintic polynomial counterpart, a constructive approach to solve the first-order Hermite interpolation problem in ℝ3 is provided. Comparisons with the polynomial case are illustrated to point out the greater flexibility of ATPH curves with respect to polynomial PH curves.
KeywordsSpace curve Pythagorean-Hodograph Algebraic-Trigonometric Bézier basis Arc length First-order Hermite interpolation
Mathematics Subject Classification (2010)65D17 65D05 41A30 41A05
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- 7.González, C., Albrecht, G., Paluszny, M., Lentini, M.: Design of C 2 algebraic-trigonometric pythagorean-hodograph splines with shape parameters. Comp. Appl. Math. (2016). https://doi.org/10.1007/s40314-016-0404-y