Abstract
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.
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Communicated by: Larry L. Schumaker
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Romani, L., Montagner, F. Algebraic-Trigonometric Pythagorean-Hodograph space curves. Adv Comput Math 45, 75–98 (2019). https://doi.org/10.1007/s10444-018-9606-8
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DOI: https://doi.org/10.1007/s10444-018-9606-8
Keywords
- Space curve
- Pythagorean-Hodograph
- Algebraic-Trigonometric Bézier basis
- Arc length
- First-order Hermite interpolation