Kosinka, Jiří; Jüttler, Bert \(C^{1}\) Hermite interpolation by Pythagorean hodograph quintics in Minkowski space. (English) Zbl 1173.65008 Adv. Comput. Math. 30, No. 2, 123-140 (2009). The powerful machinery of Clifford algebra is applied to the problem of constructing Minkowski Pythagorean hodograph (MPH) plane curves of degree \(5\) with given endpoints and first derivatives vectors at the endpoints.For example, Lorentz transformations are used to parameterize all possible interpolants and to reduce the input data into a standard position.It is shown that if the input data for the \(C^1\)-Hermite interpolation problem are computed from a sufficiently smooth, and sufficiently small, space-like curve, then among all possible interpolants there is just one solution having approximation order \(4\) whereas all other solutions have only approximation order \(1\). This gives a general method for approximating any spake-like \(C^\infty\) curve by a \(C^1\) MPH quintic spline. Reviewer: Juan Monterde (Burjasot) Cited in 15 Documents MSC: 65D17 Computer-aided design (modeling of curves and surfaces) 65D07 Numerical computation using splines 65D05 Numerical interpolation Keywords:Minkowski Pythagorean hodograph curves; medial axis transform; Hermite interpolation; Clifford algebra; Lorentz transformations; quintic spline × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Cho, H.Ch., Choi, H.I., Kwon, S.-H., Lee, D.S., Wee, N.-S.: Clifford algebra, Lorentzian geometry and rational parametrization of canal surfaces. Comput. Aided Geom. Design 21, 327–339 (2004) · Zbl 1069.15500 · doi:10.1016/j.cagd.2003.11.001 [2] Choi, H.I., Choi, S.W., Moon, H.P.: Mathematical theory of medial axis transform. Pacific J. Math. 181(1), 57–88 (1997) · Zbl 0885.53004 · doi:10.2140/pjm.1997.181.57 [3] Choi, H.I., Farouki, R.T., Kwon, S.-H., Moon, H.P.: Topological criterion for selection of quintic Pythagorean-hodograph hermite interpolants. Comput. Aided Geom. 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