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We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in $\mathbb R^{2,1}$, and prove that parameterizations of Enneper surfaces of the 1st and the 2nd kind and conjugates of Enneper surfaces of the 2nd kind are PH-MPH transitive. We show how to solve $C^1$ Hermite interpolation problems in $\mathbb R^{2,1}$, for an admissible $C^1$ Hermite data-set, by using the parametrization of Enneper surfaces of the 1st kind. We also show that we can obtain interpolants for at least some inadmissible data-sets by using MPH biarcs on Enneper surfaces of the 1st kind.
목차
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참고문헌 (25)
참고문헌 신청
G. Albrecht / 1996 / Construction of C2 Pythagorean-hodograph interpolating splines by the homotopy method / Adv. Comput. Math 5(4):417~442
H. I. Choi / 1997 / Mathematical theory of medial axis transform / Pacific J. Math 181(1):57~88
H. I. Choi / 2002 / Clifford algebra, spin representation, and rational parameterization of curves and surfaces / Adv. Comput. Math 17(1-2):5~48
R. T. Farouki / 2008 / Pythagorean-hodograph curves: algebra and geometry inseparable / Springer
R. T. Farouki / 2015 / Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves / IMA J. Numer. Anal 35(1):478~498
H. I. Choi / 1997 / Mathematical theory of medial axis transform / Pacific J. Math 181(1):57~88
H. I. Choi / 2002 / Clifford algebra, spin representation, and rational parameterization of curves and surfaces / Adv. Comput. Math 17(1-2):5~48
R. T. Farouki / 2008 / Pythagorean-hodograph curves: algebra and geometry inseparable / Springer
R. T. Farouki / 2015 / Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves / IMA J. Numer. Anal 35(1):478~498
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