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C^1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs

Citace: BASTL, B., BIZZARRI, M., KRAJNC, M., LÁVIČKA, M., MICHÁLKOVÁ, K., ŠÍR, Z., VITRIH, V., ŽAGAR, E. C^1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, roč. 257, č. February, s. 65-78. ISSN: 0377-0427
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: C^1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs
Rok vydání: 2014
Autoři: Doc. Ing. Bohumír Bastl Ph.D. , Mgr. Michal Bizzarri , Marjeta Krajnc , Doc. RNDr. Miroslav Lávička Ph.D. , Ing. Kristýna Michálková , Zbyněk Šír , Vito Vitrih , Emil Žagar
Abstrakt EN: In this paper the C1 Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates C1 data at one point and they are then joined together with a C1 continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally C1 continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.
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