TY  - JOUR
T1  - C 1 Hermite interpolation with spatial Pythagorean-hodograp h cubic biarcs
A1  - Bastl, Bohumír
A1  - Bizzarri, Michal
A1  - Krajnc, Marjeta
A1  - Lávička, Miroslav
A1  - Slabá, K.
A1  - Šír, Zbyněk
A1  - Vitrih, V.
A1  - Žagar, Emil
JA  - Journal of Computational and Applied Mathematics
Y1  - 2014
VL  - 257
SP  - 65
EP  - 78
M2  - doi: 10.1016/j.cam.2013.08.007
KW  - Biarc
KW  - Cubic
KW  - Hermite
KW  - Interpolation
KW  - Pythagorean-hodograph
KW  - Spatial
N2  - In this paper the C1C1 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 C1C1 data at one point and they are then joined together with a C1C1 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 C1C1 continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 06
M1  - Preprint ID = NCMM/2014/06
ER  -