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Hermitian interpolation with spherical Pythagorean-hodograph curves. (Chinese. English summary) Zbl 1174.65330

Summary: The \(C^1\) Hermitian interpolation with spherical Pythagorean-hodograph(PH) curve is discussed. Under the stereographic projection, the initial data on the sphere are projected to a plane. A planar PH curve is then constructed. Thirdly, by projecting the curve to the sphere, a spherical rational PH curve is generated. During the above process, the stereographic projection preserving PH is utilized and the spherical \(C^1\) PH curve is constructed, which can be used in the design for the locus of robots and computerized numerical control interpolation, etc.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D05 Numerical interpolation
41A05 Interpolation in approximation theory
41A63 Multidimensional problems
70Q05 Control of mechanical systems
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