A fully data-dependent criterion for free angles selection in spatial PH cubic biarc Hermite interpolation

Sestini, Alessandra; Ferjančič, Karla; Manni, Carla; Sampoli, Maria Lucia

doi:10.1016/j.cagd.2014.06.003

Cited by 5 publications

(1 citation statement)

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“…While general C 1 Hermite data can always be interpolated by cubic polynomial splines, the PH condition reduces the available degrees of freedom and PH cubic interpolants with C 1 or G 1 continuity not always exist [9,10,11]. To avoid this problem the PH spline degree can be raised to 5 [5,6,13] or the cubic spline segment can be subdivided in two (or more) segments [1,12]. In a similar way, spatial C 2 PH spline interpolants can be (always) obtained either with PH curves of higher (nine) degree [14] or with low-degree PH spline arcs of different kind.…”

Section: Introductionmentioning

confidence: 99%

A local $C^2$ Hermite interpolation scheme with PH quintic splines for 3D data streams

Giannelli,

Sacco,

Sestini

2021

Preprint

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The construction of smooth spatial paths with Pythagorean-hodograph (PH) quintic spline biarcs is proposed. To facilitate real-time computations of C 2 PH quintic splines, an efficient local data stream interpolation algorithm is introduced. Each spline segment interpolates second and first order Hermite data at the initial and final endpoint, respectively. In the spline extension of the scheme a C 2 smooth connection between successive spline segments is obtained by taking the locally required secondorder derivative information from the previous segment. Consequently, the data stream spline interpolant is globally C 2 continuous and can be constructed for arbitrary C 1 Hermite data configurations. A simple and effective selection of the free parameters that arise in the interpolation problem is proposed. The developed theoretical analysis proves the fourth approximation order of the local scheme while a selection of numerical examples confirms the same accuracy of its spline extension. In addition, the performances of the algorithm are also validated by considering its application to point stream interpolation with automatically generated first-order derivative information.

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Section: Introductionmentioning

confidence: 99%

A local $C^2$ Hermite interpolation scheme with PH quintic splines for 3D data streams

Giannelli,

Sacco,

Sestini

2021

Preprint

Self Cite

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New Developments in Theory, Algorithms, and Applications for Pythagorean–Hodograph Curves

Farouki

Giannelli

Sestini

2019

Advanced Methods for Geometric Modeling and Numerical Simulation

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This series will publish textbooks, multi-authors books, thesis and monographs in English language resulting from workshops, conferences, courses, schools, seminars, doctoral thesis, and research activities carried out at INDAM -Istituto Nazionale di Alta Matematica, http://www.altamatematica.it/en. The books in the series will discuss recent results and analyze new trends in mathematics and its applications.

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Interpolation of 3D data streams with C2 PH quintic splines

2022

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A fully data-dependent criterion for free angles selection in spatial PH cubic biarc Hermite interpolation

Cited by 5 publications

References 10 publications

A local $C^2$ Hermite interpolation scheme with PH quintic splines for 3D data streams

A local $C^2$ Hermite interpolation scheme with PH quintic splines for 3D data streams

New Developments in Theory, Algorithms, and Applications for Pythagorean–Hodograph Curves

Interpolation of 3D data streams with C2 PH quintic splines

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