Construction of low degree rational motions

Krajnc, Matjaž; Počkaj, Karla; Vitrih, Vito

doi:10.1016/j.cam.2013.07.014

Cited by 8 publications

(1 citation statement)

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“…Later the generalization of this approach to cubic interpolation, which leads to G 2 rational spline motions of degree six, was considered in [14]. Other geometrically continuous motions of degree six can be found in [15] and [16]. The difficulty when using geometric interpolation methods is that nonlinear equations are involved and the existence and uniqueness of an interpolant are not assured for all given data.…”

Section: Introductionmentioning

confidence: 99%

Construction of G 3 rational motion of degree eight

Ferjančič

Krajnc

Vitrih

2016

Applied Mathematics and Computation

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The paper presents a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with G 3 smoothness. The motion is determined through interpolation of positions and derivative data up to order three in the geometric sense. Nonlinearity in the spherical part of construction results in a single univariate quartic equation which yields solutions in a closed form. Sufficient conditions on the regions for the curvature data are derived, implying the existence of a real admissible solution. The algorithm how to choose appropriate data is proposed too. The theoretical results are substantiated with numerical examples.

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Section: Introductionmentioning

confidence: 99%

Construction of G 3 rational motion of degree eight

Ferjančič

Krajnc

Vitrih

2016

Applied Mathematics and Computation

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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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