Geometric Hermite interpolation by logarithmic arc splines

Yang, Xunnian

doi:10.1016/j.cagd.2014.09.001

Cited by 6 publications

(1 citation statement)

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“…Although geometric Hermite interpolation has been investigated by many 1 authors -e.g., [4,6,16,17,18,19,21,26,28,29,30,31] -the problems considered typically address only discrete local data. Satisfaction of global (integral) geometrical constraints poses a much more challenging task, if only because of the lack of simple closed-form expressions for the curve integral properties under consideration.…”

Section: Introductionmentioning

confidence: 99%

Construction of G 1 planar Hermite interpolants with prescribed arc lengths

Farouki

2016

Computer Aided Geometric Design

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The problem of constructing a plane polynomial curve with given end points and end tangents, and a specified arc length, is addressed. The solution employs planar quintic Pythagorean-hodograph (PH) curves with equal-magnitude end derivatives. By reduction to canonical form it is shown that, in this context, the problem can be expressed in terms of finding the real solutions to a system of three quadratic equations in three variables. This system admits further reduction to just a single univariate biquadratic equation, which always has positive roots. It is found that this construction of G 1 Hermite interpolants of specified arc length admits two formal solutions -of which one has attractive shape properties, and the other must be discarded due to undesired looping behavior. The algorithm developed herein offers a simple and efficient closed-form solution to a fundamental constructive geometry problem that avoids the need for iterative numerical methods.

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