Construction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si23.svg"><mml:msup><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> planar Hermite interpolants with prescribed arc lengths

Knez, Marjeta; Pelosi, Francesca; Sampoli, Maria Lucia

doi:10.1016/j.amc.2022.127092

Cited by 10 publications

(4 citation statements)

References 22 publications

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“…There are some recent attempts of interpolation with (polynomial) PH curves of prescribed length s > 0 [25][26][27]. Assuming that exact and feasible solutions exist in the interpolation space Q, they will be found by minimizing the quadratic functional…”

Section: Quadratic Functionalsmentioning

confidence: 99%

Optimal interpolation with spatial rational Pythagorean hodograph curves

Schröcker¹,

Šìr²

2023

Preprint

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Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction field is a perfect square. The basis for the curve space is given explicitly. Consequently a number of interpolation problems (G 1 , C 1 , C 2 , C 1 /G 2 ) in this space become linear, cusp avoidance can be encoded by linear inequalities, and optimization problems like minimal energy or optimal length are quadratic and can be solved efficiently via quadratic programming. We outline the interpolation/optimization strategy and demonstrate it on several examples.

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Section: Quadratic Functionalsmentioning

confidence: 99%

Optimal interpolation with spatial rational Pythagorean hodograph curves

Schröcker¹,

Šìr²

2023

Preprint

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show abstract

“…The paper [16] presents a method to compute rational PH curves by directly studying the rationality of the integral (4) which can be insured by imposing "zero residue" conditions on the integrand. These are formulated as linear equations in terms of the partial fraction coefficients of the rational function λ(t) of Equations ( 4) and (5). More precisely, performing partial fraction decomposition, we can write…”

Section: Second Way -Zero Residue Conditionsmentioning

confidence: 99%

“…In order to obtain not only a rational curve but also a rational arc length function we must impose also the rationality of the real integral (5). For this purpose the residue vector condition (11) is to be augmented with the residue of the integrand in (5). Quite remarkably this can be done using the same expression as in Section 3.1.…”

Section: Second Way -Zero Residue Conditionsmentioning

confidence: 99%