A new fast normal-based interpolating subdivision scheme by cubic Bézier curves

Mao, Aihua; Luo, Jie; Chen, Jun; Li, Guiqing

doi:10.1007/s00371-015-1175-y

Cited by 14 publications

(10 citation statements)

References 27 publications

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“…We extend this idea and come up with a new averaging method. The modified schemes with this method generate curves that lack cusps, whatever the input data is, in contrast to the scheme in [1]. We prove that the limit normals of such a converging scheme are the normals of the limit curve.…”

Section: Our Contributionmentioning

confidence: 87%

“…Note that the generated curves are without cusps. The result obtained in [1] by a similar construction lacks this property (see Table 1 there). Also note, that the result Algorithm 1 Modified Lane-Riesenfeld algorithm Input: m ∈ N 0 , P i = (p i , n i ), i ∈ Z.…”

Section: Examples Of Modified Schemesmentioning

confidence: 94%

“…We exploit the idea in [1] to use a Bezier curve as an auxiliary object to sample a point and a normal from. We extend this idea and come up with a new averaging method.…”

Section: Our Contributionmentioning

confidence: 99%

“…Remark 3.1. It is shown in [6] that a cubic Bezier curve approximates well a circle arc if the distances |c 0 c 1 | and |c 2 c 3 | are computed as in (1). So, if the pairs P 0 and P 1 are taken from a circle then P ω is very close to the point and normal sampled from the corresponding position on that circle.…”

Section: Notationmentioning

confidence: 99%

“…Further developments consider combined types of input data, such as point-normal pairs (e.g. [3], [1], [11]) or point-tangent pairs (e.g. [17]).…”

Section: Introductionmentioning

confidence: 99%

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Subdivision of point-normal pairs with application to smoothing feasible robot path

Lipovetsky¹

2019

Preprint

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In a previous paper [11] we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D, and converge to limit curves and limit normals. Such a scheme has the disadvantage that the limit normals are not the normals of the limit curve. In this paper we solve this problem by proposing a new averaging method, and obtaining a new family of algorithms based on it. We demonstrate their new editing capabilities and apply this subdivision technique to smooth a precomputed feasible polygonal point robot path.

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Section: Our Contributionmentioning

confidence: 87%

Section: Examples Of Modified Schemesmentioning

confidence: 94%

“…We exploit the idea in [1] to use a Bezier curve as an auxiliary object to sample a point and a normal from. We extend this idea and come up with a new averaging method.…”

Section: Our Contributionmentioning

confidence: 99%

Section: Notationmentioning

confidence: 99%

“…Further developments consider combined types of input data, such as point-normal pairs (e.g. [3], [1], [11]) or point-tangent pairs (e.g. [17]).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations