Polyline approach for approximating Hausdorff distance between planar free-form curves

Bai, Yan-Bing; Yong, Jun-Hai; Liu, Changyuan; Liu, Xiaoming; Meng, Yu Qin

doi:10.1016/j.cad.2011.02.008

Cited by 29 publications

(29 citation statements)

References 21 publications

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“…[2,3,9,10], etc.). Only a general method for estimating the distance between two space curves (not necessarily bounded) is presented in [8].…”

Section: Discussionmentioning

confidence: 96%

“…The results obtained in this paper do not provide an alternative method to this question, but a way of applying important and effective existing methods to the case in which some assumptions on the input curves are not satisfied, as for instance the boundedness (see e.g. [2,3,9,10], etc.) or the finiteness of the Hausdorff distance between them (see [7,8]).…”

Section: Algorithm and Examplesmentioning

confidence: 90%

“…Many authors have addressed some problems in this frame (see e.g. [2,3,[7][8][9][10], etc.) but all of them assume that the given curves are bounded or that the Hausdorff distance between them is finite.…”

Section: Asymptotic Behavior and Hausdorff Distancementioning

confidence: 99%

“…Once one has ensured that the Hausdorff distance between the two curves is finite, some additional existing methods can be applied to estimate the Hausdorff distance between two not bounded curves (see [8]), or for a chosen bounded frame of the input curves (see e.g. [2,3,9,10], etc. ).…”

Section: Algorithm and Examplesmentioning

confidence: 99%

“…Only some results for bounding or estimating the Hausdorff distance as well as computing it for some special cases can be found. For instance, in [9], the Hausdorff distance between planar free-form curves using a polyline approach is estimated. More precisely, the input curves are approximated with polylines and the precise Hausdorff distance between polylines is computed.…”

Section: Introductionmentioning

confidence: 99%

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Characterizing the finiteness of the Hausdorff distance between two algebraic curves

Blasco

Pérez–Díaz

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the n-dimensional space (parametrically or implicitly defined) to be finite. The characterization is related with the asymptotic behavior of the two curves and it can be easily checked. More precisely, the Hausdorff distance between two curves C and C is finite if and only if for each infinity branch of C there exists an infinity branch of C such that the terms with positive exponent in the corresponding series are the same, and reciprocally.

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“…[2,3,9,10], etc.). Only a general method for estimating the distance between two space curves (not necessarily bounded) is presented in [8].…”

Section: Discussionmentioning

confidence: 96%

Section: Algorithm and Examplesmentioning

confidence: 90%

Section: Asymptotic Behavior and Hausdorff Distancementioning

confidence: 99%

Section: Algorithm and Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characterizing the finiteness of the Hausdorff distance between two algebraic curves

Blasco

Pérez–Díaz

2015

Journal of Computational and Applied Mathematics

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Generation of human walking paths

2015

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This work investigates the way humans plan their paths in a goal-directed motion, assuming that a person acts as an optimal controller that plans the path minimizing a certain (unknown) cost function. Taking this viewpoint, the problem can be formulated as an inverse optimal control one, i.e., starting from control and state trajectories one wants to figure out the cost function used by a person while planning the path. The so-obtained model can be used to support the design of safe human–robot interaction systems, as well as to plan human-like paths for humanoid robots. To test the envisaged ideas, a set of walking paths of different volunteers were recorded using a motion capture facility. The collected data were used to compare two solutions to the inverse optimal control problem coming from the literature to a novel one. The obtained results, ranked using the discrete Fréchet distance, show the effectiveness of the proposed approach

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Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

Zhong

Luo

Chang

et al. 2019

Int. J. Autom. Comput.

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Driven by the ever increasing demand in function integration, more and more next generation high value-added products, such as head-up displays, solar concentrators and intra-ocular-lens, etc., are designed to possess freeform (i.e., non-rotational symmetric) surfaces. The toolpath, composed of high density of short linear and circular segments, is generally used in computer numerical control (CNC) systems to machine those products. However, the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration, which will decrease the machining efficiency and product surface finish. Driven by the ever-increasing need for high-speed high-precision machining of those products, many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry, aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods. This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications. The advantages and disadvantages of these approaches are discussed. Possible future research directions are also offered.

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Polyline approach for approximating Hausdorff distance between planar free-form curves

Cited by 29 publications

References 21 publications

Characterizing the finiteness of the Hausdorff distance between two algebraic curves

Characterizing the finiteness of the Hausdorff distance between two algebraic curves

Generation of human walking paths

Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

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