Planar point set fairing and fitting by arc splines

Yang, Xunnian; Wang, Guozhao

doi:10.1016/s0010-4485(00)00059-2

Cited by 53 publications

(18 citation statements)

References 12 publications

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“…With these fitting methods, the approximated curve is close to the ''real'' shape (in L 2 or L 1 sense, for example), but oscillates around it (Yang, 2001). We chose Bézier curves to approximate the shape of the roots, and curvature as a measure of shape fidelity.…”

Section: Curve Approximationmentioning

confidence: 99%

Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development

Cervantés¹

2005

Journal of Plant Physiology

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Section: Curve Approximationmentioning

confidence: 99%

Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development

Cervantés¹

2005

Journal of Plant Physiology

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“…Then the optimal problem is introduced and the iteration computation has to be used. One typical method is biarc method [8,9,10]. It is efficient and often combined with polygon line approximation in practice application [11].…”

Section: Rational Conic Bezier Fittingmentioning

confidence: 99%

<title>Error bounded conic spline approximation for NC code</title>

Shen

2012

SPIE Proceedings

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Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed.

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“…One can obtain a series of arcs according to arc interpolation segments by using the arc spline fitting method or the biarc spline method. 10,11 In this study, the biarc segments are used to approximate the profile of grinding wheel by using the allowed maximum deviation distance between the wheel shape and the biarcs as the approximation criterion. 12 The arcs generated by the biarc method can be post-processed for NC code generation on machining the base body of the CBN grinding wheel.…”

Section: Calculation Of Cbn Wheelmentioning

confidence: 99%

Study on precision grinding of screw rotors using CBN wheel

Wei

Zhang

et al. 2010

Int. J. Precis. Eng. Manuf.

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With increasing demands for high-speed and high-precision machining technology, CBN shape grinding is an effective means in the field of precision machining for screw rotors. Aiming at the high precision machining of screw rotors, a mathematical model for the axial profiles of the CBN wheel for machining screw rotors is developed based on theory of gear engagement. Small electroplated CBN wheel is firstly used to grinding screw rotors. Taking the backlash of screw rotors and the coating thickness of CBN layer into consideration, the modification of the base body of the wheel shape is introduced into the design of CBN wheel. For reducing the tooth profile errors of screw rotors induced by mounting errors and wears of CBN wheel, a mathematical model of the error analyses is established and the influence curves of the profile errors affected by mounting errors and radius error of grinding wheel are proposed. The electroplated CBN wheels for the screw rotors are made to verify the validity and effectiveness of the presented method and the machining experiments were performed. Results of this study reveals that the method proposed in this paper can be used as the precision grinding of screw rotors.

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Planar point set fairing and fitting by arc splines

Cited by 53 publications

References 12 publications

Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development

Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development

<title>Error bounded conic spline approximation for NC code</title>

Study on precision grinding of screw rotors using CBN wheel

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