Degree reduction of Bézier curves with restricted control points area

Gospodarczyk, Przemysław

doi:10.1016/j.cad.2014.11.009

Cited by 11 publications

(29 citation statements)

References 15 publications

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“…In previous researches, least square error which represents the distance between the given Bézier curve and degree-reduced curve is always taken as an optimal function [5] [13] [14], then the optimal problem can be:…”

Section: Description About Degree Reduction Of Bézier Curvesmentioning

confidence: 99%

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Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization

Han¹,

Yang²

2016

JAMP

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In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect.

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Section: Description About Degree Reduction Of Bézier Curvesmentioning

confidence: 99%

“…For solving the similar degree reduction problem, Przemysław [13] impose restrictions of the control point area to get more intuitive location of the control points. Xu [14] used the method of energy-minimizing to construct curves.…”

Section: Introductionmentioning

confidence: 99%

Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization

Han¹,

Yang²

2016

JAMP

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“…In [4], one of us proposed a new approach to the problem of degree reduction of Bézier curves. The author noticed that as a result of the conventional degree reduction, the computed control points can be located far away from the plot of the curve.…”

Section: Introductionmentioning

confidence: 99%

Merging of Bézier curves with box constraints

Gospodarczyk

Woźny

2016

Journal of Computational and Applied Mathematics

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In this paper, we present a novel approach to the problem of merging of Bézier curves with respect to the L 2 -norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for further modification and applications. As in the case of the degree reduction problem, we apply the so-called restricted area approach -proposed recently in (P. Gospodarczyk, Computer-Aided Design 62 (2015), 143-151) -to avoid certain defects and make the resulting curve more useful. A method of solving the new problem is based on box-constrained quadratic programming approach.

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“…Since the most of conic sections cannot be accurately represented by polynomials in explicit form, the parameter polynomials are used to approximate the conic sections. Bézier curves and surfaces [1][2][3][4] are the modeling tools widely used in CAD/CAM systems. Most of the previous work on conic sections approximation is based on quartic Bézier curves.…”

Section: Introductionmentioning

confidence: 99%

A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

Zhi¹,

Wei²,

Tan

et al. 2016

ACM

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Abstract:A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous quartic Bézier approximation methods. A quartic G 2 -continuous spline approximation of conic sections is obtained by using the subdivision scheme at the shoulder point of the conic section.

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Degree reduction of Bézier curves with restricted control points area

Cited by 11 publications

References 15 publications

Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization

Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization

Merging of Bézier curves with box constraints

A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

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Degree reduction of Bézier curves with restricted control points area

Cited by 11 publications

References 15 publications

Multi-Degree Reduction of B&#233;zier Curves with Distance and Energy Optimization

Multi-Degree Reduction of B&#233;zier Curves with Distance and Energy Optimization

Merging of Bézier curves with box constraints

A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

Contact Info

Product

Resources

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Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization

Multi-Degree Reduction of Bézier Curves with Distance and Energy Optimization