Approximation of circular arcs using quartic Bezier curves with barycentric coordinates satisfying G^2 data

The paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model. The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves.

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An approximation of circular arcs by quartic Bézier curves

Computer-Aided Design ◽

10.1016/j.cad.2007.01.004 ◽

2007 ◽

Vol 39 (6) ◽

pp. 490-493 ◽

Cited By ~ 44

Author(s):

Seon-Hong Kim ◽

Young Joon Ahn

Keyword(s):

Bezier Curves ◽

Bézier Curves ◽

Circular Arcs

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Approximation of circular arcs and offset curves by Bézier curves of high degree

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2003.10.008 ◽

2004 ◽

Vol 167 (2) ◽

pp. 405-416 ◽

Cited By ~ 32

Author(s):

Young Joon Ahn ◽

Yeon soo Kim ◽

Youngsuk Shin

Keyword(s):

Bezier Curves ◽

Bézier Curves ◽

Circular Arcs ◽

Offset Curves ◽

High Degree

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Curvature approximation of circular arcs by low-degree parametric polynomials

Journal of Numerical Mathematics ◽

10.1515/jnma-2014-0046 ◽

2016 ◽

Vol 24 (2) ◽

Cited By ~ 2

Author(s):

Boštjan Kovač ◽

Emil Žagar

Keyword(s):

Bezier Curves ◽

Bézier Curves ◽

New Methods ◽

Circular Arcs ◽

Low Degree ◽

Parametric Polynomials ◽

Curvature Approximation

AbstractIn this paper some new methods for curvature approximation of circular arcs by low-degree Bézier curves are presented. Interpolation by geometrically continuous (

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An Approximation of Bézier Curves by a Sequence of Circular Arcs

Information Technology And Control ◽

10.5755/j01.itc.50.2.25178 ◽

2021 ◽

Vol 50 (2) ◽

pp. 213-223

Author(s):

Taweechai Nuntawisuttiwong ◽

Natasha Dejdumrong

Keyword(s):

New Method ◽

Bézier Curve ◽

Bezier Curve ◽

Circular Path ◽

Arbitrary Degree ◽

Bezier Curves ◽

Bézier Curves ◽

Circular Arc ◽

Circular Arcs ◽

The Given

Some researches have investigated that a Bézier curve can be treated as circular arcs. This work is to proposea new scheme for approximating an arbitrary degree Bézier curve by a sequence of circular arcs. The sequenceof circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraicapproximation schemes. The technique used for segmentation is to simply investigate the inner anglesand the tangent vectors along the corresponding circles. It is obvious that a Bézier curve can be subdivided intothe form of subcurves. Hence, a given Bézier curve can be expressed by a sequence of calculated points on thecurve corresponding to a parametric variable t. Although the resulting points can be used in the circular arcconstruction, some duplicate and irrelevant vertices should be removed. Then, the sequence of inner angles arecalculated and clustered from a sequence of consecutive pixels. As a result, the output dots are now appropriateto determine the optimal circular path. Finally, a sequence of circular segments of a Bézier curve can be approximatedwith the pre-defined resolution satisfaction. Furthermore, the result of the circular arc representationis not exceeding a user-specified tolerance. Examples of approximated nth-degree Bézier curves by circular arcsare shown to illustrate efficiency of the new method.

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