scholarly journals Approximating offset Curves using Bezier curves with high accuracy

2020 ◽  
Vol 10 (2) ◽  
pp. 1648 ◽  
Author(s):  
Abedallah Rababah ◽  
Moath Jaradat
Keyword(s):  
Uniform Approximation ◽  
High Accuracy ◽  
New Method ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Best Uniform Approximation ◽  
Offset Curves

In this paper, a new method for the approximation of offset curves is presented using the idea of the parallel derivative curves. The best uniform approximation of degree 3 with order 6 is used to construct a method to find the approximation of the offset curves for Bezier curves. The proposed method is based on the best uniform approximation, and therefore; the proposed method for constructing the offset curves induces better outcomes than the existing methods.

Degree reduction of Bézier curves by uniform approximation with endpoint interpolation

1995 ◽  
Vol 27 (9) ◽  
pp. 651-661 ◽  
Author(s):  
Przemyslaw Bogacki ◽  
Stanley E Weinstein ◽  
Yuesheng Xu
Keyword(s):  
Uniform Approximation ◽  
Degree Reduction ◽  
Bezier Curves ◽  
Bézier Curves

scholarly journals Offset Approximation of Rational Trigonometric Bezier ´ Curves

2021 ◽  
pp. 351-365
Author(s):  
Uzma Bashir ◽  
Aqsa Rasheed
Keyword(s):  
Root Function ◽  
Square Root ◽  
Control Points ◽  
Bezier Curves ◽  
Bézier Curves ◽  
End Points ◽  
Control Polygon ◽  
Cad Cam ◽  
Offset Curves ◽  
Definition Of

Offset curves are one of the crucial curves, but the presence of square root function in the representation is main hindrance towards their applications in CAD/CAM. The presented technique is based on offset approximation using rational trigonometric Bezier curves. The idea is ´ to construct a new control polygon parallel to original one. The two end points of the offset control polygon have been taken as exact offset end points, while the middle control points and weights have been computed using definition of parallel curves. As a result, offsets of rational and nonrational trigonometric Bezier curves have been approximated by rational ´ cubic trigonometric Bezier curve. An error between exact and approxi- ´ mated offset curves have also been computed to show the efficacy of the method.

scholarly journals The best uniform quadratic approximation of circular arcs with high accuracy

2016 ◽  
Vol 14 (1) ◽  
pp. 118-127 ◽  
Author(s):  
Abedallah Rababah
Keyword(s):  
Explicit Form ◽  
Approximation Method ◽  
Uniform Approximation ◽  
Error Function ◽  
Approximation Order ◽  
High Accuracy ◽  
Circular Arc ◽  
Numerical Examples ◽  
Best Uniform Approximation ◽  
Circular Arcs

AbstractIn this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.

scholarly journals An Approximation of Bézier Curves by a Sequence of Circular Arcs

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.

Quadratic Bezier Curves for Multi-Agent Coordinated Arrival in the Presence of Obstacles

2021 ◽  
Author(s):  
Satyanarayana G. Manyam ◽  
David Casbeer ◽  
Isaac E. Weintraub ◽  
Dzung M. Tran ◽  
Justin M. Bradley ◽  
...  
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Multi Agent

Curves used in highway design and Bezier curves

2021 ◽  
Vol Accepted ◽  
Author(s):  
Bayram Şahin ◽  
Aslı Ayar
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Highway Design
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