4.5 Article

Circular arc approximation by hexic polynomial curves

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

Arc length preserving G2 Hermite interpolation of circular arcs

Emil Zagar

Summary: This paper focuses on the interpolation problem of two points, two corresponding tangent directions, curvatures, and arc length sampled from a circular arc (circular arc data). A general approach using Planar Pythagorean-hodograph (PH) curves of degree seven is presented, and the strong dependence of the solution on the general data is demonstrated. For circular arc data, a complicated system of nonlinear equations is reduced to a numerical solution of only one algebraic equation of degree 6, and the existence of admissible solutions is analyzed. Criteria for selecting the most appropriate solution in the case of multiple solutions are described, and an asymptotic analysis is provided. Numerical examples are used to validate the theoretical results.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2023)

Article Mathematics, Applied

On optimal polynomial geometric interpolation of circular arcs according to the Hausdorff distance

Ales Vavpetic et al.

Summary: This article discusses the optimal approximation of circular arcs using parametric polynomial curves, with an optimization related to the Hausdorff distance that has not been studied before. A general theory is presented with a rigorous analysis for special cases, including practical interpolation scenarios. Several numerical examples are provided to confirm theoretical results.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2021)

Article Mathematics, Applied

Circle approximation by G2 Bezier curves of degree n with 2n-1 extreme points

Young Joon Ahn

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2019)

Article Mathematics, Applied

A general framework for the optimal approximation of circular arcs by parametric polynomial curves

Ales Vavpetic et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2019)

Article Mathematics, Applied

On parametric polynomial circle approximation

Gasper Jaklic et al.

NUMERICAL ALGORITHMS (2018)

Article Mathematics, Applied

Sequence of Gn LN polynomial curves approximating circular arcs

Young Joon Ahn et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2018)

Article Mathematics, Applied

Circular sector area preserving approximation of circular arcs by geometrically smooth parametric polynomials

Emil Zagar

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2018)

Article Mathematics, Applied

Approximation of conic section by quartic Bezier curve with endpoints continuity condition

Yu Liu et al.

APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B (2017)

Article Computer Science, Software Engineering

Uniform approximation of a circle by a parametric polynomial curve

Gasper Jaklic

COMPUTER AIDED GEOMETRIC DESIGN (2016)

Article Computer Science, Software Engineering

An algorithm for G2 offset approximation based on circle approximation by G2 quadratic spline

Soo Won Kim et al.

COMPUTER-AIDED DESIGN (2016)

Article Mathematics, Applied

Circle approximation using LN Bezier curves of even degree and its application

Young Joon Ahn et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2014)

Article Mathematics

High-Order Parametric Polynomial Approximation of Conic Sections

Gasper Jaklic et al.

CONSTRUCTIVE APPROXIMATION (2013)

Article Computer Science, Software Engineering

Curvature continuous offset approximation based on circle approximation using quadratic Bezier biarcs

Young Joon Ahn et al.

COMPUTER-AIDED DESIGN (2011)

Article Mathematics, Applied

The best G1 cubic and G2 quartic Bezier approximations of circular arcs

Seok Hur et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2011)

Article Mathematics, Applied

Approximation of conic sections by curvature continuous quartic Bezier curves

Young Joon Ahn

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2010)

Article Computer Science, Software Engineering

An approximation of circular arcs by quartic Bezier curves

Seon-Hong Kim et al.

COMPUTER-AIDED DESIGN (2007)