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Curvature continuity and offsets for piecewise conics

Editor: R. Daniel Bergeron Author:

G. FarinAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 8, Issue 2

Pages 89 - 99

https://doi.org/10.1145/62054.62056

Published: 01 April 1989 Publication History

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Abstract

In this paper the construction of curvature continuous, planar curves (open or closed) that consist of conic segments, represented in the rational Bézier form, is discussed, and an iterative procedure to compute their offset curves is outlined.

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Lu JYang RHu GHussien A(2024)Ameliorated Snake Optimizer-Based Approximate Merging of Disk Wang–Ball CurvesBiomimetics10.3390/biomimetics90301349:3(134)Online publication date: 22-Feb-2024
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Incesu MEvren SGursoy O(2022)On the Bertrand Pairs of Open Non-Uniform Rational B-Spline CurvesMathematical Analysis and Applications10.1007/978-981-16-8177-6_11(167-184)Online publication date: 23-Mar-2022
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Ramanantoanina AHormann K(2021)New shape control tools for rational Bézier curve designComputer Aided Geometric Design10.1016/j.cagd.2021.102003(102003)Online publication date: May-2021
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Curvature continuity and offsets for piecewise conics

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Reviews

Reviewer: George H. Williams

This paper extends the work on curve fitting with conic splines. The author cites two applications: curve design and font detail design. For curve design, the problem is, given a set of control points for a curve, to find the rational quadratic equations for a set of tangent continuous conic splines and to include parameters which can be modified so that the curve is curvature continous. In effect, this makes it possible to fine-tune the curve without going from quadratic to cubic form. For font detail design, the problem is to generate the equations for a curve that is offset from the original curve by a constant distance. The author uses a recursive algorithm to subdivide the intervals as he develops the equations for the offset curve. The paper extends the ideas of piecewise conic curves and rational quadratic Bezier curves. It should be of interest to people working in this specific area.

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 8, Issue 2

April 1989

56 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/62054

Editor:
R. Daniel Bergeron

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1989

Published in TOG Volume 8, Issue 2

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Lu JYang RHu GHussien A(2024)Ameliorated Snake Optimizer-Based Approximate Merging of Disk Wang–Ball CurvesBiomimetics10.3390/biomimetics90301349:3(134)Online publication date: 22-Feb-2024
https://doi.org/10.3390/biomimetics9030134
Incesu MEvren SGursoy O(2022)On the Bertrand Pairs of Open Non-Uniform Rational B-Spline CurvesMathematical Analysis and Applications10.1007/978-981-16-8177-6_11(167-184)Online publication date: 23-Mar-2022
https://doi.org/10.1007/978-981-16-8177-6_11
Ramanantoanina AHormann K(2021)New shape control tools for rational Bézier curve designComputer Aided Geometric Design10.1016/j.cagd.2021.102003(102003)Online publication date: May-2021
https://doi.org/10.1016/j.cagd.2021.102003
Incesu M(2021)The new characterization of ruled surfaces corresponding dual Bézier curvesMathematical Methods in the Applied Sciences10.1002/mma.739845:18(12030-12045)Online publication date: 8-Apr-2021
https://doi.org/10.1002/mma.7398
Incesu M(2020)LS (3)-equivalence conditions of control points and application to spatial Bézier curves and surfacesAIMS Mathematics10.3934/math.20200845:2(1216-1246)Online publication date: 2020
https://doi.org/10.3934/math.2020084
İNCESU MGÜRSOY O(2020)On the G-Similarities of two open B-spline curves in R3R3 de Açık B-Spline Eğrilerinin G-BenzerliklerMuş Alparslan Üniversitesi Fen Bilimleri Dergisi10.18586/msufbd.8071538:2(785-795)Online publication date: 13-Dec-2020
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Jin YZhao SWang Y(2019)An Optimal Feed Interpolator Based on G2 Continuous Bézier Curves for High-Speed Machining of Linear Tool PathChinese Journal of Mechanical Engineering10.1186/s10033-019-0360-832:1Online publication date: 9-May-2019
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Bae SAhn Y(2016)Comparison of Offset Approximation Methods of Conics with Explicit Error BoundsJournal of the Chosun Natural Science10.13160/ricns.2016.9.1.109:1(10-15)Online publication date: 30-Mar-2016
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Estrada Sarlabous JHernández Mederos VMartínez Morera DVelho LLópez Gil N(2012)Conic-like subdivision curves on surfacesThe Visual Computer10.1007/s00371-012-0728-628:10(971-982)Online publication date: 30-May-2012
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Recommendations

G1 Continuity Conics for Curve Fitting Using Particle Swarm Optimization

From Conics to NURBS: A Tutorial and Survey

Rational continuity: parametric, geometric, and Frenet frame continuity of rational curves

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