research-article

Comparing Offset Curve Approximation Methods

Authors:

Myung-Soo KimAuthors Info & Claims

IEEE Computer Graphics and Applications, Volume 17, Issue 3

Pages 62 - 71

https://doi.org/10.1109/38.586019

Published: 01 May 1997 Publication History

Abstract

Offset curves have diverse engineering applications, spurring extensive research on various offset techniques. This article is intended to fill an important gap in the literature. In a recent paper on offset curve approximation, the authors suggested a new approach based on approximating the offset circle instead of the offset curve itself. To demonstrate the effectiveness of this approach, they compared it extensively with previous methods, conducting qualitative as well as quantitative comparisons employing various contemporary offset approximation methods for freeform curves in the plane. They measured the efficiency of the offset approximation in terms of the number of control points generated while making the approximations within a prescribed tolerance.

References

[1]

J. Hoschek, "Spline Approximation of Offset Curves," Computer Aided Geometric Design, Vol. 5, No. 1, June 1988, pp. 33-40.

Digital Library

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J. Hoschek and N. Wissel, "Optimal Approximate Conversion of Spline Curves and Spline Approximation of Offset Curves," Computer-Aided Design, Vol. 20, No. 8, Oct. 1988, pp. 475-483.

Digital Library

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R. Farouki and C. Neff, "Analytic Properties of Plane Offset Curves," Computer Aided Geometric Design, Vol. 7, 1990, pp. 83-99.

Digital Library

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R. Farouki and C. Neff, "Algebraic Properties of Plane Offset Curves," Computer Aided Geometric Design, Vol. 7, 1990, pp. 101-127.

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Digital Library

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I.-K. Lee M.-S. Kim and G. Elber, "Planar Curve Offset Based on Circle Approximation," Computer-Aided Design, Vol. 28, No. 8, Aug. 1996, pp. 617-630.

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W. Tiller and E. Hanson, "Offsets of Two Dimensional Profiles," IEEE Computer Graphics and Applications, Vol. 4, No. 9, Sept. 1984, pp. 36-46.

Digital Library

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G. Elber and E. Cohen, "Error Bounded Variable Distance Offset Operator for Free Form Curves and Surfaces," Int'l J. Computational Geometry and Applications, Vol. 1, No. 1, Mar. 1991, pp. 67-78.

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G. Elber, Free Form Surface Analysis Using a Hybrid of Symbolic and Numeric Computation, PhD dissertation, Computer Science Department, University of Utah, Salt Lake City, Utah, 1992.

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R. Klass, "An Offset Spline Approximation for Plane Cubic Splines," Computer-Aided Design, Vol. 15, No. 5, Sept. 1983, pp. 297-299.

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B. Pham, "Offset Approximation of Uniform B-Splines," Computer-Aided Design, Vol. 20, No. 8, Oct. 1988, pp. 471-474.

Digital Library

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I.-K. Lee M.-S. Kim and G. Elber, "New Approximation Methods for Planar Curve Offset and Convolution Curves," to appear in Theory and Practice of Geometric Modeling, W. Strasser, ed., Springer-Verlag, Heidelberg, 1997.

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Cited By

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Comparing Offset Curve Approximation Methods

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cover image IEEE Computer Graphics and Applications

IEEE Computer Graphics and Applications Volume 17, Issue 3

May 1997

83 pages

ISSN:0272-1716

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Copyright © Copyright © 1997 IEEE. All Rights Reserved.

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IEEE Computer Society Press

Washington, DC, United States

Publication History

Published: 01 May 1997

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Cited By

Fang LLi Y(2022)Algebraic and geometric characterizations of a class of Algebraic-Hyperbolic Pythagorean-Hodograph curvesComputer Aided Geometric Design10.1016/j.cagd.2022.10212197:COnline publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1016/j.cagd.2022.102121
Nehab D(2020)Converting stroked primitives to filled primitivesACM Transactions on Graphics10.1145/3386569.339239239:4(137:1-137:17)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392392
Ghaffari MTangen KAlaraj ADu XCharbel FLinninger A(2017)Large-scale subject-specific cerebral arterial tree modeling using automated parametric mesh generation for blood flow simulationComputers in Biology and Medicine10.1016/j.compbiomed.2017.10.02891:C(353-365)Online publication date: 1-Dec-2017
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Lu XZheng JCai YZhao G(2016)Geometric characteristics of a class of cubic curves with rational offsetsComputer-Aided Design10.1016/j.cad.2015.07.00670:C(36-45)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.cad.2015.07.006
Sánchez-Reyes JChacón J(2015)A polynomial Hermite interpolant for C 2 quasi arc-length approximationComputer-Aided Design10.1016/j.cad.2014.12.00162:C(218-226)Online publication date: 1-May-2015
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Lee JKim YKim MElber G(2015)Efficient offset trimming for deformable planar curves using a dynamic hierarchy of bounding circular arcsComputer-Aided Design10.1016/j.cad.2014.08.03158:C(248-255)Online publication date: 1-Jan-2015
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Nguyen VKerfriden PBordas SRabczuk T(2014)Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithmComputer-Aided Design10.1016/j.cad.2014.05.00455(49-63)Online publication date: 1-Oct-2014
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Barringer RGribel CAkenine-Möller T(2012)High-quality curve rendering using line sampled visibilityACM Transactions on Graphics10.1145/2366145.236618131:6(1-10)Online publication date: 1-Nov-2012
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Ruf EOwens JPharr MDachsbacher CMark WPantaleoni J(2011)An inexpensive bounding representation for offsets of quadratic curvesProceedings of the ACM SIGGRAPH Symposium on High Performance Graphics10.1145/2018323.2018346(143-150)Online publication date: 5-Aug-2011
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Ahn YHoffmann C(2011)Approximate convolution with pairs of cubic Bézier LN curvesComputer Aided Geometric Design10.1016/j.cagd.2011.06.00628:6(357-367)Online publication date: 1-Aug-2011
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