Planar curve offset based on circle approximation

In Kwon Lee, Myung Soo Kim, Gershon Elber

Research output: Contribution to journalArticle

94 Citations (Scopus)

Abstract

An algorithm is presented to approximate planar offset curves within an arbitrary tolerance ∈ > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bézier curve segments within the tolerance c. The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic Bézier curve segments. For a polynomial curve C(t) of degree d, the offset curve Cr(t) is approximated by planar rational curves, Ca r (t)s, of degree 3d - 2. For a rational curve C(t) of degree d, the offset curve is approximated by rational curves of degree 5d - 4. When they have no self-intersections, the approximated offset curves, Ca r(t)s, are guaranteed to be within edistance from the exact offset curve Cr(t). The effectiveness of this approximation technique is demonstrated in the offset computation of planar curved objects bounded by polynomial/ rational parametric curves.

Original languageEnglish
Pages (from-to)617-630
Number of pages14
JournalCAD Computer Aided Design
Volume28
Issue number8
DOIs
Publication statusPublished - 1996 Jan 1

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Polynomials
Convolution

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

Cite this

Lee, In Kwon ; Kim, Myung Soo ; Elber, Gershon. / Planar curve offset based on circle approximation. In: CAD Computer Aided Design. 1996 ; Vol. 28, No. 8. pp. 617-630.
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Planar curve offset based on circle approximation. / Lee, In Kwon; Kim, Myung Soo; Elber, Gershon.

In: CAD Computer Aided Design, Vol. 28, No. 8, 01.01.1996, p. 617-630.

Research output: Contribution to journalArticle

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