Planar curve offset based on circle approximation

In Kwon Lee, Myung Soo Kim, Gershon Elber

Research output: Contribution to journalArticlepeer-review

102 Citations (Scopus)


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, Car (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, Car(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
Issue number8
Publication statusPublished - 1996 Aug

All Science Journal Classification (ASJC) codes

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


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