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Citation:
In-Kwon Lee, Myung-Soo Kim, and Gershon Elber, "Planar Curve Offset Based on Circle Approximation", Computer-Aided Design, Vol. 28, No. 8, pp. 617-630, 1996, 1996
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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 B´ezier curve segments within the tolerance. The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic B´ezier 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 -distance 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.
