Planar curve offset based on circle approximation

An algorithm is presented to approximate planar offset curves within an arbitrary tolerance epsilon > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bezier curve segments within the tolerance E. The exact offset curve C-r(t) is then approximated by the convolution of C(t) with the quadratic Bezier curve segments. For a polynomial curve C(t) of degree d, the offset curve C-r(t) is approximated by planar rational curves, c(r)(a)(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, C-r(a)(t)s, are guaranteed to be within epsilon-distance from the exact offset curve C-r(t). The effectiveness of this approximation technique is demonstrated in the offset computation of planar curved objects bounded by polynomial/rational parametric curves. Copyright (C) 1996 Elsevier Science Ltd.