Planar curve offset based on circle approximation

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 . 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 -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.