Planar Curve Ooset Based on Circle Approximation

An algorithm is presented to approximate planar ooset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an ooset radius r, the circle of radius r is rst approximated by piecewise quadratic B ezier curve segments within the tolerance. The exact ooset curve C r (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 ooset curve C r (t) is approximated by planar rational curves, C a r (t)'s, of degree 3d ? 2. For a rational curve C(t) of degree d, the ooset curve is approximated by rational curves of degree 5d ? 4. When they have no self-intersections, the approximated ooset curves, C a r (t)'s, are guaranteed to be within-distance from the exact ooset curve C r (t). The eeectiveness of this approximation technique is demonstrated in the ooset computation of planar curved objects bounded by polynomial/rational parametric curves.