An algorithm is presented to approximate planar offset curves within a
n 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 cur
ve 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-distan
ce from the exact offset curve C-r(t). The effectiveness of this appro
ximation technique is demonstrated in the offset computation of planar
curved objects bounded by polynomial/rational parametric curves. Copy
right (C) 1996 Elsevier Science Ltd.