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 c. 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, 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 edistance 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.
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering