G1 continuous approximate curves on NURBS surfaces

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a parabola approximation method based on the cubic reparameterization of rational Bézier surfaces, which generates G continuous approximate curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified tolerance. Examples are given to show the performance of our algorithm.► We present a method to generate G1 continuous approximate curves on NURBS surfaces. ► We give the cubic reparameterizations of rational Bezier surfaces. ► The Hausdorff distance between the approximate and exact curves is controlled. ► The approximate curve is lying completely on the NURBS surface. ► Iso-parameter curves of the reparameterized surfaces constitute the resulting curve.