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 Bezier surfaces, which generates G1 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. Highlights? 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.

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