Projection of curves on B-spline surfaces using quadratic reparameterization

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is εT–G1 continuous, where εT is the user-specified angle tolerance. Examples are given to show the performance of our algorithm.