This paper proposes an algorithm for calculating the directional projection ofparametric curves onto B-spline surfaces. It consists of a second order tracing methodwith which we construct a polyline to approximate the pre-image curve of thedirectional projection curve in the parametric domain of the base surface. The final 3Dapproximate curve is obtained by mapping the approximate polyline onto the basesurface. The Hausdorff distance between the exact directional projection curve and theapproximate curve is controlled less than the user-specified distance tolerance. Andthe continuity of the approximate curve is 1eT -G , where T e is the user-specifiedangle tolerance. Experiments demonstrate that our algorithm is faster than theexisting first order algorithm.