Algorithm for orthogonal projection of parametric curves onto BB-spline surfaces

This paper proposes an algorithm for calculating the orthogonal projection of parametric curves onto BB-spline surfaces. It consists of a second order tracing method with which we construct a polyline to approximate the pre-image curve of the orthogonal projection curve in the parametric domain of the base surface. The final 3D approximate curve is obtained by mapping the approximate polyline onto the base surface. The Hausdorff distance between the exact orthogonal projection curve and the approximate curve is controlled under the user-specified distance tolerance. And the continuity of the approximate curve is εT−G1εT−G1, where εTεT is the user-specified angle tolerance. Experiments demonstrate that our algorithm is faster than the existing first order algorithms.

Research highlights
► Approximate the projection curve with a piecewise curve lying completely on the base surface.
► The degree of the approximate curve is comparable low.
► The approximation precision and the continuity of the approximate curve can be controlled under the user-specified tolerance.
► The efficiency of the algorithm is faster than the existing first order algorithms.