Algorithm for Directional Projection of Parametric Curves onto B-spline Surfaces

Abstract

This paper proposes an algorithm for calculating the directional projection of parametric curves onto B-spline surfaces. It consists of a second order tracing method with which we construct a polyline to approximate the pre-image curve of the directional 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 directional projection curve and the approximate curve is controlled less than the user-specified distance tolerance. And the continuity of the approximate curve is ϵ_T−G¹, where ϵ_T is the user-specified angle tolerance. Experiments demonstrate that our algorithm is faster than the existing first order algorithm.

Keywords:

• directional projection
• B-spline
• curves on surfaces
• approximation.

ACKNOWLEDGEMENTS

The research was supported by Chinese 973 Program (2010CB328001) and Chinese 863 Program (2012AA040902). The first author was supported by the NSFC (61035002, 61272235). The second author was supported by the NSFC (61063029, 61173077).