Efficient Algorithm Getting Intersection Curves for Triangular Bézier Surface

An algorithm of rapidly getting intersection curves for triangular Bezier surface is proposed, which includes four steps. The intersection regions are obtained rapidly based on the dynamic spatial indexing structure named R*S-tree of triangular Bezier surface models, so that the sets of intersection triangular Bezier patches are located exactly. Each Bezier patch is subdivided into many triangular planar patches in the scope of the precision by setting the discrete precision. The intersection line data is obtained through the intersection of triangular planar patches. The intersection curves are obtained by tracking extraction of intersection lines which have the common end point on line segments. The experimental results show that the algorithm can obtain the exact intersection curves of two complex triangular Bezier surface models rapidly, and it is proved to be applicable through generating NC tool path for triangular Bezier surface based on this algorithm. copyright 2011 Journal of Mechanical Engineering.