The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented, which use extrapolating acceleration technique, and have convergent precision of order 2. Matrix method is used to subdivide the curves or surfaces which makes the subdivision more concise and intuitive. Dividing depths of Bezier curves and surfaces are used to subdivide the curves or surfaces adaptively Therefore the convergent precision and the computing efficiency of finding the intersections of curves and surfaces have been improved by the methods proposed in the paper.
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