Computing intersections of planar spline curves using knot insertion

Authors:
Knut Mørken;Martin Reimers;Christian Schulz
Affiliations:
Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway and Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway;Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway;Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway and Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway
Venue:
Computer Aided Geometric Design
Year:
2009

Citing 6
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Abstract

We present a new method for computing intersections of two parametric B-spline curves. We use an intersection of the control polygons as an approximation for an intersection of the curves in combination with knot insertion. The resulting algorithm is asymptotically Newton-like, but without the need of a starting value. Like Newton's method, it converges quadratically at transversal intersections, the analogue to simple roots. It is a generalization of an algorithm developed by two of the authors for computing zeros of spline functions.