Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Verifiable implementation of geometric algorithms using finite precision arithmetic
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ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
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A robust method for finding points of intersection of line segments in a 2-D plane is presented. The plane is subdivided by Delaunay triangulation to localize areas where points of intersection exist and to guarantee the topological consistency of the resulting arrangement. The subdivision is refined by inserting midpoints recursively until the areas containing points of intersection are sufficiently localized. The method is robust in the sense that it does not miss points of intersection that are easily detectable when costly line-pair checking is performed. The algorithm is adaptive in the sense that most of the computational cost is incurred for the areas where finding points of intersection is difficult.