The use of floating-point arithmetic in geometric computation represents a formidable challenge for development and implementation of geometric algorithms. On one hand, one thrives to develop algorithms that are robust and produce accurate results, while on the other hand, one attempts to achieve rapid execution time. In particular for GIS applications, where large problem sizes are frequently encountered, efficiency considerations are important. In this paper, we present a floating-point filter written specifically for the important line intersection operation that is robust, outperforms existing general purpose filters and results in an accurate discovery and representation of topology from the geometric information.

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Frankel, A. (Andras), Nussbaum, D, & Sack, J.-R. (2004). Floating-point filter for the line intersection algorithm.