Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry . Modern implementations employ floatingpoint filtering techniques to combine efficiency and robustness . If the input to these predicates is an intermediate construction, its floating point representation may be affected by anapproximation error, and correctness is no longer guaranteed . Instead of taking the intermediate construction as an explicit input, an indirect predicate considersthe primitive geometric elements which are combined to produce such aconstruction . This makes it possible to exploit efficient filters and expansion arithmeticto resolve the predicate with minimal overhead with respect to a naive floating point implementation . We show how toextend standard predicates to the case of points of intersection of linearelements (i.e. lines and planes) and show that, on classical problems, this approach outperforms state-of-the-

**Author(s) :**Marco Attene

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Keywords : predicates - geometric - indirect - input - construction -