Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
Vertex-rounding a three-dimensional polyhedral subdivision
Proceedings of the fourteenth annual symposium on Computational geometry
Interval arithmetic yields efficient dynamic filters for computational geometry
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Efficient algorithms for line and curve segment intersection using restricted predicates
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Further results on arithmetic filters for geometric predicates
Computational Geometry: Theory and Applications
A generic lazy evaluation scheme for exact geometric computations
Science of Computer Programming
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In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA allowing for efficient and exact computation with rational and algebraic geometric objects. It is the first kernel design which uses floating-point filter techniques on the level of geometric constructions. The experiments we present-partly using the CGAL framework-show a great improvement in speed and-maybe even more important for practical applications-memory consumption when dealing with more complex geometric computations.