What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Concepts: linguistic support for generic programming in C++
Proceedings of the 21st annual ACM SIGPLAN conference on Object-oriented programming systems, languages, and applications
Proceedings of the 2007 ACM symposium on Applied computing
An adaptable and extensible geometry kernel
Computational Geometry: Theory and Applications
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Robust construction of the three-dimensional flow complex
Proceedings of the twenty-fourth annual symposium on Computational geometry
LOOK: A Lazy Object-Oriented Kernel design for geometric computation
Computational Geometry: Theory and Applications
Lines through segments in 3d space
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We present a generic C++ design to perform exact geometric computations efficiently using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also important for many applications, hence the need for delaying the costly exact computations at run time until they are actually needed, if at all. Our approach is generic and extensible in the sense that it is possible to make it a library that users can apply to their own geometric objects and primitives. It involves techniques such as generic functor-adaptors, static and dynamic polymorphism, reference counting for the management of directed acyclic graphs, and exception handling for triggering exact computations when needed. It also relies on multi-precision arithmetic as well as interval arithmetic. We apply our approach to the whole geometry kernel of Cgal.