Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Reliable and efficient computational geometry via controlled perturbation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Computing with geometric objects (points, curves, and surfaces) is central for many engineering disciplines and lies at the heart of computer aided design systems. Implementing geometric algorithms is notoriously difficult and most actual implementations are incomplete: they are known to crash or deliver the wrong result on some instances. In the introductory part of the talk, we illustrate the pitfalls of geometric computing [5] and explain for one algorithm in detail where the problem lies and what goes wrong.