Computational geometry: an introduction
Computational geometry: an introduction
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Verifiable implementation of geometric algorithms using finite precision arithmetic
Artificial Intelligence - Special issue on geometric reasoning
Recipes for geometry and numerical analysis - Part I: an empirical study
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A solid modelling system free from topological inconsistency
Journal of Information Processing
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Symbolic treatment of geometric degeneracies
Journal of Symbolic Computation
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Topology-oriented divide-and-conquer algorithm for Voronoi diagrams
Graphical Models and Image Processing
On degeneracy in geometric computations
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Three-dimensional convex hull as a fruitful source of diagrams
Theoretical Computer Science
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Experimental study on acceleration of an exact-arithmetic geometric algorithm
SMA '97 Proceedings of the 1997 International Conference on Shape Modeling and Applications (SMA '97)
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An incremental algorithm for constructing the four-dimensional convex hull is implemented using exact arithmetic together with the symbolic perturbation technique. Exact judgement of the topological structure of the four-dimensional convex hull requires about four times higher precision than the input. To decrease this computational cost, the lazy evaluation scheme is used. Experiments show that the computation can be accelerated more than one hundred times for non-degenerate input and more than three times even for highly degenerate input.