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
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
A solid modelling system free from topological inconsistency
Journal of Information Processing
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
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
Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams
CVGIP: Graphical Models and Image Processing
Robust gift wrapping for the three-dimensional convex hull
Journal of Computer and System Sciences
Topology-oriented divide-and-conquer algorithm for Voronoi diagrams
Graphical Models and Image Processing
Why is the 3D Delaunay triangulation difficult to construct?
Information Processing Letters
Consistent calculations for solids modeling
SCG '85 Proceedings of the first annual symposium on Computational geometry
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
A Topology Oriented Algorithm for the Voronoi Diagram of Polygons
Proceedings of the 8th Canadian Conference on Computational Geometry
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)
Stable maintenance of point set triangulations in two dimensions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
The topology-oriented approach is a principle for translating geometric algorithms into practically valid computer software. In this principle, the highest priority is placed on the topological consistency of the geometric objects; numerical values are used as lower-priority information. The resulting software is completely robust in the sense that no matter how large numerical errors arise, the algorithm never fail. The basic idea of this approach and various examples are surveyed.