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
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
Obtaining robust Boolean set operations for manifold solids by avoiding and eliminating redundancy.
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
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
Topology-oriented divide-and-conquer algorithm for Voronoi diagrams
Graphical Models and Image Processing
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
Robust proximity queries: an illustration of degree-driven algorithm design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient exact evaluation of signs of determinants
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing exact geometric predicates using modular arithmetic with single precision
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Consistent calculations for solids modeling
SCG '85 Proceedings of the first annual symposium on Computational geometry
An Intersection Algorithm Based on Delaunay Triangulation
IEEE Computer Graphics and Applications
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)
Finite-resolution computational geometry
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Stable maintenance of point set triangulations in two dimensions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Safe and effective determinant evaluation
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A robust algorithm for bisecting a triconnected graph with two resource sets
Theoretical Computer Science
Proceedings of the twenty-fourth annual symposium on Computational geometry
Consistent digital line segments
Proceedings of the twenty-sixth annual symposium on Computational geometry
| Hi-index | 0.00 |
The paper surveys a method, called the "topology-oriented method", for designing numerically robust geometric algorithms. In this method, higher priority is placed on the consistency of the topological structures of geometric objects than on numerical values. The resulting software is completely robust in the sense that inconsistency never arizes no matter how large numerical errors take place. The basic idea of this method and typical examples are shown.