Algebraic methods for geometric reasoning
Annual review of computer science: vol. 3, 1988
Recipes for geometry and numerical analysis - Part I: an empirical study
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Towards implementing robust geometric computations
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
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Numerical stability of algorithms for line arrangements
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The n-dimensional extended convex differences tree (ECDT) for representing polyhedra
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Numerical stability of algorithms for 2D Delaunay triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Resolvable representation of polyhedra
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
Intersecting solids on a massively parallel processor
ACM Transactions on Graphics (TOG)
Geometric modeling: a new fundamental framework and its practical implications
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Face-based data structure and its application to robust geometric modeling
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Rendering parametric surfaces in pen and ink
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Parallel robust algorithms for constructing strongly convex hulls
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
A perturbation scheme for spherical arrangements with application to molecular modeling
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Vertex-rounding a three-dimensional polyhedral subdivision
Proceedings of the fourteenth annual symposium on Computational geometry
Exact algorithms for circles on the sphere
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Analysis of boundary representation model rectification
Proceedings of the sixth ACM symposium on Solid modeling and applications
ESOLID---A System for Exact Boundary Evaluation
Proceedings of the seventh ACM symposium on Solid modeling and applications
Robust algorithms for constructing strongly convex hulls in parallel
Theoretical Computer Science
Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Topology-Oriented Approach to Robust Geometric Computation
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Applications of the Generic Programming Paradigm in the Design of CGAL
Selected Papers from the International Seminar on Generic Programming
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Exact Computation of 4-D Convex Hulls with Perturbation and Acceleration
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
VG '03 Proceedings of the 2003 Eurographics/IEEE TVCG Workshop on Volume graphics
Handling degeneracies in exact boundary evaluation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Sliver-free perturbation for the Delaunay tetrahedrization
Computer-Aided Design
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Exact and approximate construction of offset polygons
Computer-Aided Design
Modelling three-dimensional geoscientific fields with the Voronoi diagram and its dual
International Journal of Geographical Information Science
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Approximating centroids for the maximum intersection of spherical polygons
Computer-Aided Design
Volume CAD-CW-complexes based approach
Computer-Aided Design
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
A point inclusion test algorithm for simple polygons
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
A content-based publish/subscribe matching algorithm for 2d spatial objects
Middleware'11 Proceedings of the 12th ACM/IFIP/USENIX international conference on Middleware
A content-based publish/subscribe matching algorithm for 2D spatial objects
Proceedings of the 12th International Middleware Conference
Collision free region determination by modified polygonal Boolean operations
Computer-Aided Design
Consistency analysis of decision-making programs
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Hi-index | 4.10 |
Practical implementation of geometric operations remains error-prone, and the goal of implementing correct and robust systems for carrying out geometric computation remains elusive. The problem is variously characterized as a matter of achieving sufficient numerical precision, as a fundamental difficulty in dealing with interacting numeric and symbolic data, or as a problem of avoiding degenerate positions. The author examines these problems, surveys some of the approaches proposed, and assesses their potential for devising complete and efficient solutions. He restricts the analysis to objects with linear elements, since substantial problems already arise in this case. Three perturbation-free methods are considered: floating-point computation, limited-precision rational arithmetic, and purely symbolic representations. Some perturbation approaches are also examined, namely, representation and model, altering the symbolic data, and avoiding degeneracies.