Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Consistent calculations for solids modeling
SCG '85 Proceedings of the first annual symposium on Computational geometry
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Geometry, graphics, and numerical analysis
Geometry, graphics, and numerical analysis
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Coordinate representation of order types requires exponential storage
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Incremental computation of planar maps
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
An algorithm for generalized point location and its applications
Journal of Symbolic Computation
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Parallel robust algorithms for constructing strongly convex hulls
Proceedings of the twelfth annual symposium on Computational geometry
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
Exact Computation of 4-D Convex Hulls with Perturbation and Acceleration
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
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Geometric computations, like all numerical procedures, are extremely prone to roundoff error. However, virtually none of the numerical analysis literature directly applies to geometric calculations. Even for line intersection, the most basic geometric operation, there is no robust and efficient algorithm. Compounding the difficulties, many geometric algorithms perform iterations of calculations reusing previously computed data. In this paper, we explore some of the main issues in geometric computations and the methods that have been proposed to handle roundoff errors. In particular, we focus on one method and apply it to a general iterative intersection problem. Our initial results seem promising and will hopefully lead to robust solutions for more complex problems of computational geometry.