On the theory of graded structures
Journal of Symbolic Computation
Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Edge-skeletons in arrangements with applications
Algorithmica
Information Sciences: an International Journal
Term Orderings on the Polynominal Ring
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Coordinate representation of order types requires exponential storage
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Applications of random sampling in computational geometry, II
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
Calculating approximate curve arrangements using rounded arithmetic
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Efficient parallel computation of arrangements of hyperplanes in d dimensions
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
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 efficient approach to removing geometric degeneracies
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
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
Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
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
Testing bipartiteness of geometric intersection graphs
ACM Transactions on Algorithms (TALG)
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
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In a previous paper, we introduced a generic solution to the problem of data degeneracy in geometric algorithms. The scheme is simple to use: algorithms qualifying under our requirements just have to use a prescribed blackbox for polynomial evaluation in order to achieve a symbolic perturbation of data. In this paper, we introduce the concept of an infinitesimal perturbation and show that our method is consistent relative to such perturbations.