New results for random determination of equivalence of expressions
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
The complexity of robot motion planning
The complexity of robot motion planning
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
A solid modelling system free from topological inconsistency
Journal of Information Processing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Signature functions for algebraic numbers
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
IEEE Transactions on Computers
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A strong and easily computable separation bound for arithmetic expressions involving square roots
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Look — a Lazy Object-Oriented Kernel for geometric computation
Proceedings of the sixteenth annual symposium on Computational geometry
Computable analysis: an introduction
Computable analysis: an introduction
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Robot Motion Planning and Control
Robot Motion Planning and Control
Principles of Digital Image Synthesis
Principles of Digital Image Synthesis
C-XSC: A C++ Class Library for Extended Scientific Computing
C-XSC: A C++ Class Library for Extended Scientific Computing
Foundation of a computable solid modelling
Theoretical Computer Science
Using PVS to validate the algorithms of an exact arithmetic
Theoretical Computer Science - Real numbers and computers
An Efficient Stochastic Method for Round-Off Error Analysis
Proceedings of the Symposium on Accurate Scientific Computations
Randomized Zero Testing of Radical Expressions and Elementary Geometry Theorem Proving
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Precision and Robustness in Geometric Computations
Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems
The CGAL Kernel: A Basis for Geometric Computation
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Constructive root bound for k-ary rational input numbers
Proceedings of the nineteenth annual symposium on Computational geometry
Numerical decomposition of geometric constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Shortest circuits with given homotopy in a constellation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Proving by example and gap theorems
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
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The study of robustness problems for computational geometry algorithms is a topic that has been subject to intensive research efforts from both computer science and mathematics communities. Robustness problems are caused by the lack of precision in computations involving floating-point instead of real numbers. This paper reviews methods dealing with robustness and inaccuracy problems. It discusses approaches based on exact arithmetic, interval arithmetic and probabilistic methods. The paper investigates the possibility to use randomness at certain levels of reasoning to make geometric constructions more robust.