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
Constructing strongly convex hulls using exact or rounded arithmetic
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Delaunay triangulations in three dimensions with finite precision arithmetic
Computer Aided Geometric Design
Computing convex hull in a floating point arithmetic
Computational Geometry: Theory and Applications
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Handbook of discrete and computational geometry
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
One Sided Error Predicates in Geometric Computing
IFIP World Computer Congress on Fundamentals - Foundations of Computer Science
Constructing Strongly Convex Approximate Hulls with Inaccurate Primitives
SIGAL '90 Proceedings of the International Symposium on Algorithms
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Stable maintenance of point set triangulations in two dimensions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Backward error analysis in computational geometry
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
How Reliable Are Practical Point-in-Polygon Strategies?
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
Reliable and efficient geometric computing
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Exact geometric and algebraic computations in CGAL
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
A generic lazy evaluation scheme for exact geometric computations
Science of Computer Programming
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
Controlled Perturbation of sets of line segments in R2 with smart processing order
Computational Geometry: Theory and Applications
A generic algebraic kernel for non-linear geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
A general approach to the analysis of controlled perturbation algorithms
Computational Geometry: Theory and Applications
Robust and efficient delaunay triangulations of points on or close to a sphere
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Formal study of plane delaunay triangulation
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Designing and proving correct a convex hull algorithm with hypermaps in Coq
Computational Geometry: Theory and Applications
A robust algorithm for geometric predicate by error-free determinant transformation
Information and Computation
Computer Science Review
SMI 2013: Shape grammars on convex polyhedra
Computers and Graphics
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The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations to fail. Although this is well known, there are no concrete examples with a comprehensive documentation of what can go wrong and why. In this paper, we provide a case study of what can go wrong and why. For our study, we have chosen two simple algorithms which are often taught, an algorithm for computing convex hulls in the plane and an algorithm for computing Delaunay triangulations in space. We give examples that make the algorithms fail in many different ways. We also show how to construct such examples systematically and discuss the geometry of the floating-point implementation of the orientation predicate. We hope that our work will be useful for teaching computational geometry.