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
Verifiable implementations of geometric algorithms using finite precision arithmetic
Verifiable implementations of geometric algorithms using finite precision arithmetic
Numerical stability of algorithms for line arrangements
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A rational rotation method for robust geometric algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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)
Splitting a complex of convex polytopes in any dimension
Proceedings of the twelfth annual symposium on Computational geometry
Efficient exact evaluation of signs of determinants
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
IEEE Transactions on Computers
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
One useful generalization of the convex hull of a set S of points is the &egr;-strongly convex &dgr;-hull. It is defined to be a convex polygon Rgr; with vertices taken from S such that no point in S lies farther than &dgr; outside Rgr; and such that even if the vertices of Rgr; are perturbed by as much as &egr;, Rgr; remains convex. It was an open question as to whether an &egr;-strongly convex &Ogr;(&egr;)-hull existed for all positive &egr;. We give here an &Ogr;(n log n) algorithm for constructing it (which thus proves its existence). This algorithm uses exact rational arithmetic. We also show how to construct an &egr;-strongly convex &Ogr;(&egr; + &mgr;)-hull in &Ogr;(n log n) time using rounded arithmetic with rounding unit &mgr;. This is the first rounded arithmetic convex hull algorithm which guarantees a convex output and which has error independent of n.