Efficient algorithms for common transversals
Information Processing Letters
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
A convex hull algorithm for discs, and applications
Computational Geometry: Theory and Applications
Constructing levels in arrangements and higher order Voronoi diagrams
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Convex Hull Problem with Imprecise Input
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Largest bounding box, smallest diameter, and related problems on imprecise points
Computational Geometry: Theory and Applications
The Directed Hausdorff Distance between Imprecise Point Sets
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The directed Hausdorff distance between imprecise point sets
Theoretical Computer Science
Largest and smallest tours and convex hulls for imprecise points
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Largest bounding box, smallest diameter, and related problems on imprecise points
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Range counting coresets for uncertain data
Proceedings of the twenty-ninth annual symposium on Computational geometry
On some geometric problems of color-spanning sets
Journal of Combinatorial Optimization
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We study accuracy guaranteed solutions of geometric problems denned on convex region under an assumption that input points are known only up to a limited accuracy, that is, each input point is given by a convex region that represents the possible locations of the point. We show how to compute tight error bounds for basic problems such as convex hull, Minkowski sum of convex polygons, diameter of points, and so on. To compute tight error bound from imprecise coordinates, we represent a convex region by a set of half-planes whose intersection gives the region. Error bounds are computed by applying rotating caliper paradigm to this representation.