A survey of ray tracing acceleration techniques
An introduction to ray tracing
Linear programming and convex hulls made easy
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The upper envelope of Voronoi surfaces and its applications
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Helly theorems and generalized linear programming
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On geometric optimization with few violated constraints
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Helly theorems and generalized linear programming
Helly theorems and generalized linear programming
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Rectilinear and polygonal p-piercing and p-center problems
Proceedings of the twelfth annual symposium on Computational geometry
Recognition Using Region Correspondences
International Journal of Computer Vision
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
3-D to 2-D Pose Determination with Regions
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Conservative visibility preprocessing for walkthroughs of complex urban scenes
VRST '00 Proceedings of the ACM symposium on Virtual reality software and technology
IEEE Transactions on Computers
Violator spaces: structure and algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Violator spaces: Structure and algorithms
Discrete Applied Mathematics
Efficient selectivity estimation by histogram construction based on subspace clustering
SSDBM'11 Proceedings of the 23rd international conference on Scientific and statistical database management
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In the first part of this paper, we reduce two geometric optimization problems to convex programming: finding the largest axis-aligned box in the intersection of a family of convex sets, and finding the translation and scaling that minimizes the Hausdorff distance between two polytopes. These reductions imply that important cases of these problems can be solved in expected linear time. In the second part of the paper, we use convex programming to give a new, short proof of an interesting Helly-type theorem, first conjectured by Gru¨nbaum and Motzkin.