Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
Computing the link center of a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Finding the visibility graph of a simple polygon in time proportional to its size
SCG '87 Proceedings of the third annual symposium on Computational geometry
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
The all-geodesic furthest neighbor problem for simple polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
An optimal O(n log n) algorithm for contour reconstruction from rays
SCG '87 Proceedings of the third annual symposium on Computational geometry
Visibility problems for polyhedral terrains
Journal of Symbolic Computation
Implicitly representing arrangements of lines or segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An efficient output-sensitive hidden surface removal algorithm and its parallelization
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An efficient algorithm for link-distance problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Ray shooting and other applications of spanning trees with low stabbing number
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
On solving geometric optimization problems using shortest paths
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
An Optimal Algorithm for Detecting Weak Visibility of a Polygon
IEEE Transactions on Computers
Dynamic trees and dynamic point location
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Visibility preprocessing for interactive walkthroughs
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Applying parallel processing techniques to classification problems in constructive solid geometry
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
An Improved Output-size Sensitive Parallel Algorithm for Hidden-Surface Removal for Terrains
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
Efficient computation of query point visibility in polygons with holes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Query point visibility computation in polygons with holes
Computational Geometry: Theory and Applications
Finding the minimum-distance schedule for a boundary searcher with a flashlight
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
An efficient output-sensitive hidden-surface removal algorithm for polyhedral terrains
Mathematical and Computer Modelling: An International Journal
Direct multiple shooting method for solving approximate shortest path problems
Journal of Computational and Applied Mathematics
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We develop new data structures for solving various visibility and intersection problems about a simple polygon P on n vertices. Among our results are a simple &Ogr;(n log n) algorithm for computing the illuminated subpolygon of P from a luminous side, and an &Ogr;(log n) algorithm for determining which side of P is first hit by a bullet fired from a point in a certain direction. The latter method requires preprocessing on P which takes time &Ogr;(n log n) and space &Ogr;(n). Our main new tool in attacking these problems is geometric duality on the two-sided plane.