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Implicit Convex Polygons
 Proc. 14th European Workshop on Computational Geometry
, 2000
"... Convex polygons in the plane can be de ned explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as GIS, robotics and computer graphics. In this paper, we investigate many fund ..."
Abstract

Cited by 4 (4 self)
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Convex polygons in the plane can be de ned explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as GIS, robotics and computer graphics. In this paper, we investigate many fundamental problems for implicitly represented polygons and give simple and fast algorithms that are easy to implement. We uncover an interesting partition of the problems into two classes: those that exhibit an Omega(n log n) lower bound on their complexity, and those that yield O(n) time algorithms via pruneandsearch methods.
Bridging Vector and Raster Representation in GIS
, 1998
"... Representations in Geoinformation Systems (GIS) are classified into vector and raster representation. They are dual with regard to space bounding and space filling. Spatial concepts are also dual with entitybased and fieldbased concepts. In this situation a hybrid representation is investigated. I ..."
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Cited by 4 (1 self)
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Representations in Geoinformation Systems (GIS) are classified into vector and raster representation. They are dual with regard to space bounding and space filling. Spatial concepts are also dual with entitybased and fieldbased concepts. In this situation a hybrid representation is investigated. It will show that the hybrid representation is a promising approach of integration, useful for data fusion and interoperability.
unknown title
, 2000
"... Abstract Convex polygons in the plane can be defined explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as GIS, robotics and computer graphics. In this paper, we investigate ..."
Abstract
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Abstract Convex polygons in the plane can be defined explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as GIS, robotics and computer graphics. In this paper, we investigate many fundamental problems for implicitly represented polygons and give simple and fast algorithms that are easy to implement. We uncover an interesting partition of the problems into two classes: those that exhibit an \Omega (n log n) lower bound on their complexity, and those that yield O(n) time algorithms via pruneandsearch methods.