2D Arrangement
This package can be used to construct, maintain, alter, and display arrangements in the plane. Once an arrangement is constructed, the package can be used to obtain results of various queries on the arrangement, such as point location. The package also includes generic implementations of two algorithmic frameworks, that are, computing the zone of an arrangement, and line-sweeping the plane, the arrangements is embedded on. These frameworks are used in turn in the implementations of other operations on arrangements. Computing the overlay of two arrangements, for example, is based on the sweep-line framework. Arrangements and arrangement components can also be extended to store additional data. An important extension stores the construction history of the arrangement, such that it is possible to obtain the originating curve of an arrangement subcurve.
Keywords for this software
References in zbMATH (referenced in 29 articles )
Showing results 21 to 29 of 29.
Sorted by year (- Berberich, Eric; Kerber, Michael; Sagraloff, Michael: Exact geometric-topological analysis of algebraic surfaces (2008)
- Eigenwillig, Arno; Kerber, Michael: Exact and efficient 2D-arrangements of arbitrary algebraic curves (2008)
- Emeliyanenko, Pavel; Kerber, Michael: Visualizing and exploring planar algebraic arrangements: a web application (2008)
- Fogel, Efi; Setteer, Ophir; Halperin, Dan: Arrangements of geodesic arcs on the sphere (2008)
- Berberich, Eric; Fogel, Efi; Halperin, Dan; Mehlhorn, Kurt; Wein, Ron: Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)
- Wein, Ron; Fogel, Efi; Zukerman, Baruch; Halperin, Dan: Advanced programming techniques applied to CGALâ€™s arrangement package (2007)
- Wein, Ron; van den Berg, Jur P.; Halperin, Dan: The visibility-Voronoi complex and its applications (2007)
- Meyerovitch, Michal: Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces (2006)
- Wein, Ron: Exact and efficient construction of planar Minkowski sums using the convolution method (2006)