LOOK: A lazy object-oriented kernel design for geometric computation. We describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA allowing for efficient and exact computation with rational and algebraic geometric objects. It is the first kernel design which uses floating-point filter techniques on the level of geometric constructions. The experiments we present – partly using the CGAL framework – show a great improvement in speed and – maybe even more important for practical applications – memory consumption when dealing with more complex geometric computations.

References in zbMATH (referenced in 12 articles , 2 standard articles )

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  1. Pion, Sylvain; Fabri, Andreas: A generic lazy evaluation scheme for exact geometric computations (2011) ioport
  2. de Castro, Pedro M.M.; Cazals, Frédéric; Loriot, Sébastien; Teillaud, Monique: Design of the CGAL 3D spherical kernel and application to arrangements of circles on a sphere (2009)
  3. Schirra, Stefan: Much ado about zero (2009)
  4. Hert, Susan; Hoffmann, Michael; Kettner, Lutz; Pion, Sylvain; Seel, Michael: An adaptable and extensible geometry kernel (2007)
  5. Devillers, Olivier; Guigue, Philippe: Inner and outer rounding of Boolean operations on lattice polygonal regions (2006)
  6. Devillers, Olivier; Teillaud, Monique: Perturbations and vertex removal in a 3D Delaunay triangulation (2003)
  7. Nanevski, Aleksandar; Blelloch, Guy; Harper, Robert: Automatic generation of staged geometric predicates (2003)
  8. Berberich, Eric; Eigenwillig, Arno; Hemmer, Michael; Hert, Susan; Mehlhorn, Kurt; Schömer, Elmar: A computational basis for conic arcs and boolean operations on conic polygons (2002)
  9. Devillers, Olivier; Fronville, Alexandra; Mourrain, Bernard; Teillaud, Monique: Algebraic methods and arithmetic filtering for exact predicates on circle arcs (2002)
  10. Funke, Stefan; Mehlhorn, Kurt: LOOK: A lazy object-oriented kernel design for geometric computation (2002)
  11. Wein, Ron: High-level filtering for arrangements of conic arcs (Extended abstract) (2002)
  12. Funke, Stefan; Mehlhorn, Kurt: LOOK -- a lazy object-oriented kernel for geometric computation (2000)