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Arak::Geometry Namespace Reference


Classes

class  VisitingFace

Typedefs

typedef CGAL::Cartesian< CGAL::Gmpq > ExactCxnKernel
typedef CGAL::Simple_cartesian<
double > 		InexactKernel
typedef CGAL::Filtered_kernel<
InexactKernel > 		ExactPredKernel
typedef InexactKernel Kernel
typedef Kernel::Point_2 Point
typedef Kernel::Line_2 Line
typedef Kernel::Segment_2 Segment
typedef Kernel::Direction_2 Direction
typedef Kernel::Vector_2 Vector
typedef Kernel::Ray_2 Ray
typedef Kernel::Iso_rectangle_2 Rectangle
typedef Kernel::Triangle_2 Triangle
typedef CGAL::Polygon_2< Kernel > Polygon
typedef CGAL::Pm_segment_traits_2<
ExactPredKernel > 		Traits
typedef CGAL::Pm_dcel< CGAL::Pm_vertex_base<
Traits::Point >, CGAL::Pm_halfedge_base<
Traits::X_curve >, Arak::Geometry::VisitingFace > 		Dcel
typedef Traits::X_monotone_curve_2 Curve
typedef CGAL::Planar_map_2<
Dcel, Traits > 		PlanarMap
typedef PlanarMap::Locate_type LocateType
typedef PlanarMap::Vertex_handle VertexHandle
typedef PlanarMap::Halfedge_handle HalfedgeHandle
typedef PlanarMap::Face_handle FaceHandle
typedef PlanarMap::Halfedge_iterator HalfedgeIterator
typedef PlanarMap::Holes_iterator HolesIterator
typedef PlanarMap::Ccb_halfedge_circulator CCBHalfedgeCirculator
typedef ExactPredKernel::Point_2 ExactPredPoint
typedef ExactPredKernel::Segment_2 ExactPredSegment

Functions

bool crosses (const Segment &s, const Point &a, const Point &b)
 Determines if two line segments cross, i.e., if they intersect at a point that is not a shared vertex.

Rectangle boundingRectangle (const Point &u, const Point &v, const Point &w)
 This is a helper function that computes the smallest rectangle that encloses the supplied points.

Rectangle boundingRectangle (const Point &t, const Point &u, const Point &v, const Point &w)
 This is a helper function that computes the smallest rectangle that encloses the supplied points.

double logSineB (const Point &a, const Point &b, const Point &c)
 Computes the logarithm of the sine of an angle specified by three points.

Geometry::Point project (const Geometry::Point &p, const Geometry::Rectangle &r)
 Projects a point orthogonally onto the closure of a rectangle.

void n_gon (int n, double radius, Polygon &poly)
 Creates a regular $n$-gon with the supplied number of vertices and radius.

ExactPredPoint toExactPredPoint (const Point &p)
ExactPredSegment toExactPredSegment (const Segment &s)

Typedef Documentation

typedef PlanarMap::Ccb_halfedge_circulator Arak::Geometry::CCBHalfedgeCirculator
 

Definition at line 34 of file planar_map.hpp.

typedef Traits::X_monotone_curve_2 Arak::Geometry::Curve
 

Definition at line 26 of file planar_map.hpp.

typedef CGAL::Pm_dcel<CGAL::Pm_vertex_base<Traits::Point>, CGAL::Pm_halfedge_base<Traits::X_curve>, Arak::Geometry::VisitingFace > Arak::Geometry::Dcel
 

Definition at line 25 of file planar_map.hpp.

typedef Kernel::Direction_2 Arak::Geometry::Direction
 

Definition at line 80 of file geometry.hpp.

Referenced by Arak::closer(), Arak::compare(), Arak::computeFirstSonarImpact(), Arak::computeSonarImpacts(), Arak::cone_subset(), Arak::cones_intersect(), Arak::coneTrace(), Arak::ScanEdge::init(), Arak::intersection(), Arak::ScanVertexComparator::operator()(), Arak::outerApprox(), Arak::ScanVertexComparator::ScanVertexComparator(), Arak::OccupancyGrid::sonar(), Arak::SonarImpact::SonarImpact(), and Arak::ArakPosteriorSonarObs::SonarObs::SonarObs().

typedef CGAL::Cartesian<CGAL::Gmpq> Arak::Geometry::ExactCxnKernel
 

Definition at line 58 of file geometry.hpp.

typedef CGAL::Filtered_kernel<InexactKernel> Arak::Geometry::ExactPredKernel
 

Definition at line 67 of file geometry.hpp.

typedef ExactPredKernel::Point_2 Arak::Geometry::ExactPredPoint
 

Definition at line 36 of file planar_map.hpp.

Referenced by toExactPredPoint().

typedef ExactPredKernel::Segment_2 Arak::Geometry::ExactPredSegment
 

Definition at line 37 of file planar_map.hpp.

Referenced by toExactPredSegment().

typedef PlanarMap::Face_handle Arak::Geometry::FaceHandle
 

Definition at line 31 of file planar_map.hpp.

typedef PlanarMap::Halfedge_handle Arak::Geometry::HalfedgeHandle
 

Definition at line 30 of file planar_map.hpp.

typedef PlanarMap::Halfedge_iterator Arak::Geometry::HalfedgeIterator
 

Definition at line 32 of file planar_map.hpp.

typedef PlanarMap::Holes_iterator Arak::Geometry::HolesIterator
 

Definition at line 33 of file planar_map.hpp.

typedef CGAL::Simple_cartesian<double> Arak::Geometry::InexactKernel
 

Definition at line 62 of file geometry.hpp.

typedef InexactKernel Arak::Geometry::Kernel
 

Definition at line 75 of file geometry.hpp.

Referenced by Arak::Coloring::toTriangulation().

typedef Kernel::Line_2 Arak::Geometry::Line
 

Definition at line 78 of file geometry.hpp.

Referenced by Arak::intersection(), Arak::OccupancyGrid::laser_scan(), and Arak::SonarImpact::SonarImpact().

typedef PlanarMap::Locate_type Arak::Geometry::LocateType
 

Definition at line 28 of file planar_map.hpp.

typedef CGAL::Planar_map_2<Dcel,Traits> Arak::Geometry::PlanarMap
 

Definition at line 27 of file planar_map.hpp.

typedef Kernel::Point_2 Arak::Geometry::Point
 

Definition at line 77 of file geometry.hpp.

Referenced by Arak::ArakPosteriorBernoulliObs::ArakPosteriorBernoulliObs(), Arak::ArakPosteriorGaussianObs::ArakPosteriorGaussianObs(), Arak::ArakPosteriorRangeObs::ArakPosteriorRangeObs(), Arak::ArakPosteriorSonarObs::ArakPosteriorSonarObs(), Arak::Coloring::boundary(), boundingRectangle(), Arak::Grid< ItemType >::Cell::center(), Arak::closer(), Arak::QueryPointIndex::closest(), Arak::Coloring::color(), Arak::Coloring::compatible(), Arak::computeFirstSonarImpact(), Arak::computeSonarImpacts(), Arak::coneTrace(), Arak::CriticalStatsEstimator::CriticalStatsEstimator(), crosses(), Arak::Coloring::InteriorEdge::crosses(), Arak::Coloring::deleteBdTriangle(), Arak::Coloring::deleteCornerTriangle(), Arak::Coloring::deleteIntTriangle(), Arak::Coloring::deleteVertex(), Arak::Grid< ItemType >::LineCellIteratorBase< GridType, CellType >::direction(), Arak::Grid< PointColorEstimator * >::getCell(), Arak::Grid< PointColorEstimator * >::getCellCoords(), Arak::Coloring::getPointWithColor(), Arak::GridColorEstimator::GridColorEstimator(), Arak::CN94Proposal::inCastingBox(), Arak::ScanEdge::init(), Arak::Coloring::interior(), Arak::intersection(), Arak::OccupancyGrid::laser(), Arak::OccupancyGrid::laser_scan(), Arak::Grid< ItemType >::LineCellIteratorBase< GridType, CellType >::LineCellIteratorBase(), Arak::Coloring::Vertex::logSine(), logSineB(), Arak::Coloring::moveBdVertexPastCorner(), Arak::Coloring::moveIntVertex(), Arak::Coloring::moveVertexAlongBd(), n_gon(), Arak::Coloring::newBoundaryTriangle(), Arak::Coloring::newCornerTriangle(), Arak::Coloring::newInteriorTriangle(), Arak::Coloring::newVertex(), Arak::OccupancyGrid::OccupancyGrid(), operator<<(), Arak::outerApprox(), Arak::Coloring::outside(), Arak::Coloring::Vertex::point(), Arak::PointColorEstimator::PointColorEstimator(), project(), Arak::CN94Proposal::proposeBdTriangleDeath(), Arak::CN94Proposal::proposeIntTriangleDeath(), Arak::CN94Proposal::proposeIntVertexDeath(), Arak::QueryPoint::QueryPoint(), Arak::QueryPointIndex::QueryPointIndex(), Arak::Coloring::randomPoint(), Arak::Coloring::BoundaryEdge::randomPoint(), Arak::Coloring::Edge::randomPoint(), Arak::ArakPosteriorRangeObs::RangeObs::RangeObs(), Arak::Coloring::read(), Arak::Coloring::readBinary(), Arak::QueryPointIndex::recolor(), Arak::ArakPosteriorSonarObs::recolored(), Arak::ArakPosteriorRangeObs::recolored(), Arak::GridColorEstimator::recolored(), Arak::Coloring::Listener::recolored(), Arak::Coloring::recolored(), Arak::ArakPrior::recolored(), Arak::ModifiedCN94Proposal::SlideInteriorVertex::reset(), Arak::CN94Proposal::CornerCutBirth::reset(), Arak::CN94Proposal::BoundaryTriangleBirth::reset(), Arak::CN94Proposal::MoveVertexAlongBdEdge::reset(), Arak::CN94Proposal::MoveInteriorVertex::reset(), Arak::CN94Proposal::InteriorVertexBirth::reset(), Arak::CN94Proposal::MoveBdVertexPastCorner::reset(), Arak::CN94Proposal::InteriorTriangleBirth::reset(), Arak::ArakPosteriorRangeObs::retraceObs(), Arak::ModifiedCN94Proposal::sampleBoundaryTriangleBirth(), Arak::CN94Proposal::sampleBoundaryTriangleBirth(), Arak::CN94Proposal::sampleCornerCutBirth(), Arak::CN94Proposal::sampleInCastingBox(), Arak::CN94Proposal::sampleInteriorTriangleBirth(), Arak::CN94Proposal::sampleInteriorVertexBirth(), Arak::CN94Proposal::sampleMoveBdVertexPastCorner(), Arak::CN94Proposal::sampleMoveInteriorVertex(), Arak::CN94Proposal::sampleMoveVertexAlongBd(), Arak::ModifiedCN94Proposal::sampleSlideInteriorVertex(), Arak::OccupancyGrid::sonar(), Arak::SonarImpact::SonarImpact(), Arak::ArakPosteriorSonarObs::SonarObs::SonarObs(), Arak::Coloring::splitEdge(), toExactPredPoint(), Arak::Coloring::toTriangulation(), Arak::Coloring::trace(), Arak::Util::Random::uniform(), Arak::ArakPosteriorSonarObs::update(), Arak::ArakPosteriorRangeObs::update(), Arak::ArakPosteriorSonarObs::visualize(), Arak::Coloring::write(), and Arak::Coloring::writeBinary().

typedef CGAL::Polygon_2<Kernel> Arak::Geometry::Polygon
 

Definition at line 85 of file geometry.hpp.

Referenced by Arak::Grid< ItemType >::ConvexPolygonCellIteratorBase< GridType, CellType >::ConvexPolygonCellIteratorBase(), n_gon(), operator<<(), and Arak::Coloring::solid().

typedef Kernel::Ray_2 Arak::Geometry::Ray
 

Definition at line 82 of file geometry.hpp.

typedef Kernel::Iso_rectangle_2 Arak::Geometry::Rectangle
 

Definition at line 83 of file geometry.hpp.

Referenced by Arak::QueryPointIndex::apply(), Arak::ArakPosteriorRangeObs::ArakPosteriorRangeObs(), Arak::ArakPosteriorSonarObs::ArakPosteriorSonarObs(), Arak::ArakPosteriorSonarObs::boundary(), Arak::ArakPosteriorRangeObs::boundary(), Arak::Grid< PointColorEstimator * >::boundary(), Arak::Coloring::boundary(), boundingRectangle(), Arak::Grid< ItemType >::Cell::Cell(), Arak::Coloring::Coloring(), Arak::coneTrace(), Arak::Grid< ItemType >::ConvexPolygonCellIteratorBase< GridType, CellType >::ConvexPolygonCellIteratorBase(), Arak::Grid< PointColorEstimator * >::Grid(), Arak::GridColorEstimator::GridColorEstimator(), Arak::Coloring::initialize(), Arak::OccupancyGrid::laser_scan(), Arak::OccupancyGrid::OccupancyGrid(), Arak::QueryPointIndex::output(), Arak::PointSetColorEstimator::PointSetColorEstimator(), project(), Arak::QueryPointIndex::QueryPointIndex(), Arak::Coloring::read(), Arak::Coloring::readBinary(), Arak::QueryPointIndex::recolor(), Arak::Grid< ItemType >::RectangleCellIteratorBase< GridType, CellType >::RectangleCellIteratorBase(), Arak::CriticalStatsEstimator::report(), and Arak::Grid< ItemType >::TriangleCellIteratorBase< GridType, CellType >::TriangleCellIteratorBase().

typedef Kernel::Segment_2 Arak::Geometry::Segment
 

Definition at line 79 of file geometry.hpp.

Referenced by Arak::CriticalStatsEstimator::CriticalStatsEstimator(), crosses(), Arak::ScanEdge::init(), Arak::intersection(), Arak::OccupancyGrid::laser(), Arak::Grid< ItemType >::LineCellIteratorBase< GridType, CellType >::LineCellIteratorBase(), Arak::Coloring::newBoundaryEdge(), Arak::Coloring::newInteriorEdge(), Arak::CN94Proposal::proposeBdTriangleDeath(), Arak::CN94Proposal::proposeIntVertexDeath(), Arak::QueryPointIndex::recolor(), Arak::Coloring::recolorQuadrilateral(), Arak::CriticalStatsEstimator::report(), Arak::ModifiedCN94Proposal::sampleRecolor(), Arak::CN94Proposal::sampleRecolor(), Arak::Coloring::Edge::segment(), Arak::Coloring::test(), toExactPredSegment(), Arak::Coloring::trace(), Arak::Util::Random::uniform(), Arak::CriticalStatsEstimator::update(), Arak::ArakPosteriorSonarObs::visualize(), and Arak::ArakPosteriorRangeObs::visualize().

typedef CGAL::Pm_segment_traits_2<ExactPredKernel> Arak::Geometry::Traits
 

Definition at line 22 of file planar_map.hpp.

typedef Kernel::Triangle_2 Arak::Geometry::Triangle
 

Definition at line 84 of file geometry.hpp.

Referenced by Arak::computeFirstSonarImpact(), Arak::coneTrace(), operator<<(), Arak::outerApprox(), Arak::QueryPointIndex::recolor(), Arak::GridColorEstimator::recolored(), Arak::QueryPointIndex::RecolorQuadrilateralFunction::RecolorQuadrilateralFunction(), Arak::QueryPointIndex::RecolorTriangleFunction::RecolorTriangleFunction(), Arak::OccupancyGrid::sonar(), Arak::Grid< ItemType >::TriangleCellIteratorBase< GridType, CellType >::TriangleCellIteratorBase(), Arak::Util::Random::uniform(), Arak::ArakPosteriorSonarObs::update(), Arak::ArakPosteriorRangeObs::update(), Arak::Coloring::visualize(), and Arak::Coloring::writeXfig().

typedef Kernel::Vector_2 Arak::Geometry::Vector
 

Definition at line 81 of file geometry.hpp.

Referenced by Arak::OccupancyGrid::laser(), Arak::ArakPosteriorRangeObs::RangeObs::RangeObs(), Arak::ModifiedCN94Proposal::sampleBoundaryTriangleBirth(), Arak::CN94Proposal::sampleBoundaryTriangleBirth(), Arak::CN94Proposal::sampleInteriorVertexBirth(), Arak::CN94Proposal::sampleMoveVertexAlongBd(), Arak::ModifiedCN94Proposal::sampleSlideInteriorVertex(), Arak::Util::Random::uniform(), and Arak::ArakPosteriorSonarObs::visualize().

typedef PlanarMap::Vertex_handle Arak::Geometry::VertexHandle
 

Definition at line 29 of file planar_map.hpp.

Function Documentation

Rectangle boundingRectangle (  const Point &  t,
const Point &  u,
const Point &  v,
const Point &  w
)  [inline]
 

This is a helper function that computes the smallest rectangle that encloses the supplied points.

Definition at line 125 of file geometry.hpp.

References Point, and Rectangle.

Rectangle boundingRectangle (  const Point &  u,
const Point &  v,
const Point &  w
)  [inline]
 

This is a helper function that computes the smallest rectangle that encloses the supplied points.

Definition at line 107 of file geometry.hpp.

References Point, and Rectangle.

Referenced by Arak::coneTrace().

bool crosses (  const Segment &  s,
const Point &  a,
const Point &  b
)  [inline]
 

Determines if two line segments cross, i.e., if they intersect at a point that is not a shared vertex.

Definition at line 91 of file geometry.hpp.

References Point, and Segment.

Referenced by Arak::Coloring::InteriorEdge::crosses().

double logSineB (  const Point &  a,
const Point &  b,
const Point &  c
)  [inline]
 

Computes the logarithm of the sine of an angle specified by three points.

The Side-Angle-Side (SAS) formula for a triangle's area gives

\[ A = \frac{1}{2} x y \sin Z \]

where $A$ is the area of the triangle, $x$ and $y$ are the lengths of two sides, and $Z$ is the angle between these two sides. From this we get

\[ \log \sin Z = \log (2A) - \log (xy) \]

Parameters:
a the first point
b the second point (distinct from a)
c the third point (distinct from a and b)
Returns:
the logarithm of the sine of the angle at vertex b of the triangle abc

Definition at line 161 of file geometry.hpp.

References Arak::ln(), and Point.

Referenced by Arak::Coloring::Vertex::logSine().

void Arak::Geometry::n_gon (  int  n,
double  radius,
Polygon &  poly
) 
 

Creates a regular $n$-gon with the supplied number of vertices and radius.

Definition at line 6 of file geometry.cpp.

References Point, and Polygon.

Geometry::Point project (  const Geometry::Point &  p,
const Geometry::Rectangle &  r
)  [inline]
 

Projects a point orthogonally onto the closure of a rectangle.

This is useful to postprocess inexact constructions so that the resulting point is in the closure of the rectangle.

Parameters:
p a point
r a rectangle
Returns:
the point closest to p in the closure of r

Definition at line 180 of file geometry.hpp.

References Point, Point, and Rectangle.

ExactPredPoint toExactPredPoint (  const Point &  p  )  [inline]
 

Definition at line 39 of file planar_map.hpp.

References ExactPredPoint, and Point.

Referenced by toExactPredSegment().

ExactPredSegment toExactPredSegment (  const Segment &  s  )  [inline]
 

Definition at line 43 of file planar_map.hpp.

References ExactPredSegment, Segment, and toExactPredPoint().

Generated on Wed May 25 14:41:37 2005 for Arak by doxygen 1.3.6