SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Arr_geometry_traits/Arr_plane_3.h File Reference

#include <CGAL/basic.h>
#include <iostream>
#include <CGAL/Kernel/solve.h>

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Classes
class	Arr_plane_3< Kernel_ >
Functions
template<class Kernel >
CGAL::Object	intersect (const Arr_plane_3< Kernel > &plane1, const Arr_plane_3< Kernel > &plane2)
template<class Kernel >
Kernel::Point_2	construct_projected_xy_point (const Arr_plane_3< Kernel > &plane, const typename Kernel::Point_3 &p)
template<class Kernel >
std::ostream &	operator<< (std::ostream &os, const Arr_plane_3< Kernel > &plane)

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Detailed Description

Construct and maintain a plane in 3D that contains the origin. A plane is defined by 4 coordinates, namely a, b, c, and d. When the plane contains the origin, the last coordinate d vanishes. This simplifies arithmetic expressions involved with the construction of the plane and other operations applied to planes.

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Function Documentation

template<class Kernel >

Kernel::Point_2 construct_projected_xy_point	(	const Arr_plane_3< Kernel > &	plane,
		const typename Kernel::Point_3 &	p
	)

Compute the image point of the projection of p under an affine transformation, which maps the plane onto the xy-plane, with the z-coordinate removed.

Parameters:

plane	the plane
p	the point

Returns:

the image point

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template<class Kernel >

CGAL::Object intersect	(	const Arr_plane_3< Kernel > &	plane1,
		const Arr_plane_3< Kernel > &	plane2
	)

Intersect 2 planes

Parameters:

plane1	the first plane
plane2	the second plane

Returns:

a geometric object that represents the intersection. Could be the line of intersection, or a plane in case plane1 and plane2 coincide.

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template<class Kernel >

std::ostream& operator<<	(	std::ostream &	os,
		const Arr_plane_3< Kernel > &	plane
	)		[inline]

Export a plane to an output stream

Parameters:

os	the output stream
plane	the plane

Returns:

the output stream