predicates_on_pointsS3.h File Reference

#include <CGAL/predicates/kernel_ftC3.h>

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Functions
template<class FT >
CGAL_BEGIN_NAMESPACE Comparison_result	compare_lexicographically_xyz (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
Comparison_result	compare_lexicographically_xy (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	lexicographically_xyz_smaller_or_equal (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	lexicographically_xyz_smaller (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	lexicographically_xy_smaller (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	x_equal (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	y_equal (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	z_equal (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	equal_xy (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	equal_xyz (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
Comparison_result	compare_x (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
Comparison_result	compare_y (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
Comparison_result	compare_z (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	less_x (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	less_y (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	less_z (const PointS3< FT > &p, const PointS3< FT > &q)
template<class FT >
bool	collinear (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r)
template<class FT >
Orientation	orientation (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s)
template<class FT >
bool	coplanar (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s)
template<class FT >
bool	are_positive_oriented (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s)
template<class FT >
bool	are_negative_oriented (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s)
template<class FT >
bool	are_ordered_along_line (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r)
template<class FT >
bool	collinear_are_ordered_along_line (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r)
template<class FT >
bool	are_strictly_ordered_along_line (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r)
template<class FT >
bool	collinear_are_strictly_ordered_along_line (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r)
template<class FT >
Orientation	coplanar_orientation (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s)
template<class FT >
Oriented_side	side_of_oriented_sphere (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s, const PointS3< FT > &test)
template<class FT >
Bounded_side	side_of_bounded_sphere (const PointS3< FT > &p, const PointS3< FT > &q, const PointS3< FT > &r, const PointS3< FT > &s, const PointS3< FT > &test)

Function Documentation

bool are_negative_oriented ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r, const PointS3< FT > &  s  )

inline

Definition at line 210 of file predicates_on_pointsS3.h.

References NEGATIVE, and orientation().

{
  return orientation(p,q,r,s) == NEGATIVE;
}

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bool are_ordered_along_line ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r  )

inline

Definition at line 221 of file predicates_on_pointsS3.h.

References collinear(), and collinear_are_ordered_along_line().

{
  return (collinear(p, q, r)) ? collinear_are_ordered_along_line(p, q, r)
                              : false;
}

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bool are_positive_oriented ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r, const PointS3< FT > &  s  )

inline

Definition at line 199 of file predicates_on_pointsS3.h.

References orientation(), and POSITIVE.

{
  return orientation(p,q,r,s) == POSITIVE;
}

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bool are_strictly_ordered_along_line ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r  )

inline

Definition at line 246 of file predicates_on_pointsS3.h.

References collinear(), and collinear_are_strictly_ordered_along_line().

{
  return (collinear(p, q, r))
         ? collinear_are_strictly_ordered_along_line(p, q, r)
         : false;
}

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bool collinear	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q,
		const PointS3< FT > &	r
	)

Definition at line 162 of file predicates_on_pointsS3.h.

References collinearC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

{
  return collinearC3(p.x(), p.y(), p.z(),
                     q.x(), q.y(), q.z(),
                     r.x(), r.y(), r.z());
}

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bool collinear_are_ordered_along_line ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r  )

inline

Definition at line 232 of file predicates_on_pointsS3.h.

References CGAL_kernel_exactness_precondition, collinear(), collinear_are_ordered_along_lineC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

{
  CGAL_kernel_exactness_precondition( collinear(p, q, r) );
  return collinear_are_ordered_along_lineC3(p.x(),p.y(),p.z(),
                                            q.x(),q.y(),q.z(),
                                            r.x(),r.y(),r.z());
}

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bool collinear_are_strictly_ordered_along_line ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r  )

inline

Definition at line 259 of file predicates_on_pointsS3.h.

References CGAL_kernel_exactness_precondition, collinear(), collinear_are_strictly_ordered_along_lineC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

{
  CGAL_kernel_exactness_precondition( collinear(p, q, r) );
  return collinear_are_strictly_ordered_along_lineC3(p.x(),p.y(),p.z(),
                                                     q.x(),q.y(),q.z(),
                                                     r.x(),r.y(),r.z());
}

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Comparison_result compare_lexicographically_xy	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q
	)

Definition at line 68 of file predicates_on_pointsS3.h.

References compare_lexicographically_xyC2(), PointS3< FT >::x(), and PointS3< FT >::y().

{
  return compare_lexicographically_xyC2(p.x(),p.y(),
                                        q.x(),q.y());
}

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CGAL_BEGIN_NAMESPACE Comparison_result compare_lexicographically_xyz	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q
	)

Definition at line 60 of file predicates_on_pointsS3.h.

References compare_lexicographically_xyzC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

Referenced by lexicographically_xyz_smaller(), lexicographically_xyz_smaller_or_equal(), and Compare_xyz::operator()().

{
  return compare_lexicographically_xyzC3(p.x(),p.y(),p.z(),
                                         q.x(),q.y(),q.z());
}

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Comparison_result compare_x ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 125 of file predicates_on_pointsS3.h.

References CGAL_NTS, CGAL::compare(), and PointS3< FT >::x().

{ return CGAL_NTS compare(p.x(), q.x()); }

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Comparison_result compare_y ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 132 of file predicates_on_pointsS3.h.

References CGAL_NTS, CGAL::compare(), and PointS3< FT >::y().

{ return CGAL_NTS compare(p.y(), q.y()); }

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Comparison_result compare_z ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 139 of file predicates_on_pointsS3.h.

References CGAL_NTS, CGAL::compare(), and PointS3< FT >::z().

Referenced by RayS3< FT >::collinear_has_on(), and Compare_z::operator()().

{ return CGAL_NTS compare(p.z(), q.z()); }

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bool coplanar ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r, const PointS3< FT > &  s  )

inline

Definition at line 188 of file predicates_on_pointsS3.h.

References COLLINEAR, and orientation().

Referenced by coplanar_orientation(), and Coplanar::operator()().

{
  return orientation(p, q, r, s) == COLLINEAR;
}

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Orientation coplanar_orientation	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q,
		const PointS3< FT > &	r,
		const PointS3< FT > &	s
	)

Definition at line 272 of file predicates_on_pointsS3.h.

References CGAL_kernel_exactness_precondition, collinear(), coplanar(), coplanar_orientationC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

{
  CGAL_kernel_exactness_precondition( ! collinear(p, q, r) );
  CGAL_kernel_exactness_precondition( coplanar(s, p, q, r) );
  return coplanar_orientationC3(p.x(), p.y(), p.z(),
                                q.x(), q.y(), q.z(),
                                r.x(), r.y(), r.z(),
                                s.x(), s.y(), s.z());
}

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bool equal_xy ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 113 of file predicates_on_pointsS3.h.

References PointS3< FT >::x(), and PointS3< FT >::y().

{ return p.x() == q.x() && p.y() == q.y(); }

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bool equal_xyz ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 119 of file predicates_on_pointsS3.h.

References PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

Referenced by Equal_xyz::operator()().

{ return p.x() == q.x() && p.y() == q.y() && p.z() == q.z(); }

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bool less_x ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 145 of file predicates_on_pointsS3.h.

References PointS3< FT >::x().

{ return p.x() < q.x(); }

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bool less_y ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 151 of file predicates_on_pointsS3.h.

References PointS3< FT >::y().

{ return p.y() < q.y(); }

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bool less_z ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 157 of file predicates_on_pointsS3.h.

References PointS3< FT >::z().

{ return p.z() < q.z(); }

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bool lexicographically_xy_smaller ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 88 of file predicates_on_pointsS3.h.

References compare_lexicographically_xy(), and SMALLER.

{ return compare_lexicographically_xy(p,q) == SMALLER; }

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bool lexicographically_xyz_smaller	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q
	)

Definition at line 82 of file predicates_on_pointsS3.h.

References compare_lexicographically_xyz(), and SMALLER.

Referenced by SegmentS3< FT >::max(), SegmentS3< FT >::min(), Less_xyz::operator()(), and PointS3< FT >::operator<().

{ return compare_lexicographically_xyz(p,q) == SMALLER; }

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bool lexicographically_xyz_smaller_or_equal	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q
	)

Definition at line 76 of file predicates_on_pointsS3.h.

References compare_lexicographically_xyz(), and LARGER.

{ return compare_lexicographically_xyz(p,q) != LARGER; }

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Orientation orientation ( const PointS3< FT > &  p, const PointS3< FT > &  q, const PointS3< FT > &  r, const PointS3< FT > &  s  )

inline

Definition at line 174 of file predicates_on_pointsS3.h.

References orientationC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

{
  return orientationC3(p.x(), p.y(), p.z(),
                       q.x(), q.y(), q.z(),
                       r.x(), r.y(), r.z(),
                       s.x(), s.y(), s.z());
}

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Bounded_side side_of_bounded_sphere	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q,
		const PointS3< FT > &	r,
		const PointS3< FT > &	s,
		const PointS3< FT > &	test
	)

Definition at line 304 of file predicates_on_pointsS3.h.

References side_of_bounded_sphereC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

Referenced by Side_of_bounded_sphere::operator()().

{
  return side_of_bounded_sphereC3(p.x(),p.y(),p.z(),
                                  q.x(),q.y(),q.z(),
                                  r.x(),r.y(),r.z(),
                                  s.x(),s.y(),s.z(),
                                  test.x(),test.y(),test.z());
}

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Oriented_side side_of_oriented_sphere	(	const PointS3< FT > &	p,
		const PointS3< FT > &	q,
		const PointS3< FT > &	r,
		const PointS3< FT > &	s,
		const PointS3< FT > &	test
	)

Definition at line 288 of file predicates_on_pointsS3.h.

References side_of_oriented_sphereC3(), PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

Referenced by Side_of_oriented_sphere::operator()().

{
  return side_of_oriented_sphereC3(p.x(),p.y(),p.z(),
                                   q.x(),q.y(),q.z(),
                                   r.x(),r.y(),r.z(),
                                   s.x(),s.y(),s.z(),
                                   test.x(),test.y(),test.z());
}

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bool x_equal ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 94 of file predicates_on_pointsS3.h.

References PointS3< FT >::x().

{ return p.x() == q.x(); }

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bool y_equal ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 101 of file predicates_on_pointsS3.h.

References PointS3< FT >::y().

{ return p.y() == q.y(); }

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bool z_equal ( const PointS3< FT > &  p, const PointS3< FT > &  q  )

inline

Definition at line 107 of file predicates_on_pointsS3.h.

References PointS3< FT >::z().

Referenced by Equal_z::operator()().

{ return p.z() == q.z(); }

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