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predicates_on_points_2.h File Reference
#include <CGAL/Point_2.h>
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Functions

template<class R >
CGAL_BEGIN_NAMESPACE bool x_equal (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool y_equal (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
Comparison_result compare_x (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
Comparison_result compare_y (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
Comparison_result compare_deltax_deltay (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r, const Point_2< R > &s)
 
template<class R >
Comparison_result compare_lexicographically_xy (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_xy_smaller_or_equal (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_xy_smaller (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_xy_larger_or_equal (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_xy_larger (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
Comparison_result compare_lexicographically_yx (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_yx_smaller_or_equal (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_yx_smaller (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_yx_larger_or_equal (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool lexicographically_yx_larger (const Point_2< R > &p, const Point_2< R > &q)
 
template<class R >
bool are_ordered_along_line (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool collinear_are_ordered_along_line (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool are_strictly_ordered_along_line (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool collinear_are_strictly_ordered_along_line (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool collinear (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool leftturn (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool rightturn (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
bool rightturn (const Origin &o, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
Orientation orientation (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
 
template<class R >
Oriented_side side_of_oriented_circle (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r, const Point_2< R > &test)
 
template<class R >
Bounded_side side_of_bounded_circle (const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r, const Point_2< R > &test)
 

Function Documentation

bool are_ordered_along_line ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 247 of file predicates_on_points_2.h.

Referenced by SegmentS3< FT >::has_on(), and Are_ordered_along_line::operator()().

250 {
251  typedef typename R::Point_2_base RPoint_2;
252  return are_ordered_along_line((const RPoint_2&)p,
253  (const RPoint_2&)q,
254  (const RPoint_2&)r);
255 }
are_ordered_along_line
bool are_ordered_along_line(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:247

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bool are_strictly_ordered_along_line ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 273 of file predicates_on_points_2.h.

Referenced by Are_strictly_ordered_along_line::operator()().

276 {
277  typedef typename R::Point_2_base RPoint_2;
278  return are_strictly_ordered_along_line((const RPoint_2&)p,
279  (const RPoint_2&)q,
280  (const RPoint_2&)r);
281 }
are_strictly_ordered_along_line
bool are_strictly_ordered_along_line(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:273

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bool collinear ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 298 of file predicates_on_points_2.h.

Referenced by are_ordered_along_line(), are_strictly_ordered_along_line(), collinear_are_ordered_along_line(), collinear_are_strictly_ordered_along_line(), SegmentS2< FT >::collinear_has_on(), RayS3< FT >::collinear_has_on(), coplanar_orientation(), SegmentS2< FT >::has_on(), RayS3< FT >::has_on(), LineS3< FT >::has_on(), RayS2< FT >::has_on(), and Collinear::operator()().

301 {
302  typedef typename R::Point_2_base RPoint_2;
303  return (collinear((const RPoint_2&)p,
304  (const RPoint_2&)q,
305  (const RPoint_2&)r));
306 }
collinear
bool collinear(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:298

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bool collinear_are_ordered_along_line ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 260 of file predicates_on_points_2.h.

Referenced by are_ordered_along_line(), SegmentS3< FT >::collinear_has_on(), p_Less_rotate_ccw< Point >::operator()(), p_Less_rotate_ccw_safer< Point >::operator()(), and Collinear_are_ordered_along_line::operator()().

263 {
264  typedef typename R::Point_2_base RPoint_2;
265  return collinear_are_ordered_along_line((const RPoint_2&)p,
266  (const RPoint_2&)q,
267  (const RPoint_2&)r);
268 }
collinear_are_ordered_along_line
bool collinear_are_ordered_along_line(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:260

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bool collinear_are_strictly_ordered_along_line ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 285 of file predicates_on_points_2.h.

Referenced by are_strictly_ordered_along_line(), and Collinear_are_strictly_ordered_along_line::operator()().

288 {
289  typedef typename R::Point_2_base RPoint_2;
290  return
291  collinear_are_strictly_ordered_along_line((const RPoint_2&)p,
292  (const RPoint_2&)q,
293  (const RPoint_2&)r);
294 }
collinear_are_strictly_ordered_along_line
bool collinear_are_strictly_ordered_along_line(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:285

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Comparison_result compare_deltax_deltay ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r,
const Point_2< R > &  s 
)
inline

Definition at line 121 of file predicates_on_points_2.h.

125 {
126  typedef typename R::Point_2_base RPoint_2;
127  return compare_deltax_deltay((const RPoint_2&)p,
128  (const RPoint_2&)q,
129  (const RPoint_2&)r,
130  (const RPoint_2&)s);
131 }
compare_deltax_deltay
Comparison_result compare_deltax_deltay(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r, const Point_2< R > &s)
Definition: predicates_on_points_2.h:121
Comparison_result compare_lexicographically_xy ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 136 of file predicates_on_points_2.h.

Referenced by CGAL::do_intersect(), lexicographically_xy_smaller(), lexicographically_xy_smaller_or_equal(), and Compare_xy::operator()().

138 {
139  typedef typename R::Point_2_base RPoint_2;
140  return compare_lexicographically_xy((const RPoint_2&)p,
141  (const RPoint_2&)q);
142 }
compare_lexicographically_xy
Comparison_result compare_lexicographically_xy(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:136

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Comparison_result compare_lexicographically_yx ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 192 of file predicates_on_points_2.h.

Referenced by lexicographically_yx_smaller(), and lexicographically_yx_smaller_or_equal().

194 {
195  typedef typename R::Point_2_base RPoint_2;
196  return compare_lexicographically_yx((const RPoint_2&)p,
197  (const RPoint_2&)q);
198 }
compare_lexicographically_yx
Comparison_result compare_lexicographically_yx(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:192

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Comparison_result compare_x ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 102 of file predicates_on_points_2.h.

Referenced by RayS3< FT >::collinear_has_on(), RayS2< FT >::collinear_has_on(), and Compare_x::operator()().

104 {
105  typedef typename R::Point_2_base RPoint_2;
106  return compare_x((const RPoint_2&)p, (const RPoint_2&)q);
107 }
compare_x
Comparison_result compare_x(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:102

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Comparison_result compare_y ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 111 of file predicates_on_points_2.h.

Referenced by RayS3< FT >::collinear_has_on(), RayS2< FT >::collinear_has_on(), and Compare_y::operator()().

113 {
114  typedef typename R::Point_2_base RPoint_2;
115  return compare_y((const RPoint_2&)p, (const RPoint_2&)q);
116 }
compare_y
Comparison_result compare_y(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:111

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bool leftturn ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 311 of file predicates_on_points_2.h.

Referenced by Triangulation::in_cone(), p_Left_of_line_2p< Point >::operator()(), p_Left_of_line_2p_safer< Point >::operator()(), p_Leftturn< Point >::operator()(), CGAL::seg_seg_do_intersect_contained(), and CGAL::seg_seg_do_intersect_crossing().

314 {
315  typedef typename R::Point_2_base RPoint_2;
316  return leftturn((const RPoint_2&)p,
317  (const RPoint_2&)q,
318  (const RPoint_2&)r);
319 }
leftturn
bool leftturn(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:311

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bool lexicographically_xy_larger ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 180 of file predicates_on_points_2.h.

References lexicographically_xy_smaller_or_equal().

Referenced by p_Greater_xy< Point >::operator()().

182 {
183  typedef typename R::Point_2_base RPoint_2;
184  return !lexicographically_xy_smaller_or_equal((const RPoint_2&)p,
185  (const RPoint_2&)q);
186 }
lexicographically_xy_smaller_or_equal
bool lexicographically_xy_smaller_or_equal(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:147

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bool lexicographically_xy_larger_or_equal ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 169 of file predicates_on_points_2.h.

References lexicographically_xy_smaller().

171 {
172  typedef typename R::Point_2_base RPoint_2;
173  return !lexicographically_xy_smaller((const RPoint_2&)p,
174  (const RPoint_2&)q);
175 }
lexicographically_xy_smaller
bool lexicographically_xy_smaller(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:158

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bool lexicographically_xy_smaller ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 158 of file predicates_on_points_2.h.

Referenced by CGAL::do_intersect(), lexicographically_xy_larger_or_equal(), SegmentS2< FT >::max(), SegmentS2< FT >::min(), p_Less_xy< Point >::operator()(), p_Less_dist_to_line_2p< Point >::operator()(), p_Less_negative_dist_to_line_2p< Point >::operator()(), r_Less_negative_dist_to_line< R >::operator()(), r_Less_dist_to_line< R >::operator()(), r_Less_in_direction< R >::operator()(), Less_xy::operator()(), and PointS2< FT >::operator<().

160 {
161  typedef typename R::Point_2_base RPoint_2;
162  return lexicographically_xy_smaller((const RPoint_2&)p,
163  (const RPoint_2&)q);
164 }
lexicographically_xy_smaller
bool lexicographically_xy_smaller(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:158

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bool lexicographically_xy_smaller_or_equal ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 147 of file predicates_on_points_2.h.

Referenced by lexicographically_xy_larger().

149 {
150  typedef typename R::Point_2_base RPoint_2;
151  return lexicographically_xy_smaller_or_equal((const RPoint_2&)p,
152  (const RPoint_2&)q);
153 }
lexicographically_xy_smaller_or_equal
bool lexicographically_xy_smaller_or_equal(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:147

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bool lexicographically_yx_larger ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 236 of file predicates_on_points_2.h.

References lexicographically_yx_smaller_or_equal().

Referenced by p_Greater_yx< Point >::operator()().

238 {
239  typedef typename R::Point_2_base RPoint_2;
240  return !lexicographically_yx_smaller_or_equal((const RPoint_2&)p,
241  (const RPoint_2&)q);
242 }
lexicographically_yx_smaller_or_equal
bool lexicographically_yx_smaller_or_equal(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:203

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bool lexicographically_yx_larger_or_equal ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 225 of file predicates_on_points_2.h.

References lexicographically_yx_smaller().

227 {
228  typedef typename R::Point_2_base RPoint_2;
229  return !lexicographically_yx_smaller((const RPoint_2&)p,
230  (const RPoint_2&)q);
231 }
lexicographically_yx_smaller
bool lexicographically_yx_smaller(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:214

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bool lexicographically_yx_smaller ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 214 of file predicates_on_points_2.h.

Referenced by CGAL::do_intersect(), lexicographically_yx_larger_or_equal(), p_Less_yx< Point >::operator()(), and Less_yx::operator()().

216 {
217  typedef typename R::Point_2_base RPoint_2;
218  return lexicographically_yx_smaller((const RPoint_2&)p,
219  (const RPoint_2&)q);
220 }
lexicographically_yx_smaller
bool lexicographically_yx_smaller(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:214

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bool lexicographically_yx_smaller_or_equal ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 203 of file predicates_on_points_2.h.

Referenced by lexicographically_yx_larger().

205 {
206  typedef typename R::Point_2_base RPoint_2;
207  return lexicographically_yx_smaller_or_equal((const RPoint_2&)p,
208  (const RPoint_2&)q);
209 }
lexicographically_yx_smaller_or_equal
bool lexicographically_yx_smaller_or_equal(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:203

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Orientation orientation ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 348 of file predicates_on_points_2.h.

Referenced by are_negative_oriented(), are_positive_oriented(), collinear(), coplanar(), leftturn(), p_Less_rotate_ccw< Point >::operator()(), p_Less_rotate_ccw_safer< Point >::operator()(), p_Less_rotate_ccw_E< Point >::operator()(), p_Orientation< Point >::operator()(), CGAL::seg_seg_do_intersect_contained(), and CGAL::seg_seg_do_intersect_crossing().

351 {
352  typedef typename R::Point_2_base RPoint_2;
353  return orientation((const RPoint_2&)p,
354  (const RPoint_2&)q,
355  (const RPoint_2&)r);
356 }
orientation
Orientation orientation(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:348

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bool rightturn ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 324 of file predicates_on_points_2.h.

Referenced by Triangulation::in_cone(), p_Right_of_line_2p< Point >::operator()(), p_Rightturn< Point >::operator()(), rightturn(), CGAL::seg_seg_do_intersect_contained(), and CGAL::seg_seg_do_intersect_crossing().

327 {
328  typedef typename R::Point_2_base RPoint_2;
329  return rightturn((const RPoint_2&)p,
330  (const RPoint_2&)q,
331  (const RPoint_2&)r);
332 }
rightturn
bool rightturn(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:324

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bool rightturn ( const Origin &  o,
const Point_2< R > &  q,
const Point_2< R > &  r 
)
inline

Definition at line 337 of file predicates_on_points_2.h.

References rightturn().

340 {
341  typedef typename R::Point_2_base RPoint_2;
342  return rightturn(o, (const RPoint_2&)q, (const RPoint_2&)r);
343 }
rightturn
bool rightturn(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r)
Definition: predicates_on_points_2.h:324

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Bounded_side side_of_bounded_circle ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r,
const Point_2< R > &  test 
)
inline

Definition at line 376 of file predicates_on_points_2.h.

Referenced by Side_of_bounded_circle::operator()().

380 {
381  typedef typename R::Point_2_base RPoint_2;
382  return side_of_bounded_circle((const RPoint_2&)p,
383  (const RPoint_2&)q,
384  (const RPoint_2&)r,
385  (const RPoint_2&)test);
386 }
side_of_bounded_circle
Bounded_side side_of_bounded_circle(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r, const Point_2< R > &test)
Definition: predicates_on_points_2.h:376

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Oriented_side side_of_oriented_circle ( const Point_2< R > &  p,
const Point_2< R > &  q,
const Point_2< R > &  r,
const Point_2< R > &  test 
)
inline

Definition at line 361 of file predicates_on_points_2.h.

Referenced by Side_of_oriented_circle::operator()().

365 {
366  typedef typename R::Point_2_base RPoint_2;
367  return side_of_oriented_circle((const RPoint_2&)p,
368  (const RPoint_2&)q,
369  (const RPoint_2&)r,
370  (const RPoint_2&)test);
371 }
side_of_oriented_circle
Oriented_side side_of_oriented_circle(const Point_2< R > &p, const Point_2< R > &q, const Point_2< R > &r, const Point_2< R > &test)
Definition: predicates_on_points_2.h:361

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CGAL_BEGIN_NAMESPACE bool x_equal ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 83 of file predicates_on_points_2.h.

Referenced by Equal_x::operator()().

85 {
86  typedef typename R::Point_2_base RPoint_2;
87  return x_equal((const RPoint_2&)p, (const RPoint_2&)q);
88 }
x_equal
CGAL_BEGIN_NAMESPACE bool x_equal(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:83

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bool y_equal ( const Point_2< R > &  p,
const Point_2< R > &  q 
)
inline

Definition at line 92 of file predicates_on_points_2.h.

Referenced by Equal_y::operator()().

94 {
95  typedef typename R::Point_2_base RPoint_2;
96  return y_equal((const RPoint_2&)p, (const RPoint_2&)q);
97 }
y_equal
bool y_equal(const Point_2< R > &p, const Point_2< R > &q)
Definition: predicates_on_points_2.h:92

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