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Sébastien Loriot 3de45905c0 use a dedicated version of the function assigning points to region in case 
at least two extreme points are identical.

for the archive here is the result of the benchmark like done for r69398.
br_spl correspond to the same code but replacing the implementation of 
ch_akl_toussaint_assign_points_to_regions_deg by:
  for ( ; first != last; ++first )
  {
    //note that e!=w and s!=n except if the convex hull is a point (they are lexicographically sorted)
    if ( left_turn(*e, *w, *first ) )   
    {
        if (s!=w && left_turn( *s, *w, *first ) )       region1.push_back( *first );
        else if (e!=s && left_turn( *e, *s, *first ) )  region2.push_back( *first );
    }
    else
    {
        if (n!=e && left_turn( *n, *e, *first ) )       region3.push_back( *first );
        else if (w!=n && left_turn( *w, *n, *first ) )  region4.push_back( *first );
    }
  }  

The conclusion is that that version is always the fastest.

2 extreme points 
    using vector
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |  1.34  |  2.61  | 16.15  | 16.69 |  18.31 |  20.91  |
    |branch   |  0.10  |  0.74  |  9.24  | 11.0  |  12.74 |  15.24  |
    |br_spl   |  0.12  |  0.91  | 10.18  | 11.88 |  13.68 |  15.88  |
    |--------------------------------------------------------------- 

    using list
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |  1.27  |  2.66  |  16.09 | 16.66 |  18.19  | 21.21  |
    |branch   |  0.10  |  0.8   |   9.49 | 11.36 |  13.09  | 15.55  |
    |br_spl   |  0.13  |  0.9   |  10.32 | 12.00 |  13.93  | 16.14  |
    --------------------------------------------------------------- |

 
3 extreme points
    using vector
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |   1.34 |   2.46 |  14.26 | 14.81 |   16.40 | 18.48  |
    |branch   |   0.18 |   0.87 |  10.07 | 11.76 |   13.52 | 15.59  |
    |br_spl   |   0.12 |   0.98 |  10.41 | 12.07 |   13.94 | 15.93  |
    |---------------------------------------------------------------| 

    using list
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |   1.32 |   2.45 |  14.17 | 14.76 |   16.62 | 18.61  |
    |branch   |   0.19 |   0.86 |  10.21 | 12.03 |   13.66 | 15.96  |
    |br_spl   |   0.16 |   0.94 |  10.74 | 12.38 |   14.39 | 16.31  |
    |---------------------------------------------------------------| 

Convex hull is 2 points
    using vector
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |  0.19  |  1.39  |  13.54 | 13.46 |  14.16  | 14.05  |
    |branch   |  0.11  |  0.54  |   5.02 |  4.96 |   5.09  |  5.06  |
    |br_spl   |  0.12  |  0.94  |   9.02 |  9.0  |   8.98  |  9.13  |
    |---------------------------------------------------------------| 

    using list
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |   0.18 |   1.46 |  13.89 | 13.88 |   14.44 | 14.11  |
    |branch   |   0.14 |   0.58 |   5.12 |  5.07 |    5.07 |  5.29  |
    |br_spl   |   0.14 |   0.97 |   9.28 |  9.28 |    9.30 |  9.54  |
    |---------------------------------------------------------------| 

4 extreme points
    using vector
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------| 
    |next     |   2.37 |   2.97 |   9.84 |  8.07 |    7.76 | 9.0    |
    |branch   |   0.10 |   0.50 |   6.76 |  7.36 |    7.42 | 8.66   |
    |br_spl   |   0.13 |   0.46 |   6.74 |  7.30 |    7.38 | 8.65   |
    |---------------------------------------------------------------|

    using list
    |nb pts   |     10 |   100  |   1000 | 10000 |  100000 | 1000000|
    |nb runs  | 100001 | 100001 | 100001 | 10001 |    1001 |     101|
    |---------------------------------------------------------------|
    |next     |   2.34 |   3.07 |   9.91 |  8.01 |    7.78 | 9.17   |
    |branch   |   0.11 |   0.54 |   6.78 |  7.44 |    7.58 | 8.93   |
    |br_spl   |   0.14 |   0.50 |   6.82 |  7.44 |    7.51 | 8.94   |
    |---------------------------------------------------------------|
 		2012-05-31 12:48:42 +00:00
..
Convex_hull_2 use a dedicated version of the function assigning points to region in case 2012-05-31 12:48:42 +00:00
IO Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
Convex_hull_projective_xy_traits_2.h deprecation warnings 2012-05-28 07:28:03 +00:00
Convex_hull_projective_xz_traits_2.h deprecation warnings 2012-05-28 07:28:03 +00:00
Convex_hull_projective_yz_traits_2.h deprecation warnings 2012-05-28 07:28:03 +00:00
ch_akl_toussaint.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_bykat.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_eddy.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_function_objects_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_graham_andrew.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_jarvis.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_melkman.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
ch_selected_extreme_points_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
convex_hull_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
convex_hull_constructive_traits_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
convex_hull_traits_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
convexity_check_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00
segment_intersection_points_2.h Turn QPL into LGPLv3+ 2012-01-13 16:33:35 +00:00