[/
    Copyright (c) 2008-2010 Joachim Faulhaber

    Distributed under the Boost Software License, Version 1.0.
    (See accompanying file LICENSE_1_0.txt or copy at
    http://www.boost.org/LICENSE_1_0.txt)
]


[/ //= Interval Construction ===================================================================]
[section Interval Construction]

[table
[[T]                                       [__ch_dsc_itv__] [__ch_cnt_itv__] [__ch_ro_itv__] [__ch_lo_itv__]  [__ch_cl_itv__] [__ch_op_itv__]      ]
[[Interval bounds]                                     [dynamic]  [dynamic]    [static]     [static]     [static]    [static]    ]
[[Form]                                                [ ]        [ ]          [asymmetric] [asymmetric] [symmetric] [symmetric] ]
[[['*Construct*]]                                      [ ]        [ ]          [ ]          [ ]          [ ]         [ ]         ]
[[`T singleton(const P&)`]                             [__d]      [__c]        [__d]        [__d]        [__d]       [__d]       ]
[[`T construct(const P&, const P&)`]                   [__d]      [__c]        [__dc]       [__dc]       [__d]       [__d]       ]
[[``
T construct(const P&, const P&, 
            interval_bounds   )
``]                                                    [__d]      [__c]        [ ]          [ ]          [ ]         [ ]         ]
[[`T hull(const P&, const P&)`]                        [__d]      [__c]        [__dc]       [__dc]       [__d]       [__d]       ]
[[`T span(const P&, const P&)`]                        [__d]      [__c]        [__dc]       [__dc]       [__d]       [__d]       ]
[[`static T right_open(const P&, const P&)`]           [__d]      [__c]        [ ]          [ ]          [ ]         [ ]         ]
[[`static T left_open(const P&, const P&)`]            [__d]      [__c]        [ ]          [ ]          [ ]         [ ]         ]
[[`static T closed(const P&, const P&)`]               [__d]      [__c]        [ ]          [ ]          [ ]         [ ]         ]
[[`static T open(const P&, const P&)`]                 [__d]      [__c]        [ ]          [ ]          [ ]         [ ]         ]
]

The table above shows the availability of functions, that allow the construction
of intervals. All interval constructin functins are of ['*constant time and space complexity*].

[table
[[['*Construct*]]                                      [Description]         ]
[[`T singleton(const P& value)`]                       [Constructs an interval that contains exactly one element `value`. 
                                                        For all interval types of the icl sigletons can be constructed
                                                        for /discrete/ domain types. For continuous domain types, only
                                                        __ct_itv__ is capable to construct a singleton. ]       ]
[[`T construct(const P& lower, const P& upper)`]       [Contructs an interval with lower bound `lower` and upper bound `upper` ] ]
[[``
T construct(const P& lower, const P& upper,
            interval_bounds bounds 
            = interval_bounds::right_open())
``]  
                                                       [For dynamically bounded intervals this function constructs an
                                                        interval with interval bounds specified by the third parameter. ]     ]
[[`T hull(const P& x1, const P& x2)`]                  [`hull(x1,x2)` constructs the smallest interval that contains both `x1` and `x2`.
                                                        `x2` may be smaller than `x1`. ]       ]
[[`T span(const P& x1, const P& x2)`]                  [`span(x1,x2)` constructs the interval `construct(min(x1,x2), max(x1,x2))`.
                                                        Note the differences between `span`, `hull` and `construct`:
``
span<right_open_interval<int> >(2,1)      == [1,2) // does NOT contain 2
hull<right_open_interval<int> >(2,1)      == [1,3) // contains 2
construct<right_open_interval<int> >(2,1) == [)    // is empty
``                                                                   
                                                                   ]   ]
[[``
static T right_open(const P&, const P&)
static T left_open(const P&, const P&)
static T closed(const P&, const P&)
static T open(const P&, const P&)
``                                       ]             [For dynamically bounded intervals there are for static functions to
                                                        construct intervals with the four interval bound types:
``
discrete_interval<int>      itv1 = discrete_interval<int>::closed(0,42);
continuous_interval<double> itv2 = continuous_interval<double>::right_open(0.0, 1.0);
``
                                                               ]         ]
[[['*Using the interval default*]]                     [ ]]                                                        
[[`interval<P>::type`]                                 [There is a library default, for all interval containers of the *icl*.
                                                        The intension of the library default is to minimize the need for parameter
                                                        specification, when working with *icl* class templates.
                                                        We can get the library default interval type as `interval<P>::type`. 
                                                        The library default uses ['*dynamically bounded intervals*]. You
                                                        can switch to ['*statically bounded intervals*] by 
                                                        `#define BOOST_ICL_USE_STATIC_BOUNDED_INTERVALS` prior to icl includes. ]]
[[``
static T right_open(const P&, const P&)
static T left_open(const P&, const P&)
static T closed(const P&, const P&)
static T open(const P&, const P&)
``                                     ]               [For template struct `interval` that always uses the library default
                                                        the static functions for the four interval bound types are also available. 
``
interval<int>::type    itv1 = interval<int>::closed(0,42);
interval<double>::type itv2 = interval<double>::right_open(0.0, 1.0);
``
                                                        This works with the statically bounded intervals as well, 
                                                        with the restriction that for continuous domain types the 
                                                        matching function has to be used:
``
#define BOOST_ICL_USE_STATIC_BOUNDED_INTERVALS
. . .
// library default is the statically bounded right_open_interval
interval<int>::type    itv1 = interval<int>::closed(0,42); //==[0,43) //ok, bounds are shifted
interval<double>::type itv2 = interval<double>::right_open(0.0, 1.0); //ok. right_open matches
interval<double>::type itv3 = interval<double>::closed(0.0, 1.0);     //will NOT compile
``
                                                        See also examples 
                                                        [link boost_icl.examples.dynamic_interval Dynamic intervals] and
                                                        [link boost_icl.examples.static_interval Static intervals]   
                                                        ]]
] 

['*See also . . .*]
[table
[]
[[[link boost_icl.examples.dynamic_interval ['*Example: Dynamically bounded intervals and the library default*]] ]]
[[[link boost_icl.examples.static_interval  ['*Example: Statically bounded intervals, changing the library default*]] ]]
]

['*Back to section . . .*]
[table
[]
[[[link additional_interval_functions ['*Additional interval functions*]] ]]
[[[link function_synopsis_table ['*Function Synopsis*]]          ]]
[[[link boost_icl.interface ['*Interface*]]                      ]]
]

[endsect][/ Interval Construction]