
disjoint2_optional(+Rectangles)

   Constrains the position (and possibly size) of the (possibly optional) rectangles in Rectangles so that none overlaps.

Arguments
   Rectangles          Collection of rect{} structures specifying
 the position and size of rectangles on a grid.

Type
   library(gfd)

Description

    A two dimensional disjunctive constraint that constrains the replacement
    of a collection of rectangles specified by Rectangles to not overlap in
    their areas. The placement of each rectangle can be optional, i.e.
    they may not need to be placed.

    Each rectangle is defined by a rect named structure, using the
    following fields:

      x: The x co-ordinate of the left side of the rectangle 
      y: The y co-ordinate of the bottom side of the rectangle.
      w: The width of the rectangle
      h: The height of the rectangle
      b: Boolean specifying if rectangle is placed or not

    x, y, w, h can be domain variables or integers. If w and h are
    integers, then the rectangle is of a fixed size. o is a 0/1
    integer or domain variable, 1 specifies that the rectangle needs
    to be placed, and 0 that it is not placed. 

    Note that the constraint is implemented by different Gecode propagators,
    depending on if all the rectangles are of fixed size or not. If at
    least one rectangle is not of fixed size, then the Gecode
    propagator requires additional variables for the right and top
    sides of the rectangles, plus additional constraints
        
      Xright #= Xleft + Width
      Ytop   #= Ybot + Height

    for each rectangles. These are posted as part of the constraint (the Xright 
    and Ytop variables are not accessible by the user).

    Any input variables which are not already domain variables will be
    converted into domain variables with default bounds.

    A version of this constraint, generalised from two to multi-
    dimension, and without optional placement, is known as diffn in
    the Global Constraint Catalog. It is implemented using Gecode's 
    nooverlap() constraint (variant with optional placement).


See Also
   disjoint2 / 1, eclipse_6 : collection_to_list / 2, lists : collection_to_list / 2
