F4.11.2} Region editing

   **************************
   The most import action of editing a region is to define its
   mathematical expression. flair in the geometry editor will split
   the region expression into a list of zones.
   If parenthesis are used they will be treated as one zone.
   The user can manipulate the zones either with the keyboard or
   graphically

   e.g.  +a +b | +c | +e -(+f -g | +h)

         will be split into 3 zones
         zone01: +a +b
         zone02: +c
         zone03: +e -(+f -g | +h)



    Keyboard
    ********
     - To add a new zone enter the appropriate expression in the
       "+zone" field
     - To modify an existing zone, click with the mouse the
       appropriate zone##
     - To delete a zone select with the mouse or keyboard the zone##
       rows and either hit the [Del]ete key inside the listbox or
       with the mouse Right-Click -> Delete


    Graphically
    ***********
    The recipe is the following:
    - Select the desired REGION. If a new region is to be created
      do not select anything
    - During the following process maintain the REGION selected.
      In case of accidental unselection of the REGION, press [Ctrl]
      and reselect the REGION

    - Add a new zone:
       * Verify that there is no zone selected in the property listbox.
       * If there is any hit [Esc]ape to unselect them
       * Add onto the selection ONLY the bodies representing the borders
         of the zone
         (Holding [Ctrl], select by clicking on the desired bodies)
       * Right-click or [Space]->Zone  or with the
         shortcut [d]efine.
         Note: [D]efine (capital D) will first unselect any zone)
       * Move the mouse and click in any of the viewports, a point that
         belong to the wished zone
       * Automatically the zone expression will be created

    - Modify/Edit an existing zone:
       * IMPORTANT: Select the zone## either on the property listbox
         or graphically in any viewport clicking a point that belongs to it.
       * Automatically ALL bodies involved in the zone expression
         will be selected
       * With the zone selected, select or unselect additional bodies
         if needed
       * Then like in the "Add a new zone" click on "Zone" or with
         shortcut [d]efine (small)
       * Move the mouse and click in any of the viewports, a point that
         belong to the wished zone
       * Automatically the zone expression will be replaced

     Note:
      - DO NOT select bodies that you don't need
      - There is an automatic optimization of unwanted bodies but is
        far from perfect.
      - Verify if you don't have accidentally locked some bodies.


    Step by step example
    ********************
    In this example we will create a sphere with a cylindrical hole cut
    with a tilted plane.

               {image:zone_edit2.gif}

    * First we have to create all necessary bodies
       - sphere
       - infinite cylinder
       - tilted plane

    * Select the sphere body
      The sphere outline will be highlighted.
                 
      Each selected body divides the space into 2 zones
           1: +sphere     inside the sphere
           2: -sphere     outside the sphere

    * Add to the selection the infinite cylinder
      with [Ctrl] + Left mouse click
                 
      The 2 selected bodies divides the space into 4 zones
           1: +sphere +cylinder
           2: +sphere -cylinder
           3: -sphere +cylinder
           4: -sphere -cylinder

    * Add to the selection with [Ctrl]+left-click on the tilted plane.
                 
      Now the space is divided into 8 zones
           1: +sphere +cylinder +plane
           2: +sphere +cylinder -plane
           3: +sphere -cylinder +plane
           4: +sphere -cylinder -plane
           5: -sphere +cylinder +plane
           6: -sphere +cylinder -plane
           7: -sphere -cylinder +plane
           8: -sphere -cylinder -plane

      Tip: The number of valid zones <= 2^bodies

    * Press [Spacebar] and select the action Zone 
      or with the shortcut [d]efine.
      - Moving the mouse, flair shows the various subdivisions of
        space with their optimized expression.
      - Point and click with the mouse somewhere inside zone 4
      - A new REGION will be created
      - Automatically the zone expression

               zone01:  +sphere -cylinder -plane

        will be added to the REGION as a new zone
      - all bodies will be automatically unselected
      - the new REGION will remain selected.
                 

    * Press [F2] or use the mouse to change the name of the region
    * Press [m] or use the mouse to change the material of the region

    * Finally we have to add as second zone the lower half of
      the sphere. Select again the sphere and the plane (pressing [Ctrl])
      (NOT the infinite cylinder this time)
                 
      Again the space is divided into 4 zones
           1: +sphere +plane
           2: +sphere -plane
           3: -sphere +plane
           4: -sphere -plane

    * Press [Spacebar] and select the action Zone 
      or with the shortcut [d]efine.
      - Point and click with the mouse somewhere inside zone 1
      - Automatically the zone expression

               zone02:   +sphere +plane

        will be added to the REGION as a new zone.
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