class TGeoCompositeShape: public TGeoBBox

 TGeoCompositeShape - class handling Boolean composition of shapes

   Composite shapes are Boolean combination of two or more shape
 components. The supported boolean operations are union (+), intersection (*)
 and subtraction. Composite shapes derive from the base TGeoShape class,
 therefore providing all shape features : computation of bounding box, finding
 if a given point is inside or outside the combination, as well as computing the
 distance to entering/exiting. It can be directly used for creating volumes or
 used in the definition of other composite shapes.
   Composite shapes are provided in order to complement and extend the set of
 basic shape primitives. They have a binary tree internal structure, therefore
 all shape-related geometry queries are signals propagated from top level down
 to the final leaves, while the provided answers are assembled and interpreted
 back at top. This CSG hierarchy is effective for small number of components,
 while performance drops dramatically for large structures. Building a complete
 geometry in this style is virtually possible but highly not recommended.

   Structure of composite shapes

   A composite shape can always be regarded as the result of a Boolean operation
 between only two shape components. All information identifying these two
 components as well as their positions with respect to the frame of the composite
 is represented by an object called Boolean node. A composite shape just have
 a pointer to such a Boolean node. Since the shape components may also be
 composites, they will also contain binary Boolean nodes branching other two
 shapes in the hierarcy. Any such branch ends-up when the final leaves are no
 longer composite shapes, but basic primitives.

   Suppose that A, B, C and D represent basic shapes, we will illustrate
 how the internal representation of few combinations look like. We do this
 only for the sake of understanding how to create them in a proper way, since
 the user interface for this purpose is in fact very simple. We will ignore
 for the time being the positioning of components. The definition of a composite
 shape takes an expression where the identifiers are shape names. The
 expression is parsed and decomposed in 2 sub-expressions and the top-level
 Boolean operator.

 1.     A+B+C
   This represent the union of A, B and C. Both union operators are at the
 same level. Since:
        A+B+C = (A+B)+C = A+(B+C)
 the first (+) is taken as separator, hence the expression splitted:
        A and B+C
 A Boolean node of type TGeoUnion("A", "B+C") is created. This tries to replace
 the 2 expressions by actual pointers to corresponding shapes.
 The first expression (A) contains no operators therefore is interpreted as
 representing a shape. The shape named "A" is searched into the list of shapes
 handled by the manager class and stored as the "left" shape in the Boolean
 union node. Since the second expression is not yet fully decomposed, the "right"
 shape in the combination is created as a new composite shape. This will split
 at its turn B+C into B and C and create a TGeoUnion("B","C"). The B and C
 identifiers will be looked for and replaced by the pointers to the actual shapes
 into the new node. Finally, the composite "A+B+C" will be represented as:

                 A
                |
   [A+B+C] = (+)             B
                |           |
                 [B+C] = (+)
                            |
                             C

 where [] is a composite shape, (+) is a Boolean node of type union and A, B,
 C are pointers to the corresponding shapes.
   Building this composite shapes takes the following line :
      TGeoCompositeShape *cs1 = new TGeoCompositeShape("CS1", "A+B+C");

 2.      (A+B)\(C+D)
   This expression means: subtract the union of C and D from the union of A and
 B. The usage of paranthesys to force operator precedence is always recommended.
 The representation of the corresponding composite shape looks like:

                                   A
                                  |
                       [A+B] = (+)
                      |           |
   [(A+B)\(C+D)] = (\)           C B
                      |         |
                       [C+D]=(+)
                                |
                                 D

      TGeoCompositeShape *cs2 = new TGeoCompositeShape("CS2", "(A+B)\(C+D)");

   Building composite shapes as in the 2 examples above is not always quite
 usefull since we were using unpositioned shapes. When suplying just shape
 names as identifiers, the created boolean nodes will assume that the shapes
 are positioned with an identity transformation with respect to the frame of
 the created composite. In order to provide some positioning of the combination
 components, we have to attach after each shape identifier the name of an
 existing transformation, separated by a colon. Obviously all transformations
 created for this purpose have to be objects with unique names in order to be
 properly substituted during parsing.
   Let's look at the code implementing the second example :

      TGeoTranslation *t1 = new TGeoTranslation("T1",0,0,-20);
      TGeoTranslation *t2 = new TGeoTranslation("T2",0,0, 20);
      TGeoRotation *r1 = new TGeoRotation("R1"); // transformations need names
      r1->SetAngles(90,30,90,120,0,0); // rotation with 30 degrees about Z
      TGeoTube *a = new TGeoTube(0, 10,20);
      a->SetName("A");                 // shapes need names too
      TGeoTube *b = new TGeoTube(0, 20,20);
      b->SetName("B");
      TGeoBBox *c = new TGeoBBox(10,10,50);
      c->SetName("C");
      TGeoBBox *d = new TGeoBBox(50,10,10);
      d->SetName("D");

      TGeoCompositeShape *cs;
      cs = new TGeoCompositeShape("CS", "(A:t1+B:t2)\(C+D:r1)");

   The newly created composite looks like 2 cylinders of different radii sitting
 one on top of the other and having 2 rectangular holes : a longitudinal one
 along Z axis corresponding to C and an other one in the XY plane due to D.
   One should have in mind that the same shape or matrix identifier can be
 used many times in the same expression. For instance:

      (A:t1-A:t2)*B:t1

 is a valid expression. Expressions that cannot be parsed or identifiers that
 cannot be substituted by existing objects generate error messages.
   Composite shapes can be subsequently used for defining volumes. Moreover,
 these volumes may have daughters but these have to obbey overlapping/extruding
 rules (see TGeoVolume). Volumes created based on composite shapes cannot be
 divided. Visualization of such volumes is currently not implemented.