class TGeoShape: public TNamed

 TGeoShape - Base abstract class for all shapes.



   Shapes are geometrical objects that provide the basic modelling
 functionality. They provide the definition of the LOCAL frame of coordinates,
 with respect to which they are defined. Any implementation of a shape deriving
 from the base TGeoShape class has to provide methods for :
  - finding out if a point defined in their local frame is or not contained
 inside;
  - computing the distance from a local point to getting outside/entering the
 shape, given a known direction;
  - computing the maximum distance in any direction from a local point that
 does NOT result in a boundary crossing of the shape (safe distance);
  - computing the cosines of the normal vector to the crossed shape surface,
 given a starting local point and an ongoing direction.
   All the features above are globally managed by the modeller in order to
 provide navigation functionality. In addition to those, shapes have also to
 implement additional specific abstract methods :
  - computation of the minimal box bounding the shape, given that this box have
 to be aligned with the local coordinates;
  - algorithms for dividing the shape along a given axis and producing resulting
 divisions volumes.

   The modeler currently provides a set of 16 basic shapes, which we will call
 primitives. It also provides a special class allowing the creation of shapes
 made as a result of boolean operations between primitives. These are called
 composite shapes and the composition operation can be recursive (composition
 of composites). This allows the creation of a quite large number of different
 shape topologies and combinations.

   Shapes are named objects and register themselves to the manager class at
 creation time. This is responsible for their final deletion. Shapes
 can be created without name if their retreival by name is no needed. Generally
 shapes are objects that are usefull only at geometry creation stage. The pointer
 to a shape is in fact needed only when referring to a given volume and it is
 always accessible at that level. A shape may be referenced by several volumes,
 therefore its deletion is not possible once volumes were defined based on it.



 Creating shapes

   Shape objects embeed only the minimum set of parameters that are fully
 describing a valid physical shape. For instance, a tube is represented by
 its half length, the minimum radius and the maximum radius. Shapes are used
 togeather with media in order to create volumes, which in their turn
 are the main components of the geometrical tree. A specific shape can be created
 stand-alone :

   TGeoBBox *box = new TGeoBBox("s_box", halfX, halfY, halfZ); // named
   TGeoTube *tub = new TGeoTube(rmin, rmax, halfZ);            // no name
   ...  (see each specific shape constructors)

   Sometimes it is much easier to create a volume having a given shape in one
 step, since shapes are not direcly linked in the geometrical tree but volumes
 are :

   TGeoVolume *vol_box = gGeoManager->MakeBox("BOX_VOL", "mat1", halfX, halfY, halfZ);
   TGeoVolume *vol_tub = gGeoManager->MakeTube("TUB_VOL", "mat2", rmin, rmax, halfZ);
   ...  (see MakeXXX() utilities in TGeoManager class)


 Shape queries

 Note that global queries related to a geometry are handled by the manager class.
 However, shape-related queries might be sometimes usefull.

 A) Bool_t TGeoShape::Contains(Double_t *point[3])
   - this method returns true if POINT is actually inside the shape. The point
 has to be defined in the local shape reference. For instance, for a box having
 DX, DY and DZ half-lengths a point will be considered inside if :
   | -DX <= point[0] <= DX
   | -DY <= point[1] <= DY
   | -DZ <= point[2] <= DZ

 B) Double_t TGeoShape::DistFromInside(Double_t *point[3], Double_t *dir[3],
                                  Int_t iact, Double_t step, Double_t *safe)
   - computes the distance to exiting a shape from a given point INSIDE, along
 a given direction. The direction is given by its director cosines with respect
 to the local shape coordinate system. This method provides additional
 information according the value of IACT input parameter :
   IACT = 0     => compute only safe distance and fill it at the location
                   given by SAFE
   IACT = 1     => a proposed STEP is supplied. The safe distance is computed
                   first. If this is bigger than STEP than the proposed step
                   is approved and returned by the method since it does not
                   cross the shape boundaries. Otherwise, the distance to
                   exiting the shape is computed and returned.
   IACT = 2     => compute both safe distance and distance to exiting, ignoring
                   the proposed step.
   IACT > 2     => compute only the distance to exiting, ignoring anything else.

 C) Double_t TGeoShape::DistFromOutside(Double_t *point[3], Double_t *dir[3],
                                  Int_t iact, Double_t step, Double_t *safe)
   - computes the distance to entering a shape from a given point OUTSIDE. Acts
 in the same way as B).

 D) Double_t Safety(Double_t *point[3], Bool_t inside)

   - compute maximum shift of a point in any direction that does not change its
 INSIDE/OUTSIDE state (does not cross shape boundaries). The state of the point
 have to be properly supplied.

 E) Double_t *Normal(Double_t *point[3], Double_t *dir[3], Bool_t inside)

   - returns director cosines of normal to the crossed shape surface from a
 given point towards a direction. One has to specify if the point is inside
 or outside shape. According to this, the normal will be outwards or inwards
 shape respectively. Normal components are statically stored by shape class,
 so it has to be copied after retreival in a different array.

 Dividing shapes

   Shapes can generally be divided along a given axis. Supported axis are
 X, Y, Z, Rxy, Phi, Rxyz. A given shape cannot be divided however on any axis.
 The general rule is that that divisions are possible on whatever axis that
 produces still known shapes as slices. The division of shapes should not be
 performed by TGeoShape::Divide() calls, but rather by TGeoVolume::Divide().
 The algorithm for dividing a specific shape is known by the shape object, but
 is always invoked in a generic way from the volume level. Details on how to
 do that can be found in TGeoVolume class. One can see how all division options
 are interpreted and which is their result inside specific shape classes.