class TGeoVolume: public TNamed, public TGeoAtt, public TAttLine, public TAttFill, public TAtt3D

   TGeoVolume, TGeoVolumeMulti, TGeoVolumeAssembly - the volume classes

   Volumes are the basic objects used in building the geometrical hierarchy.
 They represent unpositioned objects but store all information about the
 placement of the other volumes they may contain. Therefore a volume can
 be replicated several times in the geometry. In order to create a volume, one
 has to put together a shape and a medium which are already defined. Volumes
 have to be named by users at creation time. Every different name may represent a
 an unique volume object, but may also represent more general a family (class)
 of volume objects having the same shape type and medium, but possibly
 different shape parameters. It is the user's task to provide different names
 for different volume families in order to avoid ambiguities at tracking time.
 A generic family rather than a single volume is created only in two cases :
 when a generic shape is provided to the volume constructor or when a division
 operation is applied. Each volume in the geometry stores an unique
 ID corresponding to its family. In order to ease-up their creation, the manager
 class is providing an API that allows making a shape and a volume in a single step.

   Volumes are objects that can be visualized, therefore having visibility,
 colour, line and fill attributes that can be defined or modified any time after
 the volume creation. It is advisable however to define these properties just
 after the first creation of a volume namespace, since in case of volume families
 any new member created by the modeler inherits these properties.

    In order to provide navigation features, volumes have to be able to find
 the proper container of any point defined in the local reference frame. This
 can be the volume itself, one of its positioned daughter volumes or none if
 the point is actually outside. On the other hand, volumes have to provide also
 other navigation methods such as finding the distances to its shape boundaries
 or which daughter will be crossed first. The implementation of these features
 is done at shape level, but the local mother-daughters management is handled
 by volumes that builds additional optimisation structures upon geometry closure.
 In order to have navigation features properly working one has to follow the
 general rules for building a valid geometry (see TGeoManager class).

   Now let's make a simple volume representing a copper wire. We suppose that
 a medium is already created (see TGeoMedium class on how to create media).
 We will create a TUBE shape for our wire, having Rmin=0cm, Rmax=0.01cm
 and a half-length dZ=1cm :

   TGeoTube *tube = new TGeoTube("wire_tube", 0, 0.01, 1);

 One may ommit the name for the shape if no retreiving by name is further needed
 during geometry building. The same shape can be shared by different volumes
 having different names and materials. Now let's make the volume for our wire.
 The prototype for volumes constructor looks like :

   TGeoVolume::TGeoVolume(const char *name, TGeoShape *shape, TGeoMedium *med)

 Since TGeoTube derives from the base shape class, we can provide it to the volume
 constructor :

   TGeoVolume *wire_co = new TGeoVolume("WIRE_CO", tube, ptrCOPPER);

 Do not bother to delete neither the media, shapes or volumes that you have
 created since all will be automatically cleaned on exit by the manager class.
 If we would have taken a look inside TGeoManager::MakeTube() method, we would
 have been able to create our wire with a single line :

   TGeoVolume *wire_co = gGeoManager->MakeTube("WIRE_CO", ptrCOPPER, 0, 0.01, 1);

 The same applies for all primitive shapes, for which there can be found
 corresponding MakeSHAPE() methods. Their usage is much more convenient unless
 a shape has to be shared between more volumes. Let's make now an aluminium wire
 having the same shape, supposing that we have created the copper wire with the
 line above :

   TGeoVolume *wire_al = new TGeoVolume("WIRE_AL", wire_co->GetShape(), ptrAL);

 Now that we have learned how to create elementary volumes, let's see how we
 can create a geometrical hierarchy.


   Positioning volumes


   When creating a volume one does not specify if this will contain or not other
 volumes. Adding daughters to a volume implies creating those and adding them
 one by one to the list of daughters. Since the volume has to know the position
 of all its daughters, we will have to supply at the same time a geometrical
 transformation with respect to its local reference frame for each of them.
 The objects referencing a volume and a transformation are called NODES and
 their creation is fully handled by the modeler. They represent the link
 elements in the hierarchy of volumes. Nodes are unique and distinct geometrical
 objects ONLY from their container point of view. Since volumes can be replicated
 in the geometry, the same node may be found on different branches.

   An important observation is that volume objects are owned by the TGeoManager
 class. This stores a list of all volumes in the geometry, that is cleaned
 upon destruction.

   Let's consider positioning now our wire in the middle of a gas chamber. We
 need first to define the gas chamber :

   TGeoVolume *chamber = gGeoManager->MakeTube("CHAMBER", ptrGAS, 0, 1, 1);

 Now we can put the wire inside :

   chamber->AddNode(wire_co, 1);

 If we inspect now the chamber volume in a browser, we will notice that it has
 one daughter. Of course the gas has some container also, but let's keep it like
 that for the sake of simplicity. The full prototype of AddNode() is :

   TGeoVolume::AddNode(TGeoVolume *daughter, Int_t usernumber,
                       TGeoMatrix *matrix=gGeoIdentity)

 Since we did not supplied the third argument, the wire will be positioned with
 an identity transformation inside the chamber. One will notice that the inner
 radii of the wire and chamber are both zero - therefore, aren't the two volumes
 overlapping ? The answer is no, the modeler is even relaying on the fact that
 any daughter is fully contained by its mother. On the other hand, neither of
 the nodes positioned inside a volume should overlap with each other. We will
 see that there are allowed some exceptions to those rules.

 Overlapping volumes


   Positioning volumes that does not overlap their neighbours nor extrude
 their container is sometimes quite strong constraint. Some parts of the geometry
 might overlap naturally, e.g. two crossing tubes. The modeller supports such
 cases only if the overlapping nodes are declared by the user. In order to do
 that, one should use TGeoVolume::AddNodeOverlap() instead of TGeoVolume::AddNode().
   When 2 or more positioned volumes are overlapping, not all of them have to
 be declared so, but at least one. A point inside an overlapping region equally
 belongs to all overlapping nodes, but the way these are defined can enforce
 the modeler to give priorities.
   The general rule is that the deepest node in the hierarchy containing a point
 have the highest priority. For the same geometry level, non-overlapping is
 prioritized over overlapping. In order to illustrate this, we will consider
 few examples. We will designate non-overlapping nodes as ONLY and the others
 MANY as in GEANT3, where this concept was introduced:
   1. The part of a MANY node B extruding its container A will never be "seen"
 during navigation, as if B was in fact the result of the intersection of A and B.
   2. If we have two nodes A (ONLY) and B (MANY) inside the same container, all
 points in the overlapping region of A and B will be designated as belonging to A.
   3. If A an B in the above case were both MANY, points in the overlapping
 part will be designated to the one defined first. Both nodes must have the
 same medium.
   4. The slices of a divided MANY will be as well MANY.

 One needs to know that navigation inside geometry parts MANY nodes is much
 slower. Any overlapping part can be defined based on composite shapes - this
 is always recommended.

   Replicating volumes


   What can we do if our chamber contains two identical wires instead of one ?
 What if then we would need 1000 chambers in our detector ? Should we create
 2000 wires and 1000 chamber volumes ? No, we will just need to replicate the
 ones that we have already created.

   chamber->AddNode(wire_co, 1, new TGeoTranslation(-0.2,0,0));
   chamber->AddNode(wire_co, 2, new TGeoTranslation(0.2,0,0));

   The 2 nodes that we have created inside chamber will both point to a wire_co
 object, but will be completely distinct : WIRE_CO_1 and WIRE_CO_2. We will
 want now to place symetrically 1000 chambers on a pad, following a pattern
 of 20 rows and 50 columns. One way to do this will be to replicate our chamber
 by positioning it 1000 times in different positions of the pad. Unfortunatelly,
 this is far from being the optimal way of doing what we want.
 Imagine that we would like to find out which of the 1000 chambers is containing
 a (x,y,z) point defined in the pad reference. You will never have to do that,
 since the modeller will take care of it for you, but let's guess what it has
 to do. The most simple algorithm will just loop over all daughters, convert
 the point from mother to local reference and check if the current chamber
 contains the point or not. This might be efficient for pads with few chambers,
 but definitely not for 1000. Fortunately the modeler is smarter than that and
 create for each volume some optimization structures called voxels (see Voxelization)
 to minimize the penalty having too many daughters, but if you have 100 pads like
 this in your geometry you will anyway loose a lot in your tracking performance.

   The way out when volumes can be arranged according to simple patterns is the
 usage of divisions. We will describe them in detail later on. Let's think now
 at a different situation : instead of 1000 chambers of the same type, we may
 have several types of chambers. Let's say all chambers are cylindrical and have
 a wire inside, but their dimensions are different. However, we would like all
 to be represented by a single volume family, since they have the same properties.

   Volume families (TGeoVolumeMulti)

 A volume family is represented by the class TGeoVolumeMulti. It represents
 a class of volumes having the same shape type and each member will be
 identified by the same name and volume ID. Any operation applied to a
 TGeoVolume equally affects all volumes in that family. The creation of a
 family is generally not a user task, but can be forced in particular cases:

      TGeoManager::Volume(const char *vname, const char *shape, Int_t nmed);

 where VNAME is the family name, NMED is the medium number and SHAPE is the
 shape type that can be:
   box    - for TGeoBBox
   trd1   - for TGeoTrd1
   trd2   - for TGeoTrd2
   trap   - for TGeoTrap
   gtra   - for TGeoGtra
   para   - for TGeoPara
   tube, tubs - for TGeoTube, TGeoTubeSeg
   cone, cons - for TGeoCone, TgeoCons
   eltu   - for TGeoEltu
   ctub   - for TGeoCtub
   pcon   - for TGeoPcon
   pgon   - for TGeoPgon

 Volumes are then added to a given family upon adding the generic name as node
 inside other volume:
   TGeoVolume *box_family = gGeoManager->Volume("BOXES", "box", nmed);

   gGeoManager->Node("BOXES", Int_t copy_no, "mother_name",
                     Double_t x, Double_t y, Double_t z, Int_t rot_index,
                     Bool_t is_only, Double_t *upar, Int_t npar);
 here:
   BOXES   - name of the family of boxes
   copy_no - user node number for the created node
   mother_name - name of the volume to which we want to add the node
   x,y,z   - translation components
   rot_index   - indx of a rotation matrix in the list of matrices
   upar    - array of actual shape parameters
   npar    - number of parameters
 The parameters order and number are the same as in the corresponding shape
 constructors.

   Another particular case where volume families are used is when we want
 that a volume positioned inside a container to match one ore more container
 limits. Suppose we want to position the same box inside 2 different volumes
 and we want the Z size to match the one of each container:

   TGeoVolume *container1 = gGeoManager->MakeBox("C1", imed, 10,10,30);
   TGeoVolume *container2 = gGeoManager->MakeBox("C2", imed, 10,10,20);
   TGeoVolume *pvol       = gGeoManager->MakeBox("PVOL", jmed, 3,3,-1);
   container1->AddNode(pvol, 1);
   container2->AddNode(pvol, 1);

   Note that the third parameter of PVOL is negative, which does not make sense
 as half-length on Z. This is interpreted as: when positioned, create a box
 replacing all invalid parameters with the corresponding dimensions of the
 container. This is also internally handled by the TGeoVolumeMulti class, which
 does not need to be instantiated by users.

   Dividing volumes


   Volumes can be divided according a pattern. The most simple division can
 be done along one axis, that can be: X, Y, Z, Phi, Rxy or Rxyz. Let's take
 the most simple case: we would like to divide a box in N equal slices along X
 coordinate, representing a new volume family. Supposing we already have created
 the initial box, this can be done like:

      TGeoVolume *slicex = box->Divide("SLICEX", 1, N);

 where SLICE is the name of the new family representing all slices and 1 is the
 slicing axis. The meaning of the axis index is the following: for all volumes
 having shapes like box, trd1, trd2, trap, gtra or para - 1,2,3 means X,Y,Z; for
 tube, tubs, cone, cons - 1 means Rxy, 2 means phi and 3 means Z; for pcon and
 pgon - 2 means phi and 3 means Z; for spheres 1 means R and 2 means phi.
   In fact, the division operation has the same effect as positioning volumes
 in a given order inside the divided container - the advantage being that the
 navigation in such a structure is much faster. When a volume is divided, a
 volume family corresponding to the slices is created. In case all slices can
 be represented by a single shape, only one volume is added to the family and
 positioned N times inside the divided volume, otherwise, each slice will be
 represented by a distinct volume in the family.
   Divisions can be also performed in a given range of one axis. For that, one
 have to specify also the starting coordinate value and the step:

      TGeoVolume *slicex = box->Divide("SLICEX", 1, N, start, step);

 A check is always done on the resulting division range : if not fitting into
 the container limits, an error message is posted. If we will browse the divided
 volume we will notice that it will contain N nodes starting with index 1 upto
 N. The first one has the lower X limit at START position, while the last one
 will have the upper X limit at START+N*STEP. The resulting slices cannot
 be positioned inside an other volume (they are by default positioned inside the
 divided one) but can be further divided and may contain other volumes:

      TGeoVolume *slicey = slicex->Divide("SLICEY", 2, N1);
      slicey->AddNode(other_vol, index, some_matrix);

   When doing that, we have to remember that SLICEY represents a family, therefore
 all members of the family will be divided on Y and the other volume will be
 added as node inside all.
   In the example above all the resulting slices had the same shape as the
 divided volume (box). This is not always the case. For instance, dividing a
 volume with TUBE shape on PHI axis will create equal slices having TUBESEG
 shape. Other divisions can alsoo create slices having shapes with different
 dimensins, e.g. the division of a TRD1 volume on Z.
   When positioning volumes inside slices, one can do it using the generic
 volume family (e.g. slicey). This should be done as if the coordinate system
 of the generic slice was the same as the one of the divided volume. The generic
 slice in case of PHI divisioned is centered with respect to X axis. If the
 family contains slices of different sizes, any volume positioned inside should
 fit into the smallest one.
    Examples for specific divisions according to shape types can be found inside
 shape classes.

        TGeoVolume::Divide(N, Xmin, Xmax, "X");

   The GEANT3 option MANY is supported by TGeoVolumeOverlap class. An overlapping
 volume is in fact a virtual container that does not represent a physical object.
 It contains a list of nodes that are not his daughters but that must be checked
 always before the container itself. This list must be defined by users and it
 is checked and resolved in a priority order. Note that the feature is non-standard
 to geometrical modelers and it was introduced just to support conversions of
 GEANT3 geometries, therefore its extensive usage should be avoided.

   Volume assemblies (TGeoVolumeAssembly)


 Assemblies a volumes that have neither a shape or a material/medium. Assemblies
 behave exactly like normal volumes grouping several daughters together, but
 the daughters can never extrude the assembly since this has no shape. However,
 a bounding box and a voxelization structure are built for assemblies as for
 normal volumes, so that navigation is still optimized. Assemblies are useful
 for grouping hierarchically volumes which are otherwise defined in a flat
 manner, but also to avoid clashes between container shapes.
 To define an assembly one should just input a name, then start adding other
 volumes (or volume assemblies) as content.