class TGeoChecker: public TObject

 Default constructor

 Constructor for a given geometry

 Destructor

 Print current operation progress.

 Check pushes and pulls needed to cross the next boundary with respect to the
 position given by FindNextBoundary. If radius is not mentioned the full bounding
 box will be sampled.

 Check the boundary errors reference file created by CheckBoundaryErrors method.
 The shape for which the crossing failed is drawn with the starting point in red
 and the extrapolated point to boundary (+/- failing push/pull) in yellow.

 Geometry checking. Opional overlap checkings (by sampling and by mesh). Optional
 boundary crossing check + timing per volume.

 STAGE 1: extensive overlap checking by sampling per volume. Stdout need to be
  checked by user to get report, then TGeoVolume::CheckOverlaps(0.01, "s") can
  be called for the suspicious volumes.
 STAGE2 : normal overlap checking using the shapes mesh - fills the list of
  overlaps.
 STAGE3 : shooting NRAYS rays from VERTEX and counting the total number of
  crossings per volume (rays propagated from boundary to boundary until
  geometry exit). Timing computed and results stored in a histo.
 STAGE4 : shooting 1 mil. random rays inside EACH volume and calling
  FindNextBoundary() + Safety() for each call. The timing is normalized by the
  number of crossings computed at stage 2 and presented as percentage.
  One can get a picture on which are the most "burned" volumes during
  transportation from geometry point of view. Another plot of the timing per
  volume vs. number of daughters is produced.
 All histos are saved in the file statistics.root

 Propagate from START along DIR from boundary to boundary until exiting
 geometry. Fill array of hits.

 Score a hit for VOL

 Set number of points to be generated on the shape outline when checking for overlaps.

 Compute timing per "FindNextBoundary" + "Safety" call. Volume must be
 in the current path.

 Shoot nrays with random directions from starting point (startx, starty, startz)
 in the reference frame of this volume. Track each ray until exiting geometry, then
 shoot backwards from exiting point and compare boundary crossing points.

 Clean-up the mesh of pcon/pgon from useless points

 Check if the 2 non-assembly volume candidates overlap/extrude. Returns overlap object.

 Check illegal overlaps for volume VOL within a limit OVLP by sampling npoints
 inside the volume shape.

 Compute number of overlaps combinations to check per volume

 Check illegal overlaps for volume VOL within a limit OVLP.

 Print the current list of overlaps held by the manager class.

--- Draw point (x,y,z) over the picture of the daughers of the volume containing this point.
   Generates a report regarding the path to the node containing this point and the distance to
   the closest boundary.

 Test for shape navigation methods. Summary for test numbers:
  1: DistFromInside/Outside. Sample points inside the shape. Generate
    directions randomly in cos(theta). Compute DistFromInside and move the
    point with bigger distance. Compute DistFromOutside back from new point.
    Plot d-(d1+d2)
 2: Safety test. Sample points inside the bounding and compute safety. Generate
    directions randomly in cos(theta) and compute distance to boundary. Check if
 Distance to boundary is bigger than safety

  Test TGeoShape::DistFromInside/Outside. Sample points inside the shape. Generate
 directions randomly in cos(theta). Compute d1 = DistFromInside and move the
 point on the boundary. Compute DistFromOutside and propagate with d2 making sure that
 the shape is not re-entered. Swap direction and call DistFromOutside that
 should fall back on the same point on the boundary (at d2). Propagate back on boundary
 then compute DistFromInside that should be bigger than d1.
    Plot d-(d1+d2)

 Check of validity of safe distance for a given shape.
 Sample points inside the 2x bounding box and compute safety. Generate
 directions randomly in cos(theta) and compute distance to boundary. Check if
 distance to boundary is bigger than safety.

 Check of validity of the normal for a given shape.
 Sample points inside the shape. Generate directions randomly in cos(theta)
 and propagate to boundary. Compute normal and safety at crossing point, plot
 the point and generate a random direction so that (dir) dot (norm) <0.

 Generate a lego plot fot the top volume, according to option.

 Draw random points in the bounding box of a volume.

 Randomly shoot nrays from point (startx,starty,startz) and plot intersections
 with surfaces for current top node.

 shoot npoints randomly in a box of 1E-5 arround current point.
 return minimum distance to points outside
 make sure that path to current node is updated
 get the response of tgeo

 Shoot one ray from start point with direction (dirx,diry,dirz). Fills input array
 with points just after boundary crossings.
   Int_t array_dimension = 3*dim;

 Check time of finding "Where am I" for n points.

--- Geometry overlap checker based on sampling.

 Estimate weight of top level volume with a precision SIGMA(W)/W
 better than PRECISION. Option can be "v" - verbose (default).

 count voxel timing

 Returns optimal voxelization type for volume vol.
   kFALSE - cartesian
   kTRUE  - cylindrical

 constructors