class AliITSv11Geometry: public TObject

 Given the two lines, one passing by (x0,y0) with slope m and
 the other passing by (x1,y1) with slope n, returns the coordinates
 of the intersecting point (xi,yi)
 Inputs:
    Double_t   m     The slope of the first line
    Double_t  x0,y0  The x and y coord. of the first point
    Double_t   n     The slope of the second line
    Double_t  x1,y1  The x and y coord. of the second point
 Outputs:
    The coordinates xi and yi of the intersection point
 Return:
    none.
 Created:      14 Dec 2009  Mario Sitta

 Given a lines  passing by (x0,y0) with slope m and a circle with
 radius rr and center (xc,yc), returns the coordinates of the
 intersecting points (xi1,yi1) and (xi2,yi2) (xi1 > xi2)
 Inputs:
    Double_t   m     The slope of the line
    Double_t  x0,y0  The x and y coord. of the point
    Double_t   rr     The radius of the circle
    Double_t  xc,yc  The x and y coord. of the center of circle
 Outputs:
    The coordinates xi and yi of the intersection points
 Return:
    kFALSE if the line does not intercept the circle, otherwise kTRUE
 Created:      18 Dec 2009  Mario Sitta

 Given the two points (x0,y0) and (x1,y1) and the location x, returns
 the value y corresponding to that point x on the line defined by the
 two points.
 Inputs:
    Double_t  x0  The first x value defining the line
    Double_t  y0  The first y value defining the line
    Double_t  x1  The second x value defining the line
    Double_t  y1  The second y value defining the line
    Double_t   x  The x value for which the y value is wanted.
 Outputs:
    none.
 Return:
    The value y corresponding to the point x on the line defined by
    the two points (x0,y0) and (x1,y1).

 Given the two points (x0,y0) and (x1,y1) and the location y, returns
 the value x corresponding to that point y on the line defined by the
 two points.
 Inputs:
    Double_t  x0  The first x value defining the line
    Double_t  y0  The first y value defining the line
    Double_t  x1  The second x value defining the line
    Double_t  y1  The second y value defining the line
    Double_t   y  The y value for which the x value is wanted.
 Outputs:
    none.
 Return:
    The value x corresponding to the point y on the line defined by
    the two points (x0,y0) and (x1,y1).

 functions Require at parts of Volume A to be already defined.
 Retruns the value of Rmax corresponding to point z alone the line
 defined by the two points p.Rmax(i1),p-GetZ(i1) and p->GetRmax(i2),
 p->GetZ(i2).
 Inputs:
    TGeoPcon *p  The Polycone where the two points come from
    Int_t    i1  Point 1
    Int_t    i2  Point 2
    Double_t  z  The value of z for which Rmax is to be found
 Outputs:
    none.
 Return:
    Double_t Rmax the value corresponding to z

 Retruns the value of Rmin corresponding to point z alone the line
 defined by the two points p->GetRmin(i1),p->GetZ(i1) and
 p->GetRmin(i2),  p->GetZ(i2).
 Inputs:
    TGeoPcon *p  The Polycone where the two points come from
    Int_t    i1  Point 1
    Int_t    i2  Point 2
    Double_t  z  The value of z for which Rmax is to be found
 Outputs:
    none.
 Return:
    Double_t Rmax the value corresponding to z

 Retruns the value of Rmin corresponding to point z alone the line
 defined by the two points p->GetRmin(i1),p->GetZ(i1) and
 p->GetRmin(i2), p->GetZ(i2).
 Inputs:
    Double_t az  Array of z values
    Double_t  r  Array of r values
    Int_t    i1  First Point in arrays
    Int_t    i2  Second Point in arrays
    Double_t z   Value z at which r is to be found
 Outputs:
    none.
 Return:
    The value r corresponding to z and the line defined by the two points

 Retruns the value of Z corresponding to point R alone the line
 defined by the two points p->GetRmin(i1),p->GetZ(i1) and
 p->GetRmin(i2),p->GetZ(i2)
 Inputs:
    TGeoPcon *p  The Poly cone where the two points come from.
    Int_t    i1  First Point in arrays
    Int_t    i2  Second Point in arrays
    Double_t r   Value r min at which z is to be found
 Outputs:
    none.
 Return:
    The value z corresponding to r min and the line defined by
    the two points

 Retruns the value of Z corresponding to point R alone the line
 defined by the two points p->GetRmax(i1),p->GetZ(i1) and
 p->GetRmax(i2),p->GetZ(i2)
 Inputs:
    TGeoPcon *p  The Poly cone where the two points come from.
    Int_t    i1  First Point in arrays
    Int_t    i2  Second Point in arrays
    Double_t r   Value r max at which z is to be found
 Outputs:
    none.
 Return:
    The value z corresponding to r max and the line defined by
    the two points

 Retruns the value of z corresponding to point R alone the line
 defined by the two points p->GetRmax(i1),p->GetZ(i1) and
 p->GetRmax(i2),p->GetZ(i2)
 Inputs:
    Double_t  z  Array of z values
    Double_t ar  Array of r values
    Int_t    i1  First Point in arrays
    Int_t    i2  Second Point in arrays
    Double_t r   Value r at which z is to be found
 Outputs:
    none.
 Return:
    The value z corresponding to r and the line defined by the two points

 General Outer Cone surface equation Rmax.
 Intputs:
     TGeoPcon  *p   The poly cone where the initial point comes from
     Int_t     ip   The index in p to get the point location
     Double_t  tc   The angle of that part of the cone is at
     Double_t   z   The value of z to compute Rmax from
     Double_t  th   The perpendicular distance the parralell line is
                    from the point ip.
 Outputs:
     none.
 Return:
     The value Rmax correstponding to the line at angle th, offeset by
     th, and the point p->GetZ/Rmin[ip] at the location z.

 General Cone surface equation R(z).
 Intputs:
     Double_t  ar   The array of R values
     Double_t  az   The array of Z values
     Int_t     ip   The index in p to get the point location
     Double_t  tc   The angle of that part of the cone is at
     Double_t   z   The value of z to compute R from
     Double_t  th   The perpendicular distance the parralell line is
                    from the point ip.
 Outputs:
     none.
 Return:
     The value R correstponding to the line at angle th, offeset by
     th, and the point p->GetZ/Rmax[ip] at the locatin z.

 General Inner Cone surface equation Rmin.
 Intputs:
     TGeoPcon  *p   The poly cone where the initial point comes from
     Int_t     ip   The index in p to get the point location
     Double_t  tc   The angle of that part of the cone is at
     Double_t   z   The value of z to compute Rmin from
     Double_t  th   The perpendicular distance the parralell line is
                    from the point ip.
 Outputs:
     none.
 Return:
     The value Rmin correstponding to the line at angle th, offeset by
     th, and the point p->GetZ/Rmin[ip] at the location z.

 General Outer cone Surface equation for z.
 Intputs:
     TGeoPcon  *p   The poly cone where the initial point comes from
     Int_t     ip   The index in p to get the point location
     Double_t  tc   The angle of that part of the cone is at
     Double_t   r   The value of Rmax to compute z from
     Double_t  th   The perpendicular distance the parralell line is
                    from the point ip.
 Outputs:
     none.
 Return:
     The value Z correstponding to the line at angle th, offeset by
     th, and the point p->GetZ/Rmax[ip] at the location r.

 General Outer cone Surface equation for z.
 Intputs:
     Double_t  ar   The array of R values
     Double_t  az   The array of Z values
     Int_t     ip   The index in p to get the point location
     Double_t  tc   The angle of that part of the cone is at
     Double_t   r   The value of Rmax to compute z from
     Double_t  th   The perpendicular distance the parralell line is
                    from the point ip.
 Outputs:
     none.
 Return:
     The value Z correstponding to the line at angle th, offeset by
     th, and the point p->GetZ/Rmax[ip] at the locatin r.

 General Inner cone Surface equation for z.
 Intputs:
     TGeoPcon  *p   The poly cone where the initial point comes from
     Int_t     ip   The index in p to get the point location
     Double_t  tc   The angle of that part of the cone is at
     Double_t   r   The value of Rmin to compute z from
     Double_t  th   The perpendicular distance the parralell line is
                    from the point ip.
 Outputs:
     none.
 Return:
     The value Z correstponding to the line at angle th, offeset by
     th, and the point p->GetZ/Rmin[ip] at the location r.

 Given a initial point z0,r0, the initial angle theta0, and the radius
 of curvature, returns the point z1, r1 at the angle theta1. Theta
 measured from the r axis in the clock wise direction [degrees].
 Inputs:
    Double_t rc     The radius of curvature
    Double_t theta0 The starting angle (degrees)
    Double_t z0     The value of z at theta0
    Double_t r0     The value of r at theta0
    Double_t theta1 The ending angle (degrees)
 Outputs:
    Double_t &z1  The value of z at theta1
    Double_t &r1  The value of r at theta1
 Return:
    none.

 Given two lines defined by the points i1, i2,i3 in the TGeoPcon
 class p that intersect at point p->GetZ(i2) return the point z,r
 that is Cthick away in the TGeoPcon class q. If points i1=i2
 and max == kTRUE, then p->GetRmin(i1) and p->GetRmax(i2) are used.
 if points i2=i3 and max=kTRUE then points p->GetRmax(i2) and
 p->GetRmin(i3) are used. If i2=i3 and max=kFALSE, then p->GetRmin(i2)
 and p->GetRmax(i3) are used.
 Inputs:
    TGeoPcon  *p  Class where points i1, i2, and i3 are taken from
    Int_t     i1  First point in class p
    Int_t     i2  Second point in class p
    Int_t     i3  Third point in class p
    Double_t  c   Distance inside the outer surface/inner suface
                  that the point j1 is to be computed for.
    TGeoPcon  *q  Pointer to class for results to be put into.
    Int_t     j1  Point in class q where data is to be stored.
    Bool_t    max if kTRUE, then a Rmax value is computed,
                  else a Rmin valule is computed.
 Output:
    TGeoPcon  *q  Pointer to class for results to be put into.
 Return:
    none.

 Given two intersecting lines defined by the points (x0,y0), (x1,y1) and
 (x1,y1), (x2,y2) {intersecting at (x1,y1)} the point (x,y) a distance
 c away is returned such that two lines a distance c away from the
 lines defined above intersect at (x,y).
 Inputs:
    Double_t  x0 X point on the first intersecting sets of lines
    Double_t  y0 Y point on the first intersecting sets of lines
    Double_t  x1 X point on the first/second intersecting sets of lines
    Double_t  y1 Y point on the first/second intersecting sets of lines
    Double_t  x2 X point on the second intersecting sets of lines
    Double_t  y2 Y point on the second intersecting sets of lines
    Double_t  c  Distance the two sets of lines are from each other
 Output:
    Double_t  x  X point for the intersecting sets of parellel lines
    Double_t  y  Y point for the intersecting sets of parellel lines
 Return:
    none.

 Prints out the content of the TGeoTube. Usefull for debugging.
 Inputs:
   TGeoTube *a
 Outputs:
   none.
 Return:
   none.

 Prints out the content of the TGeoTubeSeg. Usefull for debugging.
 Inputs:
   TGeoTubeSeg *a
 Outputs:
   none.
 Return:
   none.

 Prints out the content of the TGeoConeSeg. Usefull for debugging.
 Inputs:
   TGeoConeSeg *a
 Outputs:
   none.
 Return:
   none.

 Prints out the content of the TGeoBBox. Usefull for debugging.
 Inputs:
   TGeoBBox *a
 Outputs:
   none.
 Return:
   none.

 Create ITS materials
 Defined media here should correspond to the one defined in galice.cuts
 File which is red in (AliMC*) fMCApp::Init() { ReadTransPar(); }
 Inputs:
    none.
 Outputs:
   none.
 Return:
   none.

 Draws a cross sectional view of the TGeoPcon, Primarily for debugging.
 A TCanvas should exist first.
  Inputs:
    TGeoPcon  *p  The TGeoPcon to be "drawn"
    Int_t  fillc  The fill color to be used
    Int_t  fills  The fill style to be used
    Int_t  linec  The line color to be used
    Int_t  lines  The line style to be used
    Int_t  linew  The line width to be used
    Int_t  markc  The markder color to be used
    Int_t  marks  The markder style to be used
    Float_t marksize The marker size
 Outputs:
   none.
 Return:
   none.

 Computes the angles, t0 and t1 corresponding to the intersection of
 the line, defined by {x0,y0} {x1,y1}, and the circle, defined by
 its center {xc,yc} and radius r. If the line does not intersect the
 line, function returns kFALSE, otherwise it returns kTRUE. If the
 line is tangent to the circle, the angles t0 and t1 will be the same.
 Inputs:
   Double_t x0   X of first point defining the line
   Double_t y0   Y of first point defining the line
   Double_t x1   X of Second point defining the line
   Double_t y1   Y of Second point defining the line
   Double_t xc   X of Circle center point defining the line
   Double_t yc   Y of Circle center point defining the line
   Double_t r    radius of circle
 Outputs:
   Double_t &t0  First angle where line intersects circle
   Double_t &t1  Second angle where line intersects circle
 Return:
    kTRUE, line intersects circle, kFALSE line does not intersect circle
           or the line is not properly defined point {x0,y0} and {x1,y1}
           are the same point.

 Basic function used to determine the ending angle and starting angles
 for rounded corners given the relative distance between the centers
 of the circles and the difference/sum of their radii. Case 0.
 Inputs:
   Double_t dx    difference in x locations of the circle centers
   Double_t dy    difference in y locations of the circle centers
   Double_t sdr   difference or sum of the circle radii
 Outputs:
   none.
 Return:
   the angle in Degrees

 Basic function used to determine the ending angle and starting angles
 for rounded corners given the relative distance between the centers
 of the circles and the difference/sum of their radii. Case 1.
 Inputs:
   Double_t dx    difference in x locations of the circle centers
   Double_t dy    difference in y locations of the circle centers
   Double_t sdr   difference or sum of the circle radii
 Outputs:
   none.
 Return:
   the angle in Degrees

 Function to compute the ending angle, for arc 0, and starting angle,
 for arc 1, such that a straight line will connect them with no
 discontinuities.

 Inputs:
    Double_t x0  X Coordinate of arc 0 center.
    Double_t y0  Y Coordinate of arc 0 center.
    Double_t r0  Radius of curvature of arc 0. For signe see figure.
    Double_t x1  X Coordinate of arc 1 center.
    Double_t y1  Y Coordinate of arc 1 center.
    Double_t r1  Radius of curvature of arc 1. For signe see figure.
 Outputs:
    Double_t t0  Ending angle of arch 0, with respect to x axis, Degrees.
    Double_t t1  Starting angle of arch 1, with respect to x axis,
                 Degrees.
 Return:
    none.

 Function to create the figure discribing how the function
 AnglesForRoundedCorners works.

 Inputs:
    Double_t x0  X Coordinate of arc 0 center.
    Double_t y0  Y Coordinate of arc 0 center.
    Double_t r0  Radius of curvature of arc 0. For signe see figure.
    Double_t x1  X Coordinate of arc 1 center.
    Double_t y1  Y Coordinate of arc 1 center.
    Double_t r1  Radius of curvature of arc 1. For signe see figure.
 Outputs:
    none.
 Return:
    none.

 Sets the debug flag for debugging output

 Clears the debug flag so no debugging output will be generated

 Returns the debug flag value

 Static functions

 Define Trig functions for use with degrees (standerd TGeo angles).
 Sine function

 Cosine function

 Tangent function

 Determine the intersection of two lines

 Output functions for debugging

 Prints out the contents of the TGeoArb8

 Prints out the contents of the TGeoPcon

 Function to create figure needed for this class' documentation