====== Titled modules ======

We can tilt the pixel barrel modules around their transverse axis by specifying the coordinates of each module. The syntax is as follows:

  Barrel PXB {
    numLayers 4
    //numModules 4
    maxZ 205                    <--- need to specify maxZ if using titled modules
    innerRadius 29
    outerRadius 161
    width 22
    length 71
    smallParity 1
    bigParity -1
    Layer 2 { tiltedLayerSpecFile pixel_BL2_tilt.csv }  <--- reference file of module coordinates here
    Layer 3 {
      radiusMode fixed
      placeRadiusHint 109
    }
  }

Note: maxZ needs to be less than the Zcoord of the last module in the csv file.
The csv file of module coordinates must have 7 columns and as many rows as modules in a rod. Each row has the coordinates of an inner and outer module of a layer, with columns Ycoord[mm] Zcoord[mm] Rotation[deg] Ycoord[mm] Zcoord[mm] Rotation[deg] Nrods. It looks like this:

  68 0   0  70 0   0  24
  68 70  10 70 70  10 24
  68 140 20 70 140 20 24
  68 210 30 70 210 30 24

{{:phase2:screen_shot_2015-01-28_at_09.52.35.png?direct&300|}}

End cap modules cannot be tilted around their transverse axis. This is an excerpt from the tkLayout paper:

    Modules can be rotated around their longitudinal axis by a skew angle α. This effectively
  increases the resolution seen by tracks by a factor cos(α), but, on the other hand, reduces the
  φ-aperture by the same amount.
    tkLayout also supports rotating barrel modules around their transverse axis by a tilt angle β,
  in a layout called “tilted barrel” (see figure 6), where barrel modules are increasingly tilted the
  further they are on the z axis (up to β = π/2 when they effectively become endcap modules). The
  advantage of the tilted layout is that the modules’ aperture in θ (the angle relative to the beam
  axis) is increased, so the number of modules to cover the same volume is reduced, to the benefit of
  material amount and cost.