If the calorimeters and the muon detectors are drawn in, e.g. the Y/X projection (5.1 Y/X Projection), the inner tracking chambers are so small that track recognition may suffer. This problem may be partially solved by applying a fisheye transformation, which allows a relative magnification of the inner chambers without increasing the outer radius. Besides, since the outer parts of the detector are in sight, tracks are still completely visible.
A fisheye transformation is available in most projections:
Y/X, φ/ρ and ρ/Z projections
When ρ (√(X2+Y2)) is known in a projection (namely Y/X (5.1 Y/X Projection), φ/ρ (5.5 φ/ρ Projection) and ρ/Z (5.4 ρ/Z Projection)), it is modified as:
ρnew = ρ × (1+d×ρmax) / (1+d×ρ)
where ρmax is the outer radius and d the fisheye distortion factor.
In Y/X (5.1 Y/X Projection) the azimuthal angle is unchanged and Xnew, Ynew are calculated from φ and ρnew, in φ/ρ (5.5 φ/ρ Projection) the azimuthal angle φ is unchanged.
In the case of the ρ/Z (5.4 ρ/Z Projection) projection the value of Z is changed according to the formula:
Znew = Z × (1+d×Zmax) / (1+d×Z)
where Zmax is the outer Z range. In this projection, radial tracks are slightly curved by the fisheye.
Other projections
In all other projections where the fisheye is available, the axes representing distance are transformed with the formula used to transform Z in the ρ/Z (5.4 ρ/Z Projection) projection.
Applying the Fisheye Transformation
The fisheye interaction is selected for the current canvas pad by clicking on the Fisheye tab of the interaction control (3.1.3 Interaction Control) in the Control Window. The label of the tab contains a toggle to activate and deactivate the fisheye and a box with the value of the distortion factor d. This value is modified by clicking the left mouse button and dragging the cursor over the picture. If the F modifier key is pressed while dragging, the data will not be updated, thus allowing for better response.
The Fisheye Pop-up Menu
The Fisheye Pop-up Menu can be accessed by right-clicking into the desired canvas pad. It contains the following set of utility operations:
Set no Fisheye - Switch off the fisheye interaction.
To Window Radius - Not implemented yet.