Suppose to have an old vertical declining dial with italic hours.
Starting from an arbitrary cartesian reference system (horizontal x axis
positive to the right, vertical y axis positive down) we take the
crossing point between the equinox line and the
17 hour line : x=92.3 , y=82.3
between the equinox line and the 19 hour line : x=121.8 , y=64.7
crossing point between the equinox line and the 21 hour line : x=137.9 ,
Let's found the original design parameters of the dial.
Define a new vertical dial in File->Parameters -> Type.
Do not care on dial parameters, the only purpose is to
define the type of dial you are dealing with : horizontal, vertical,
inclined etc. (only horizontal, vertical and inclined dials can now be
managed by the reverse engineering tool).
In the same window set "Time zone displayed" to
"true local" so that the longitude of the place will not be
considered in the problem.
Check the "measured points"
box in the Options window so that the input points will be
drawn on the dial.
Uncheck all the day lines boxes
except for the equinox line.
Uncheck "french hours" and
check "italic hours".
Uncheck the "hour lines over
the horizon only" box.
Open the Tools -> Reverse
engineering window and introduce the three measured points.
The Reverse engineering window
will look like the following one :
Now click the OK button, you will see the following graph :
Here you can see the points you have just defined (only
two are actually visible at the right of the dial). Italic hour lines
are drawn but they are still erroneous of course.
Now in the Tools -> Reverse Engineering window click the
Global search button.
After a few seconds the following window will be displayed :
This message says that after 49 iterations the algorithm
stopped because the last step was below the threshold, the RMS final
error is 0.00099, the last step in the solution vector was 1.18e-29 and
the residual error in the 4 equations is less than 0.002.
Now close the window.
The latitude, declination, ort. pos.
x and y fields contain the result to the problem : 40.01, 30.05, 24.98 ,
125.06 and 37.01 (input data have been obtained with lat=40 , decl=30
and style=25) .
Click the "Insert into the project" and then
the "OK" button.
The following graph will be displayed, showing the
resulting dial together with the input data.