I should add the prescription report also disagrees with the ZPL19 output.

Hey Sean,

I think the issue might be a round-off error in the ATAN2 subroutine of the ZPL macro, namely the ATAN2 is checking exactly for equaling 0 rather than looking at a tolerance.  I would look at changing the nested IF statements that are checking when x = 0:

SUB ATAN2
    IF x > 0
        val = ATAN(y/x)
    ELSE
        IF x < 0 & y >= 0
            # this is where TiltZ is incorrectly calculated in your file
            val = ATAN(y/x) + pi
        ELSE
            IF x < 0 & y < 0
                val = ATAN(y/x) - pi
            ELSE
                IF ABSO(x) < 1e-10 & y > 0
                    # this is where the TiltZ should be calculated
                    val = pi / 2
                ELSE
                    IF ABSO(x) < 1e-10 & y < 0
                        val = -pi / 2
                    ELSE
                        val = 9e9
                    ENDIF
                ENDIF
            ENDIF
        ENDIF
    ENDIF
RETURN

Basically, in your scenario, the ATAN2 function has x = 0 (R11) and y = 0.2181550273 (-R12).  Going through this logic, the ATAN2 should be calculated in the 4th IF statement where val = pi / 2.  It appears that your system is in the 2nd IF statement and y = 0 (so ATAN = pi) and then the macro is returning pi.

I tried to recreate your file with a simple Coordinate Break and optimizing for your global rotation matrix, but I’m unable to reproduce your results.  I used GLCR operands with the Target values set to your file & the Weight equal to 1, then optimized on TiltX, TiltY, TiltZ.  This gives me the 90deg for TiltZ:

P.S. after reviewing the logic in ATAN2, I have 2 mistakes when checking for x == 0...there should be a second equal sign to check for equality rather than the single equal sign that is used for assignment.  This still shouldn’t give the error you’re seeing because this logic is farther down the multi-part IF statements but it should still be updated.  

Hi Michael,

Thanks for the reply. I was able to recreate the issue with the sample file from the knowledgebase article. I copied the tilt Y value from my file and pasted it into the sample file. You can see the tilt Z value in the merit function editor does not agree with the multi configuration editor or the prescription report. Maybe this is due to a rounding error in the ZPL code?

Here are all the digits that I pasted in if you want to try it yourself. 

7.739930805223027E+001

Hey Sean,

Thanks for providing this feedback.  Yes, it is a roundoff error because if you look at which “case” the ATAN2 function is returning for the TiltZ, it’s the temp=2.2 case, so the ZPL is thinking that x<0 when in reality, x=0.  Since x=0 is a singular case, this should actually be checked first, and we should also rely on a threshold value as I originally mentioned.  

Here is the modified ATAN2 function that you should be able to copy & paste into your macro and have it work:

SUB ATAN2
    val = 9e9
    IF ABSO(x) < 1e-10
        IF y > 0 
            val = pi / 2
        ELSE 
            val = -pi / 2
        ENDIF
    ELSE
        IF x > 0
            val = ATAN(y / x)
        ELSE 
            IF y < 0
                val = ATAN(y / x) - pi
            ELSE 
                val = ATAN(y / x) + pi
            ENDIF
        ENDIF
    ENDIF
RETURN