Dave VanHorn wrote:

> This is hard for me. Apparently not for you. I apologize for my
> stupidity.

  I just get rather frustrated when I'm offering what I have every
confidence is the simple answer, and appear to be ignored.

> I follow, I think, I will try to code this.

  The concept of octants and normalization to the first octant rather
than the use of one all-encompassing function was also described by
another poster.  That uses simple logic functions instead of maths, and
has side-benefits, such as max(mod(X),mod(Y)) being an adequate
approximation of the Radius as a quality indicator.

> I get confused when another book uses csc (I assume cosecant) in the
> same position, same formula.

  Using the *mathematical* convention that 0¡ is the positive X-axis,
Angle=csc(Y/R)
     =atn(Y/X)

  Swap X and Y if you regard the positive Y-axis as 0¡.

  In the first octant (i.e., angle less than 45¡), R is not too
different to X, identical for small values.  Insofar as it *is*
different, I realise that the cosecant function is actually more linear
than the arctangent (for this octant - above 45¡ both are hideous).

  Since however, this requires intermediate determination of the radius
and *that* requires quite a lot of calculation including a square root,
I am sure it is far easier to use the expression for arctangent
requiring only one operation (division) on the X and Y values
beforehand.

> teachers that should have been security guards at a donut factory..)

  Hey, fair go, donut factories need good guards too!
-- 
  Cheers,
        Paul B.