Message-Id: <9210020026.AA24511@sc.zib-berlin.dbp.de>
Reply-To: Mailing list for the LaTeX3 project <LATEX-L@vm.urz.Uni-Heidelberg.de>
Date:         Thu, 1 Oct 92 20:19:57 EDT
From: Michael Barr <barr@TRIPLES.MATH.MCGILL.CA>
Sender: Mailing list for the LaTeX3 project <LATEX-L@vm.urz.Uni-Heidelberg.de>
To: Multiple recipients of <LATEX-L@vm.urz.Uni-Heidelberg.de>
Subject:      Arctan
Status: R


I think the point about arctan has gotten a bit muddied.  What Paul was saying
was that if you are using something like latex \picture mode and want to
draw a line, you are likely to know the slope, not the angle and to go from
slope to angle is an arctan (BTW, that is the inverse function to tangent
a point that is relevant) computation.  But the worst is that to draw a line
using the angle informatin requires computing the slope (that is the tangent)
because you are going to have to know how many dots to move in the x-direction
for every one in the y direction (or vice versa depending on slope less than
or greater than 1).  So not only is the arctan hard to compute, but the
device driver is going to have to invert the computation anyway.  So this
suggests that a much better form for the angular parameter to take is
the slope, or else two numbers whose ratio is the slope.  This is the
way it is done in Latex now and that seems clearly to be the best way
to go.  I assume that some variation of this is used in xypic, since
doing an arctan in tex is unthinkable.

There is a downside.  It is hard to arrange an even angular distribution
using slopes.  I assume that the xypic line segment fonts simply have an
approximation to an even distribution.  That is more or less what the
latex line fonts do.

Michael Barr