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From: akcs.mitchell@hpcvbbs.UUCP (Mitchell Dickerman)
Newsgroups: comp.sys.handhelds
Subject: Re: plotting relations
Keywords: truth, relation, plot
Message-ID: <276c3a53:1419.8comp.sys.handhelds;1@hpcvbbs.UUCP>
Date: 17 Dec 90 03:40:05 GMT
References: <62CA96D8A0002764@gacvx2.gac.edu> <1990Dec14.202128.509@portia.Stan
Lines: 49

This weekend I've been busy working on the relation-plotting problem.
Allow me to update you. I did in fact write a program to take a
plot like X^Y-Y^X<=0 and turn it into just the outline of the shaded
areas. Unfortunately, it took around 35 minutes, which on top of the
intial 15 minutes for the first plot, was unacceptable. Then I worked on
a program which, when plotted, returned the graph of where a sign change
occurs. I revised it a couple of times, and here it is:
%%HP: T(3)A(R)F(.);
\<< 'Y^X-X^Y' \->NUM
SIGN DUP X Y R\->C
C\->PX OBJ\-> DROP SWAP
DROP
  IF # 0h ==
  THEN
    IF 0 ==
    THEN 1
    ELSE 0
    END
  ELSE
    IF 0 ==
    THEN 1
    ELSE
      IF DUP ROT
ROT * -1 ==
      THEN 1
      ELSE 0
      END
    END
  END
\>>
(Note: replace 'Y^X-X^Y' with whatever relation you want to plot.)
This takes about 41 minutes to plot, which is still terribly long. About
a third of the time is that initial check to see if we're at the top of
the screen. All it's doing is getting the Y pixel coordinate. Does anyone
know of a SYSEVAL that returns it? That would speed things up
dramatically. Elaborating more on the program, it simply gets the sign at
the current point, then checks to see if we're at the top of the screen,
in which case we only check to see if the sign is 0. After that, we leave
the sign on the stack for the next point to compare against. If we're not
at the top, it checks to see if the sign is 0. If it's not, it checks to
see if the current sign times the previous one is -1, which would
indicate a sign change. Either way, it leaves the last sign on the stack
for future checks. The reason for checking for the top of the screen is
that I don't want it comparing the top sign of one column to the bottom
sign from the previous one, it wouldn't make sense. 
     To use this, simply store the program as the equation to be plotted
and choose the TRUTH plot. If someone can speed this up, it would be
greatly appreciated.
 
Mitch