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Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!mitel!sce!cognos!neptune!writer
From: writer@neptune.UUCP (Writer)
Newsgroups: comp.cog-eng,comp.sys.mac,comp.sys.mac.hypercard
Subject: Re: pie menus
Message-ID: <712@neptune.UUCP>
Date: 8 Dec 89 19:00:24 GMT
References: <4352@ur-cc.UUCP> <2477@draken.nada.kth.se>
Reply-To: writer@neptune.UUCP (Nigel Robinson)
Organization: Cognos Inc., Ottawa, Canada
Lines: 68

In article <2477@draken.nada.kth.se> krona@nada.kth.se (Kjell Krona) writes:
>I have made a VERY simple stack with pie-menus...
>... This is simple with four slices, but rapidly becomes more complicated...

This got me thinking and programming, so here is my gift to the world:
-a button that, when clicked, returns the angle from the central point
of the button.  This is based on the following assumptions (please 
don't abuse me if I did this un-mathematically... it's been years 
since a history prof has asked me to calculate the cosine of Napoleon.)

Quadrants and angles:
     ---0/360---
     ..4..|..1..
     .....|.....
 270 ----------- 90 deg
     ..3..|..2..
     .....|.....
     --180 deg--

Here's the button script:

on mouseUp
  put the rect of me into var
  put trunc((item 1 of var+item 3 of var)/2) into rx
  put trunc((item 2 of var+item 4 of var)/2) into ry
    -- rx and ry are the coordinates of the middle of the button
  if (item 1 of the clickloc)> rx
  then put "1 2" into var1 else put "3 4" into var1
    -- if the click is on the right-hand side of the vertical 
    -- centerline, then it is in quadrant 1 or 2
  if (item 2 of the clickloc)> ry
  then put "2 3" into var2 else put "1 4" into var2
    -- if the click is below the horizontal centerline,
    -- then it is in quadrant 2 or 3
  repeat with count = 1 to 4
    if var1 contains count and var2 contains count
    then put count into quad
  end repeat
    -- find the shared quadrant 
    -- quad has the appropriate quadrant number in it (see diagram)
  
  put (item 1 of the clickloc)-rx into lx
  put -1*((item 2 of the clickloc)-ry) into ly
    -- align lx and ly (the click) to the center point of the button,
    -- in standard x-y coordinates (not the edge of the screen)

  if quad = 1 then put 0 into temp
  if quad = 2 then put -180 into temp
  if quad = 3 then put 180 into temp
  if quad = 4 then put -360 into temp
    -- housekeeping to keep the angle and the quadrants correct

  put abs(trunc(temp+(atan((abs(lx)/abs(ly)))*57.730721))) into ang

  put ang -- the angle! (Yay!)

end mouseUp

So there you have it... many apologies if I've typo'd.
Your button can be any size, and if you are using it with a diagram,
then put it on the background level, or make it transparent.

Center it around a pie chart, and this should give you enough information 
to determine where in the pie the user clicked.  You could use
(lx^2+ly^2) = r^2 (where r is the radius of the pie) to check if the user
is within the bounds of the circle.

-Nigel, Waterloo co-op at large.