Points in a circular area

[Jim Hurley]

>
>Message: 2
>Date: Thu, 29 Jan 2004 15:26:38 -0800 (PST)
>From: Alejandro Tejada <capellan2000 at yahoo.com>
>Subject: Re: Points in a circular area
>To: use-revolution at lists.runrev.com
>Message-ID: <20040129232638.87440.qmail at web40504.mail.yahoo.com>
>Content-Type: text/plain; charset=us-ascii
>
>on Thu, 29 Jan 2004
>Dar Scott wrote:
>
>>  Some years ago I designed a model and library for
>>  working with abstractions of drawings and
>>  paintings in a functional (that is f()
>>  manner) way.
>>
>>  In that model the plane could be partitioned by a
>>  line or by a circle and other shapes. 
>>  A pie shape is the union (ANDing) of two line
>>  partitions and a circle partition.
>
>>  For this particular case, it might be easier for you
>>  to arctan2 points relative to the center to see
>>  if they are in the right angle range and
>>  then check the distance to see if that is small
>>  enough.
>
>If i interpret right your recommendations,
>it's similar to the procedure that Jim Hurley
>is suggesting to use. Now, i'll code a solution
>and post the script for speed enhancements. ;-)
>
>>  In rendering (or creating point lists) I am trying
>>  to use interval arithmetic and am putting that off
>>  until some performance changes in Revolution. 
>>  This method allows tests to work on
>>  whole zones of pixels in one calculation.
>
>This sounds useful. Could externals helps for
>these tasks?
>
>>  The line tests will be faster than the arctan2
>>  tests for this method, because of the ignorance
>>  involved in interval arithmetic. 
>
>I've read that assembler code is faster than c code.
>
>>  In the mean time you might try testing each pixel (I
>>  assume you mean pixels) in the bounding rect
>>  of the circle of which the arc is part.
>
>Let's see how much time does this calculation takes.


Al,

Just for an estimate of the time needed for the trial and error 
method, I ran the following handler:


on mouseUp
   put 30 into tAngle
   put 100 into R
   put "" into results
   put the sec into startTime
   startTurtle
   repeat with x = 0 to R
     repeat with y = 0 to R
       put raCor(x,y) into ra
       --Test to see if the point x,y is in the wedge.
       if item 1 of ra < R and item 2 of ra < tAngle then put x,y & 
return after results
     end repeat
   end repeat
   put results into field 1
   put the sec - starttime
   beep
end mouseUp

It determines all integer coordinates inside a circular wedge of 
radius R (100) and arc tAngle (30 degrees). There are 2,666 points 
and it takes a little over a second to compute.

(The function raCor(x,y) returns the radial coordinates (radius and 
angle) corresponding to the rectangular coordinates x,y.)

Hope this gives you some idea on times.

Jim