Re: geometry-challenged

[Jim Hurley]

Message: 4
Date: Sun, 25 Jan 2004 19:22:13 -0500
From: [EMAIL PROTECTED]
Subject: Re: geometry-challenged
To: [EMAIL PROTECTED]
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=iso-8859-1
sez [EMAIL PROTECTED]:
 I'm not sure if this helps, but the function "intersection" below
 will return the intersection of any two lines.
   I tried the function on two *non*-intersecting lines, and it gave 
me a "divide by zero" error. Not good. You need to find the 
mathematical intersection of the infinite lines defined by the two 
pairs of endpoints, and *then* decide whether or not that 
intersection point is within *both* of the line *segments* defined 
by said points.

------------------------------

Message: 5
Date: Sun, 25 Jan 2004 20:02:21 -0500
From: Brian Yennie <[EMAIL PROTECTED]>
Subject: Re: geometry-challenged
To: How to use Revolution <[EMAIL PROTECTED]>
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=US-ASCII; format=flowed
For the problem at hand, it should suffice to add a little if-logic to
the beginning.
A line between two non-overlapping objects will always intersect
exactly one of the sides of each object- you just have to pick the
right one and _then_ use the intersection function.
With that said, an intersection function should probably error
gracefully for parallel lines (i.e. non-intersecting).
- Brian
The function should yield the point of intersection of the two 
infinite lines defined by the line segments. It may or may not lie 
within the end points of either line segment.

Could you send me the points which gave you the error message.? 
(Notice that the values returned are not rounded. I you want to 
insert them as graphic points you may want to return round(x) & comma 
& round(y).)

Thanks,

Jim.

P.S. The following function helps to deal with the problem of parallel lines.

function intersection p1,p2,pp1,pp2
put item 1 of p1 into x1
  put item 2 of p1 into y1
  put item 1 of p2 into x2
  put item 2 of p2 into y2
  put item 1 of pp1 into xp1
  put item 2 of pp1 into yp1
  put item 1 of pp2 into xp2
  put item 2 of pp2 into yp2
  if x1 = x2 or xp1 = xp2 then
    if x1 = x2 then
      return x1&comma&yp2 + (x1-xp2)*(yp2-yp1)/(xp2-xp1)
    else
      return xp2&comma& y2 + (xp1-x2)*(y2-y1)/(x2-x1)
    end if
  end if
  if (y2-y1)/(x2-x1) = (yp2-yp1)/(xp2-xp1) then add .0000001 to 
y2--if lines are parallel
  -- This produces a VERY large x or y coordinate. Parallel for all 
practical purposes.
  put yp2 - y2 + x2*(y2-y1)/(x2 - x1) - xp2*(yp2 - yp1)/(xp2 - xp1) 
into numerator
  put ((y2 - y1)/(x2 - x1) -(yp2 - yp1)/(xp2-xp1)) into denom
  put numerator / denom into x
  put y2 + (x-x2) *(y2-y1)/(x2-x1) into y
  return x & comma & y
end intersection

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