OpenEuphoria

Re: geometric problem

• Posted by "Carl R. White" <C.R.White at SCM.BRAD.AC.UK> Mar 18, 1999
• 551 views

I'll attempt to sum up what I _think_ you've said :)

You have the following:

    V1
   /  \.
  /     V2
 /       |
V4       |
`-.    P `. -- All Vn to Vm lines are *supposed* to be straight :)
   `-.    |
      `-.V3

And want to translate to:

V1'------V2'
|         |
|         |
|      P' |
|         |
V4'------V3'


You never said how big V'(1,2,3,4) has to be though...

Why you want to do this (unless you're writing a ray-tracer) is beyond me,
but I'll have a go. I'm thinking on my feet here. Be warned!

The first sensible thought that occurs is the following: (this will not
provide a correct answer. Approximation only)
1) Figure out the coordinates of the rectangle (X) that would completely
   surround V(1,2,3,4).
   In this case (from the diagrams above) they're:
   X1 = {V4.x,V1.y}
   X2 = {V3.x,V1.y}
   X3 = V3
   X4 = {V4.x,V3.y}

2) Alter the P position like so:
   P.x = P.x + (X(1,2,3,4).x - V(1,2,3,4).x ) / 4
   P.y = P.y + (X(1,2,3,4).y - V(1,2,3,4).y ) / 4

   ^^^ This is really the all-important bit. There's probably a much
   better way to do this, but I'd have to sit for a few hours to work it
   out. As it stands, I've used an arithmetical mean of the differences of
   respective x and y coordinates. Maybe a geometric mean may have been
   better... ;)

3) Scale X(1,2,3,4).x, X(1,2,3,4).y and P to the sizes you want them to be
   (multiply or divide) to turn them into V'(1,2,3,4) and P'.
   You'll have to offset the coordinates so that one of the Xs is {0,0}
   for the scaling. Add the offset back in to complete the calculation.

4) If this was homework, I hope I got it horribly wrong. ;)

HTH,
Carl

PS If you don't understand the notation that I munged for this post,
   mail again and I'll explain it. :)

--
Carl R White -- cyrek- at -bigfoot.com -- http://www.bigfoot.com/~cyrek
 aka Cyrek   --    No hyphens :)    --       Bigfoot URL Alias