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From: mccaugh@s.cs.uiuc.edu
Newsgroups: comp.graphics
Subject: Re: Tilted ellipse.
Message-ID: <207400032@s.cs.uiuc.edu>
Date: 12 Oct 89 00:40:11 GMT
References: <4821@druco.ATT.COM>
Lines: 24
Nf-ID: #R:druco.ATT.COM:4821:s.cs.uiuc.edu:207400032:000:747
Nf-From: s.cs.uiuc.edu!mccaugh    Oct 10 23:35:00 1989


 connors@druco.ATT.COM (Paul Connors) writes:

> 	Does anyone have an algorithm, or code, for drawing
> 	a TILTED ellipse quickly on a bit-mapped device?

 Assuming you can plot the pixels of an un-tilted ellipse (horizontal major
 axis and vertical minor axis) -- say, from:

              (x-h)^2     (y-k)^2
              ----     +  ----     =  1,  (centered at <h,k>)
               a^2         b^2


 the new coordinates <x',y'> of the point <x,y> on the original ellispe
 rotated an angle @ about its origin (at <h,k>) are as follows:

      x'  =  u + h, where:  u = (x-h)*cos(@) - (y-k)*sin(@)

 and  y'  =  v + k, where:  v = (x-h)*sin(@) + (y-k)*cos(@)
               
 Scott McCaughrin
 University of Illinois
 (mccaugh@s.cs.uiuc.edu)