Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!iuvax!ux1.cso.uiuc.edu!ux1.cso.uiuc.edu!uxe.cso.uiuc.edu!mcdonald
From: mcdonald@uxe.cso.uiuc.edu
Newsgroups: comp.graphics
Subject: Re: Tilted ellipse.
Message-ID: <46900043@uxe.cso.uiuc.edu>
Date: 13 Oct 89 00:42:00 GMT
References: <4821@druco.ATT.COM>
Lines: 40
Nf-ID: #R:druco.ATT.COM:4821:uxe.cso.uiuc.edu:46900043:000:1542
Nf-From: uxe.cso.uiuc.edu!mcdonald    Oct 12 19:42:00 1989


/* Written 11:35 pm  Oct 10, 1989 by mccaugh@s.cs.uiuc.edu in uxe.cso.uiuc.edu:comp.graphics */
 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)
/* End of text from uxe.cso.uiuc.edu:comp.graphics */

I see that you are also at the U of Ill. Are you a grad or undergrad?
If you are an undergrad, did you take freshman English? CAn you read???

The request was for a FAST tilted ellipse drawer. I, and probably
most other people, are perfectly aware of rotation matrices. But
rotating point by point with a rotation matrix is hardly FAST. In
fact it is b...o...g s........l.........o..........w. Even with
cos and sin tables. What I am looking for is something that
can be stuck in Bresnahan's algorithm. 
And, please, have some nice way of specifying the ellipse (like
major and minor axes and rotation angle, or tangent thereof.

Doug McDonald