Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!mnetor!uunet!husc6!ut-sally!utah-cs!utah-gr!spline!thomas
From: thomas%spline.uucp@utah-gr.UUCP (Spencer W. Thomas)
Newsgroups: comp.sys.mac
Subject: Re: Rotation Algorithm needed
Message-ID: <2129@utah-gr.UUCP>
Date: Tue, 1-Sep-87 11:50:47 EDT
Article-I.D.: utah-gr.2129
Posted: Tue Sep  1 11:50:47 1987
Date-Received: Sat, 5-Sep-87 03:54:38 EDT
References: <2180@mulga.oz>
Sender: news@utah-gr.UUCP
Reply-To: thomas%spline.UUCP@utah-gr.UUCP (Spencer W. Thomas)
Organization: Univ of Utah CS Dept
Lines: 31
Keywords: Rotation, Mac

Summary:

Expires:

Sender:

Followup-To:

Distribution:



There are several algorithms for doing this, all based on a "scanline"
method.  The basic idea is to skew the image first in the X direction,
then in the Y direction.  You can accomplish a rotation up to 45deg
with this technique.  To get rotations > 45 degrees, you first rotate
by a multiple of 90 (easily accomplished).  Some references:
	Catmull, E. and Smith, A.R., "3-D Transformations of Images in
	Scanline Order", Computer Graphics, Vol 14, No 3, July 1980
	(SIGGRAPH '80 Conference Proceedings).

	Fant, K., "A Nonaliasing, Real-Time Spatial Transform
	Technique", IEEE Computer Graphics and Applications, January
	1986, (See also Letters to the Editor, IEEE CG&A, March 1986
	and July 1986.)

	Paeth, A., "A Fast Algorithm for General Raster Rotation",
	Graphics Interface '86 Proceedings, May 1986.

I will attempt a picture demonstrating the technique:

.............. 	                 ..............           ....
.            . 	 	       	.	     .           .    ...
.            . 	 X skew	       . 	    .  Y skew  ..        ...
.            . 	 ------>      .	 	   .   -----> .             ...
.            .		     .	          .          ...               ..
.            .		    .	         .              ...           ..
..............             ..............                  ...       .
                                                              ...  ..
                                                                 ..

=Spencer   ({ihnp4,decvax}!utah-cs!thomas, thomas@cs.utah.edu)