Path: utzoo!attcan!uunet!cs.utexas.edu!csd4.milw.wisc.edu!bionet!agate!shelby!portia!Jessica!stergios
From: stergios@Jessica.stanford.edu (stergios marinopoulos)
Newsgroups: comp.windows.x
Subject: Re: Rotated Fonts With X
Summary: algorithm & code for rotating bitmap
Keywords: Fonts X rotate BATMAN
Message-ID: <3144@portia.Stanford.EDU>
Date: 24 Jun 89 23:11:03 GMT
References: <432@wizard.UUCP>
Sender: USENET News System <news@Portia.stanford.edu>
Reply-To: stergios@Jessica.UUCP (stergios marinopoulos)
Organization: Stanford University
Lines: 59

Print text to a pixmap, grab the image, rotate it, send it back over
the wire.

Here is how to rotate a bitmap image.  Simply iterate over the origonal
and apply the rotation  tranformation for each pixel.

 unsigned char image[WIDTH][HEIGHT];
 rotate(angle)
      double angle;     /* rotate image 'angle' degrees */
 {
      int color;
      int xx,yy;
      for(y = 0;y < HEIGHT; y ++)
           for(x = 0;x < WIDTH; x ++) {
 	       color = image[xx][yy];
                xx = x * cos(angle) - y * sin(angle);
                yy = x * sin(angle) + y * cos(angle);
                setpixel(xx,yy,color);
           }
 }

This method will leave "holes" in the rotated image since  there is no
strict mapping of integral values between arbitary coordinate systems.

This algorithm  can   be  generalized  and improved   (eliminating the
`holes') quite easily;  simply iterate over  the output  points rather
than the input points.  Thus,

   for (P = each point in the output) {
      P2 = TRANSFORM(P) ; /* can include rotations, scaling, etc */
      setpixel(destination, P, getpixel(source, P2)) ;
   }

TRANSFORM is the usual six-element matrix, that rounds the point after
it's done.

The resulting bitmap won't be beautiful.  Better results can often be
obtained by interpolating between source pixels.  For instance, if
the unrounded transformed result was (2.3, 4.6), then a better looking
image might be obtained by using

   .3[.6[g(2,4),g(2,5)],.6[g(3,4),g(3,5)]]

where n[a,b] means ((1-n) * a + n * b) and g(x,y) means the value of
the source at pixel (x,y).

The image may be more `blurry' this way, though . . .

If you are scaling up (to more bits), this type of interpolation is
probably not a bad idea.  If you are scaling down (to less bits), it
can give odd effects; you might want to high-pass filter the image
before scaling it down.


A lot of the good info above comes from Tom Rokicki
(rokicki@polya.stanford.edu)

sm
stergios@jessica.stanford.edu