[cairo] correct arc_to error bound calculation

[Carl Worth]

On Sun, 14 Aug 2005 23:47:06 +0200, Bertram Felgenhauer wrote:
> here is a patch that does three things:
> 1st. it splits out the major axis calculation from cairo-pen.c
> 2nd. it corrects a mistake in that calculation.
> 3rd. it makes arc_to_error base its calculation on this major axis
> calculation instead of the bogus use of Eigen values.

Hi Bertram,

Thanks for this patch. I've gone through it and it all seems
correct. I'd like to see a few changes before it is committed though:

1) The bug fix of (2) above should be committed independently from the
   code re-shuffling.

2) The math in the comment should be rewritten using row-vector
   notation so that the bug fix is more obvious

3) Perhaps a,b,c,d should be initialized with  _cairo_matrix_get_affine

4) The relevant portions of the comment should move with the code
   rather than one comment pointing to a comment in another file.

5) The _cairo_matrix_unit_circle_major_axis function should be
   adjusted to accept a radius and then be renamed to:

	_cairo_matrix_transformed_circle_major_axis

> The Eigen value calculation has no users after this patch is
> applied and could be removed.

6) Yes, that should be done as well.

Thanks again!

-Carl

PS. Independent pieces of the above should be committed
independently. Did you get CVS commit access yet? That would help
here...
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