Add basic SVD support to SkMatrix. Allows you to pull out the x- and y-scale factors, sandwiched by…

Add basic SVD support to SkMatrix. Allows you to pull out the x- and y-scale factors, sandwiched by two rotations.

Committed: http://code.google.com/p/skia/source/detail?r=10322

[jvanverth1, 2013-07-17 18:56:10]

Some justification may be necessary... 

I'm working on a non-device space method for ovals, and I need to adjust my
input geometry so that I end up with a screen-space result that's a half-pixel
wider on all sides. Pulling out the non-uniform scale factors should let me do
that for rotations and skews. Since I'm doing that, I figured I could add the
full decomposition.

I can also handle arbitrarily scaled, then rotated ovals with the old method if
I know that the matrix can be decomposed into that.

I do need to do some more robustness testing -- I suspect that the results
aren't so good if the matrix values are very large.

[reed1, 2013-07-18 14:15:54]

Looks ok, but just to be conservative, does it need to be on the public api? Can
we begin by just writing this as a "library" function somewhere in src?

https://codereview.chromium.org/19569007/diff/1/include/core/SkMatrix.h
File include/core/SkMatrix.h (right):

https://codereview.chromium.org/19569007/diff/1/include/core/SkMatrix.h#newco...
include/core/SkMatrix.h:103: Returns false if the matrix is degenerate.
... or perspective?

[jvanverth1, 2013-07-18 15:01:42]

On 2013/07/18 14:15:54, reed1 wrote:
> Looks ok, but just to be conservative, does it need to be on the public api?
Can
> we begin by just writing this as a "library" function somewhere in src?

Sure, I could move the interface to SkMatrixUtils.h, if that makes sense.

> https://codereview.chromium.org/19569007/diff/1/include/core/SkMatrix.h
> File include/core/SkMatrix.h (right):
> 
>
https://codereview.chromium.org/19569007/diff/1/include/core/SkMatrix.h#newco...
> include/core/SkMatrix.h:103: Returns false if the matrix is degenerate.
> ... or perspective?

This is only doing the SVD on the upper left corner, to separate out the
rotations and scale 
factors for the linear part of the transformation. Then you can grab the
translation and 
perspective factors directly, to get a full decomposition of the matrix. But
maybe I'm 
misunderstanding how perspective affects the upper left 2x2.

[jvanverth1, 2013-07-23 15:41:23]

Okay, I've moved the function declaration to SkMatrixUtil.h, which should hide
it from public view. I also did some clean-up to make sure that we get
reasonable results out of it when we have only a scale matrix, or when we have a
scale followed by a rotation (in some cases it would output a 90 degree rotation
for the first one, then swap the scale factors). I also improved some of the
tests and added a random matrix test.

[reed1, 2013-07-23 15:42:15]

lgtm

[commit-bot: I haz the power, 2013-07-24 17:39:17]

CQ is trying da patch. Follow status at
https://skia-tree-status.appspot.com/cq/jvanverth@google.com/19569007/17001

[commit-bot: I haz the power, 2013-07-24 18:08:10]

Change committed as 10322