Do not clamp y values on internal knots of timing function bezier curves

Do not clamp y values on internal knots of timing function bezier curves

Cubic bezier timing functions are based on two knots (x1, y1) and (x2, y2) (the
other knots are assumed to be (0, 0) and (1, 1)). We require that x1, x2 lie
within (0, 1) (so that the bezier does not 'fold back' on itself), but y1, and
y2 should have no such constraint. They currently do. This CL reimplements
bezier interpolation without this restriction. This interpolation has two steps:
   1) Find the t corresponding to the desired x.
   2) Interpolate y's at the t computed in step 1.
Step 1 is an iterative minimization. Here I do bisection for simplicity, but I
could take Newton steps if this turns out to be a bottleneck.

R=ajuma@chromium.org
BUG=178070
Committed: https://src.chromium.org/viewvc/chrome?view=rev&revision=202755

[ajuma, 2013-05-27 18:10:48]

This is a nice simplification.

Please add a TimingFunctionTest where y1 or y2 is not in (0,1).  

From the description:
> within (0, 1) (so that the bezier does not 'fold back' on itself, but y1, and

Missing close-bracket.

https://chromiumcodereview.appspot.com/16112002/diff/1/cc/animation/timing_fu...
File cc/animation/timing_function.cc (right):

https://chromiumcodereview.appspot.com/16112002/diff/1/cc/animation/timing_fu...
cc/animation/timing_function.cc:81: SkScalar value = bezier_interp(x1_, y1_,
x2_, y2_, x);
bezier_interp returns a double, so we shouldn't need to do an SkScalarToFloat
conversion anymore.

[Ian Vollick, 2013-05-27 18:41:12]

On 2013/05/27 18:10:48, ajuma wrote:
> This is a nice simplification.
> 
> Please add a TimingFunctionTest where y1 or y2 is not in (0,1).  
Done.
> 
> From the description:
> > within (0, 1) (so that the bezier does not 'fold back' on itself, but y1,
and
> 
> Missing close-bracket.
Fixed.
> 
>
https://chromiumcodereview.appspot.com/16112002/diff/1/cc/animation/timing_fu...
> File cc/animation/timing_function.cc (right):
> 
>
https://chromiumcodereview.appspot.com/16112002/diff/1/cc/animation/timing_fu...
> cc/animation/timing_function.cc:81: SkScalar value = bezier_interp(x1_, y1_,
> x2_, y2_, x);
> bezier_interp returns a double, so we shouldn't need to do an SkScalarToFloat
> conversion anymore.
Removed.

[ajuma, 2013-05-27 18:48:56]

On 2013/05/27 18:41:12, vollick wrote:
> On 2013/05/27 18:10:48, ajuma wrote:
> > This is a nice simplification.
> > 
> > Please add a TimingFunctionTest where y1 or y2 is not in (0,1).  
> Done.
> > 
> > From the description:
> > > within (0, 1) (so that the bezier does not 'fold back' on itself, but y1,
> and
> > 
> > Missing close-bracket.
> Fixed.
> > 
> >
>
https://chromiumcodereview.appspot.com/16112002/diff/1/cc/animation/timing_fu...
> > File cc/animation/timing_function.cc (right):
> > 
> >
>
https://chromiumcodereview.appspot.com/16112002/diff/1/cc/animation/timing_fu...
> > cc/animation/timing_function.cc:81: SkScalar value = bezier_interp(x1_, y1_,
> > x2_, y2_, x);
> > bezier_interp returns a double, so we shouldn't need to do an
SkScalarToFloat
> > conversion anymore.
> Removed.

lgtm.

[commit-bot: I haz the power, 2013-05-27 18:51:13]

CQ is trying da patch. Follow status at
https://chromium-status.appspot.com/cq/vollick@chromium.org/16112002/4001

[commit-bot: I haz the power, 2013-05-28 19:04:36]

CQ is trying da patch. Follow status at
https://chromium-status.appspot.com/cq/vollick@chromium.org/16112002/18001

[commit-bot: I haz the power, 2013-05-29 02:52:26]

Change committed as 202755