RFR: 8176501: Method Shape.getBounds2D() incorrectly includes Bezier control points in bounding box [v5]

[Laurent Bourgès]

On Tue, 9 Nov 2021 10:03:14 GMT, Jeremy <duke at openjdk.java.net> wrote:

>> This removes code that relied on consulting the Bezier control points to calculate the Rectangle2D bounding box. Instead it's pretty straight-forward to convert the Bezier control points into the x & y parametric equations. At their most complex these equations are cubic polynomials, so calculating their extrema is just a matter of applying the quadratic formula to calculate their extrema. (Or in path segments that are quadratic/linear/constant: we do even less work.)
>> 
>> The bug writeup indicated they wanted Path2D#getBounds2D() to be more accurate/concise. They didn't explicitly say they wanted CubicCurve2D and QuadCurve2D to become more accurate too. But a preexisting unit test failed when Path2D#getBounds2D() was updated and those other classes weren't. At this point I considered either:
>> A. Updating CubicCurve2D and QuadCurve2D to use the new more accurate getBounds2D() or
>> B. Updating the unit test to forgive the discrepancy.
>> 
>> I chose A. Which might technically be seen as scope creep, but it feels like a more holistic/better approach.
>> 
>> Other shapes in java.awt.geom should not require updating, because they already identify concise bounds.
>> 
>> This also includes a new unit test (in Path2D/UnitTest.java) that fails without the changes in this commit.
>
> Jeremy has updated the pull request incrementally with one additional commit since the last revision:
> 
>   8176501: Method Shape.getBounds2D() incorrectly includes Bezier control points in bounding box
>   
>   Addressing code review recommendation to calculate polynomial coefficients using differences / vector notation.
>   
>   https://github.com/openjdk/jdk/pull/6227#discussion_r743534560
>   
>   I generally understand the intention of this change, but I don't know exactly how to test/evaluate it.
>   
>   The unit tests still pass. I ran some sample calculations involving a 100x100 Ellipse2D as it was rotated, and the two getBounds2D(..) implementations (before and after this commit) only differed by a few ulps (usually around 10^-15), as expected.

Great !
I see many duplicated lines, probably it is time to add 2 small methods to processCubic() and processQuad() that can be called on x and y equations => only 2 arrays needed for coeff and deriv_coeff. 
Maybe I prefer the previous unified solution relying on QuadCurve2D.solveQuadratic() that handles both case.

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PR: https://git.openjdk.java.net/jdk/pull/6227