RFR: 8176501: Method Shape.getBounds2D() incorrectly includes Bezier control points in bounding box [v2]

[Laurent Bourgès]

On Fri, 5 Nov 2021 04:41:34 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 some of Laurent's code review recommendations/comments:
>   
>   1. use the convention t for the parametric variable x(t),y(t)
>   2. solve the quadratic equation using QuadCurve2d.solveQuadratic() or like Helpers.quadraticRoots()
>   3. always use braces for x = (a < b) ? ...
>   4. always use double-precision constants in math or logical operations: (2 * x => 2.0 * x) and (coefficients[3] != 0) => (coefficients[3] != 0.0)
>   
>   (There are two additional recommendations not in this commit that I'll ask about shortly.)
>   
>   See https://github.com/openjdk/jdk/pull/6227#issuecomment-959757954

For math reference, this page explains how to use curve derivatives to find extrema:
https://pomax.github.io/bezierinfo/#extremities

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