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

[Laurent Bourgès]

On Fri, 12 Nov 2021 19:09:18 GMT, Laurent Bourgès <lbourges at openjdk.org> wrote:

>> I just pushed a commit ( 40bda06 ) that addresses the machine error problem to my satisfaction. It includes a unit test that failed before that commit and now passes.
>> 
>> At your convenience let me know your thoughts. (That commit continues to focus on very small doubles; it may (?) need help to address very large double errors.)
>
> That looks interesting as the new margin looks like ulp(x - bbox), however it may be not enough as the position error depends on curve polynom coefficients (magnitude).
> 
> I derived your (yesterday) test to play with the margin and try small to huge curves. 
> I found the condition number ~ sum (abs(coeffs)) so margin = math.ulp(cond). But sometimes the quad solver is giving t with few ulps error that cause high position shifts.
> 
> I will go on testing your last approach and share my experiments

As this accuracy problem is a more general issue on quad / cubic curves, I created the Marlin-Math project to ascertain the math function accuracy.
See https://github.com/bourgesl/marlin-math/blob/main/src/main/java/test/FindExtremaAccuracyTest.java

I will propose a new upper margin value that quarantees the edge condition.

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