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

[Laurent Bourgès]

On Wed, 10 Nov 2021 10:23:53 GMT, Laurent Bourgès <lbourges at openjdk.org> wrote:

>> I agree it is out of the scope of this issue to implement high-precision polynom evaluation (compensated horder scheme), that I or anybody else could implement it later.
>> To ensure bounds2D are enclosing the shape entirely, I propose to add a small margin (10 ulps or more) to ascertain precision is good enough.
>> To determine the precision level, using fuzzy testing is the good approach : generate lots ofrandom paths => check bounds2D accuracy in ulp units.
>
> @prrace @mrserb what do you think on this bug in terms of precision requirements?
> - should bbox always include control points ?
> - should ideal shape always fit in bbox ? So I propose to add a margin > numerical inaccuracies.
> 
> I can develop a numerical approach based on fuzzy testing:
> - generate random curves (high magnitude changes on control points)
> - use both this algorithm (double) and implement the same with BigDecimal
> - estimate the extrema error = max distance(pts big decimal, pts double)

Ideally jdk could provide new math methods:
- evalPoly(eqn[])
- find roots...
Based on compensated horner scheme and Math.fma() ~ 0.5 ulp

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