[OpenJDK 2D-Dev] RFC: Fix for 7036754

[Denis Lila]

> For parallel quads, is there a relationship between any of the
> following
> points that could be exploited?
> 
> original control point
> left_curve and right_curve control points
> center point on the original (and rt and lt) curve
> perpendicular of center point on the curve(s)
> center of line between endpoints

Hm. It turns out that if the parallel versions of the control
lines are extended to infinity, their intersections form a
rhombus whose centre is the second control point (i.e. of the
centre curve). The control points we're trying to compute are
two vertices of the rhombus that lie on the same diagonal. An
equation for this diagonal would be c2 + t*( (c3-c2)/||c3-c2|| + (c1-c2)/||c1-c2|| )
where c1, c2, c3 are the control points of the centre curve.

To compute the points we want we would need to know their distance
from c2.

Well, thanks for getting me thinking about this. This line of
thinking seems promising.
I'll try to code it up.

Regards,
Denis.

----- Original Message -----
> Here's an odd thought.
> 

> 
> I'm just basing this on a "gut feel" of how quad curves behave, not on
> any mathematical intuition, though. It also makes sense given that you
> are computing the intersection of parallel versions of the lines. I'm
> guessing that the intersections of all parallel lines equidistant from
> the original pair form a line themselves and that line might be
> related
> to other points we have access to.
> 
> But, it might be some food for thought on how to make parallel quads
> go
> a lot faster...
> 
> ...jim
> 
> On 4/15/2011 2:20 PM, Jim Graham wrote:
> > Hi Denis,
> >
> > The strategy I took to work around this was to simply check for a
> > zero
> > denominator in the Miter method and return the average of the
> > endpoints
> > instead of the intersection points. That makes a straight line via a
> > quad that has colinear points, but it greatly simplifies the impact
> > of
> > the fix.
> >
> > To be safe (performance-wise), I made a separate copy of the method
> > called "safecomputeMiter()" and put the test only in that copy
> > (which is
> > only used from the quad function) until I have time to do some more
> > exhaustive performance tests. To be honest, though, I don't imagine
> > that
> > single test could affect performance (given that "den" is already
> > computed as the difference of two values, the subtract operation
> > already
> > sets condition codes so it is simply a matter of how fast the
> > processor
> > can take the branch or not, and this is likely a case where branch
> > prediction would pay off a lot...)
> >
> > ...jim
> >
> > On 4/15/2011 10:38 AM, Denis Lila wrote:
> >> Hi.
> >>
> >> Jim Graham pointed out this bug to me.
> >>
> >> A fix is here:
> >> http://icedtea.classpath.org/~dlila/webrevs/7036754/webrev/
> >>
> >> It just checks for inf/nan and just emits a line joining
> >> the endpoints in that case.
> >>
> >> The stroking is no longer symmetric with respect to right
> >> and left polynomial degrees. This is a bit more general.
> >>
> >> I have a question:
> >>
> >> The "curve is a straight line" check I use is this:
> >> 737 float dotsq = (dx1 * dx3 + dy1 * dy3);
> >> 738 dotsq = dotsq * dotsq;
> >> 739 float l1sq = dx1 * dx1 + dy1 * dy1, l3sq = dx3 * dx3 + dy3 *
> >> dy3;
> >> 740 if (Helpers.within(dotsq, l1sq * l3sq, 4 * Math.ulp(dotsq))) {
> >>
> >> However, this isn't making much sense mathematically
> >> right now. I would like to avoid redoing the math
> >> so if someone can quickly confirm/deny that it works
> >> that would be nice.
> >>
> >> Thank you,
> >> Denis.