[OpenJDK 2D-Dev] X11 uniform scaled wide lines and dashed lines; STROKE_CONTROL in Pisces
Jim Graham
james.graham at oracle.com
Wed Aug 25 23:49:15 UTC 2010
Hi Denis,
At the bottom-most rendering level monotonic curves can be cool to deal
with, but I'm dubious that they help with widening. For one things, I
think you need more breaks than they would give you and also they might
sometimes break a curve when it doesn't need it.
One way in which they may not break enough is that I think that
inflections also need to be broken in order to find a parallel curve
(though I suppose a very tiny inflection might still be approximated by
a parallel curve easily) and inflections can happen at any angle without
going horizontal or vertical.
Secondly, although a circle tends to be represented by quadrant sections
which are monotonic, a circle rotated by 45 degrees would have
horizontal and vertical sections in the middle of each quadrant and you
would split those, but really they can be made parallel regardless of
angle so these would be unnecessary splits.
My belief is that lengths and angles of the control polygon help
determine if it is well-behaved and can be made parallel simply by
offsetting. Some formula involving those values would likely be happy
with circle sections regardless of their angle of rotation. I believe
the Apache Harmony version of BasicStroke used those criteria...
...jim
On 8/25/2010 2:36 PM, Denis Lila wrote:
> Hello Jim.
>
>> I think a more dynamic approach that looked at how "regular" the curve
>> was would do better. Regular is hard to define, but for instance a
>> bezier section of a circle could have parallel curves computed very
>> easily without having to flatten or subdivide further. Curves with
>> inflections probably require subdividing to get an accurate parallel
>> curve.
>
> I'm not sure if you read it, but after the email with the webrev link
> I sent another describing a different method of widening: split the
> curve at every t where dx/dt == 0 and dy/dt == 0. This guarantees that
> there will be no more than 5 curves per side, and since each curve will
> be monotonic in both x and y the curve that interpolates its parallel
> should do a pretty good job.
>
> This is far better than interpolating at regular t intervals, but I'm
> trying to find a better way. I don't like this because the split
> depend not only on the curve itself, but also on the axes. The axes are
> arbitrary, so this is not good. For example a curve like this
> |
> \_ would get widened by 1 curve per side (which is good and optimal), but
> if we rotate this curve by, say, 30 degrees it would be widened by 2 curves
> per side.
> It also doesn't handle cusps and locations of high curvature very well (although
> I think the latter is a numerical issue that could be made better by using
> doubles).
>
> Regards,
> Denis.
>
> ----- "Jim Graham"<james.graham at oracle.com> wrote:
>
>> Hi Denis,
>>
>> On 8/23/2010 4:18 PM, Denis Lila wrote:
>>> To widen cubic curves, I use a cubic spline with a fixed number
>> of curves for
>>> each curve to be widened. This was meant to be temporary, until I
>> could find a
>>> better algorithm for determining the number of curves in the spline,
>> but I
>>> discovered today that that won't do it.
>>> For example, the curve p.moveTo(0,0),p.curveTo(84.0, 62.0,
>> 32.0, 34.0, 28.0, 5.0)
>>> looks bad all the way up to ~200 curves. Obviously, this is
>> unacceptable.
>>>
>>> It would be great if anyone has any better ideas for how to go about
>> this.
>>> To me it seems like the problem is that in the webrev I chop up the
>> curve to be
>>> interpolated at equal intervals of the parameter.
>
>>
>> Perhaps looking at the rate of change of the slope (2nd and/or 3rd
>> derivatives) would help to figure out when a given section of curve
>> can
>> be approximated with a parallel version?
>>
>> I believe that the BasicStroke class of Apache Harmony returns widened
>>
>> curves, but when I tested it it produced a lot more curves than Ductus
>>
>> (still, probably a lot less than the lines that would be produced by
>> flattening) and it had some numerical problems. In the end I decided
>> to
>> leave our Ductus stuff in there until someone could come up with a
>> more
>> reliable Open Source replacement, but hopefully that code is close
>> enough to be massaged into working order.
>>
>> You can search the internet for "parallel curves" and find lots of
>> literature on the subject. I briefly looked through the web sites,
>> but
>> didn't have enough time to remember enough calculus and trigonometry
>> to
>> garner a solution out of it all with the time that I had. Maybe
>> you'll
>> have better luck following the algorithms... ;-)
>>
>> As far as flattening at the lowest level when doing scanline
>> conversion,
>> I like the idea of using forward differencing as it can create an
>> algorithm that doesn't require all of the intermediate storage that a
>>
>> subdividing flattener requires. One reference that describes the
>> technique is on Dr. Dobbs site, though I imagine there are many
>> others:
>>
>> http://www.drdobbs.com/184403417;jsessionid=O5N5MDJRDMIKHQE1GHOSKH4ATMY32JVN
>>
>> You can also look at the code in
>> src/share/native/sun/java2d/pipe/ProcessPath.c for some examples of
>> forward differencing in use (and that code also has similar techniques
>>
>> to what you did to first chop the path into vertical pieces). BUT
>> (*Nota Bene*), I must warn you that the geometry of the path is
>> somewhat
>> perturbed in that code since it tries to combine "path normalization"
>>
>> and rasterization into a single process. It's not rendering pure
>> geometry, it is rendering tweaked geometry which tries to make non-AA
>>
>> circles look round and other such aesthetics-targeted impurities.
>> While
>> the code does have good examples of how to set up and evaluate forward
>>
>> differencing equations, don't copy too many of the details or you
>> might
>> end up copying some of the tweaks and the results will look strange
>> under AA. The Dr. Dobbs article should be your numerical reference
>> and
>> that reference code a practical, but incompatible, example...
>>
>> ...jim
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