Hello.
I think I got this working. The webrev is at:
http://icedtea.classpath.org/~dlila/webrevs/bezierRoundJoins/webrev/
(NOTE: this is not a final version. I have included 2 versions
of 2 methods. Only one set should be kept. See below for more.)
My Changes:
-----------
1.
I've made LineSink into an interface, rather than an abstract
class,
because all of its methods were abstract, so it makes more sense this
way.
2.
I've introduced a new interface that extends LineSink called
PathSink,
which allows the curveTo method, so there have been no changes to
Stroker's public interface. When someone wants to create a Stroker
with a PathSink output, it simply passes its constructor a PathSink,
so the only changes outside of Stroker are in PiscesRenderingEngine,
where the methods that handle Path2D and PathConsumer2D objects
create nameless PathSinks instead of nameless LineSinks.
3. In Stroker:
I've introduced a method called drawBezRoundJoin, analogous to
computeRoundJoin. In drawRoundJoin I detect whether the output is
a PathSink. If it is, I call drawBezRoundJoin, otherwise everything
proceeds as it used to. drawBezRoundJoin uses computeBezierPoints to
compute the control points. computeBezierPoints computes the control
points
for an arc of t radians, starting at angle a, with radius r
by computing the control points of an arc of radius 1 of t radians
that
starts at angle -t/2. This is done by solving the equations resulting
from the constraints that (P3-P2) and (P1-P0) must be parallel to the
arc's tangents at P3 and P0 respectively, and that B(1/2)=(1,0). Then
the
points are scaled by r, and rotated counter clockwise by a+t/2.
Then drawBezRoundJoin emits the curve.
All this is done in a loop which is used to break up large arcs
into
more than one bezier curve. Through the iterations, the computed
control
points don't change - the only thing that changes is how they're
rotated.
So a good alternative approach would be to do the rotation outside
of
computeBezierPoints, and call computeBezierPoints once outside of the
loop,
so that the control points aren't recomputed unnecessarily.
I have included code for this in the methods computeBezierPoints2 and
drawBezRoundJoin2. This is my favoured approach, since it is almost
as clear as the other one, and it is faster.
There is one more optimization that can be made, and I've included
it
in a comment in line 703.
I would very much appreciate any comments about any of this, but
especially
about the idea in line 703 and about
computeBezierPoints2,drawBezRoundJoin2
vs. computeBezierPoints,drawBezRoundJoin.
4.
Stroker used to only have lines, but now it can emit lines and
curves, so
I needed to change the format of reverse, to not only store
coordinates, but
to also tag them as belonging to a line or a curve.
Other Approaches:
-----------------
1.
Since what needed to be done was to alter the behaviour of one
part of Stroker (drawing of round joins/caps) depending on the type
of the output object, I thought it would be appropriate to make
Stroker
an abstract factory, turn the methods that draw round joins/caps into
abstract ones, put all the common functionality in concrete methods
in Stroker, and put all the join/cap drawing methods in overriding
methods
in concrete children of Stroker (instances of which were returned
by static factories in Stroker).
However, this was a bad approach, because the round cap/join
drawing
methods are private, so the only way to call them in Stroker's
children
from public methods in Stroker is to cast "this". So the code became
littered with instanceof operators and casts. Not to mention that
Stroker's
public interface had to change, and some functionality was lost:
Stroker
allows changing it's output, so it is possible to use just 1 Stroker
object
to widen paths going to many different outputs (but not at the same
time).
This could no longer be supported with this approach.
The way I did it has none of these weaknesses.
2. As for algorithms for the circle approximation, I considered 2:
a. Compute the control points using the constraints that
B(1/3)=A(a+t/3)
and B(2/3) = A(a+2t/3) (i.e. make the arc and the bezier curve
coincide at 2
evenly spaced points in the arc). This didn't work very well: some of
the end
caps looked more like triangles.
b. Let B(1/2) = A(a+t/2), and B'(1/2) = A'(a+t/2). This worked
better, but
still not good enough.
If anyone knows of any better ways to compute the control points,
please let
me know.
I'm sorry for the length of this. I tried to make it shorter.
Thank you very much,
Denis.
----- "Jim Graham" <james.gra...@oracle.com> wrote:
Hi Denis,
Consider the case of using BasicStroke.createStrokedShape(). How do
you
know how many pixels the resulting path will occupy? You can't
reduce
to concrete samples if you don't know the transform.
So, for rendering, then you may be correct. But for cases where the
path is being asked for then beziers are the only responsible
solution...
...jim
Denis Lila wrote:
Hello Jim.
I thought about checking the output and changing the behaviour
depending on whether the output is a PC2D or a LineSink, but I
didn't
implement it because I thought the point was to get rid of the
sampling
at this stage. However, if performance is the issue, then I guess
I'll
start working on it.
Although, I wonder whether it is really worth it. I think most
lines
drawn
won't be wider than about 5 pixels, which means that the current
way
will
emit about 7 lines, so that's 14 coordinates. 2 bezier quarter
circles will
require 12 coordinates. In terms of storage, there isn't much
difference, and
for lines of width 4 or smaller the current method is more
efficient.
I'm also guessing that it's harder for the rasterizer to deal with
bezier
curves than with straight lines, so is it possible that replacing
the
3.14*lineWidth/2 lines generated by the current method with 2
bezier
quarter circles isn't worth it (for small lineWidths)?
Thanks,
Denis.
----- "Jim Graham" <james.gra...@oracle.com> wrote:
Sigh - that makes sense. One issue is that the resulting paths
it
generates are much more "verbose" than they need to be. This
would
generally mean that it takes far more storage than it would
otherwise
need - and it means that if the result needs to be transformed
then
it
would take many more computations to transform each segment than
the
bezier.
So, perhaps it would be worth having it check the type of the
output
and
do either a bezier or a bunch of lines depending on if it is a
PC2D
or
a
LineSink?
Also, it isn't really that difficult to for Renderer to include
its
own
Cubic/Quadratic flattening code, but it might involve more
calculations
than the round-cap code since it would have to be written for
arbitrary
beziers whereas if you know it is a quarter circle then it is
easier
to
know how far to subdivide... :-(
...jim
Denis Lila wrote:
So, I have been thinking about this, and I can't see a good
way to do it that wouldn't involve heavy changes to Pisces.
In order for Stroker to generate Bezier quarter circles, it
would
have to implement a curveTo method, which means Stroker should
start implementing PathConsumer2D and instead of using a
LineSink
output it would have to use a PathConsumer2D output (either
that,
or
LineSink should include a curveTo method, but then there won't
really
be any difference between a LineSink and a PathConsumer2D. By
the
way,
LineSink doesn't have any implemented methods, so why is it an
abstract
class as opposed to an interface?)
Stroker is used in 3 ways:
1. As an implementation of BasicStroke's createStrokedShape
method.
This
uses a Path2D object as output.
2. As a way of feeding a PathConsumer2D without calling
createStrokedShape
to generate an intermediate Shape. This uses a PathConsumer2D
output.
3. As a way of feeding lines to a Renderer object, which
generates
alpha
tiles used for anti-aliasing that are fed to a cache and
extracted
as needed
by an AATileGenerator. Obviously, Stroker's output here is a
Renderer.
1 and 2 aren't problems, because the underlying output objects
support
Bezier curves. 3, however, doesn't, and it seems like
implementing
a
curveTo method for Renderer would be very difficult because the
way
it
generates alpha tiles is by scanning the drawn edges with
horizontal
scan lines, and for each scan line finding the x-intersections
of
the scan
lines and the edges. Then it determines the alpha values (I'm
not
too sure
how it does this).
In order to implement Bezier curves in Renderer, we would have
to
have
a quick way of computing, for each scan line, all its
intersections
with
however many Bezier curves are being drawn.
I haven't given much thought to how this could be done, as I am
not
very
familiar with Bezier curves, but it doesn't seem easy enough to
justify
fixing such a small bug.
----- Original Message -----
From: "Jim Graham" <james.gra...@oracle.com>
To: "Denis Lila" <dl...@redhat.com>
Cc: 2d-dev@openjdk.java.net
Sent: Wednesday, June 9, 2010 7:42:33 PM GMT -05:00 US/Canada
Eastern
Subject: Re: [OpenJDK 2D-Dev] Fix for drawing round endcaps on
scaled lines.
I don't understand - why do we generate sample points based on
the
size
of the cap? Why not generate a pair of bezier quarter-circles
and
let
the rasterizer deal with sampling?
...jim
Denis Lila wrote:
Hello.
I think I have a fix for this bug:
http://icedtea.classpath.org/bugzilla/show_bug.cgi?id=506
Basically, the problem is that if there is a magnifying affine
transformation set on the graphics object and one tries to draw a
line
with small thickness and round end caps, the end caps appear
jagged.
This is because the computation of the length of the array that
contains the points on the "pen" with which the decoration is
drawn
does not take into account the size of the pen after the
magnification
of the affine transformation. So, for example, if the line length
was
set to 1, and the transformation was a scaling by 10, the
resulting
pen would have a diameter of 10, but only 3 pen points would be
computed (pi*untransformedLineWidth), so the end cap looks like a
triangle.
My fix computes an approximation of the circumference of the
transformed pen (which is an ellipse) and uses that as the number
of
points on the pen. The approximation is crude, but it is simple,
faster than alternatives
(http://en.wikipedia.org/wiki/Ellipse#Circumference), and I can
say
from observations that it works fairly well.
There is also icing on the cake, in the form of slight
improvements
in performance when the scaling is a zooming out. Example: if the
original line width was 100, but g2d.scale(0.1,0.1) was set, then
the
resulting line would have a width of 10, so only ~31 points are
necessary for the decoration to look like a circle, but without
this
patch, about 314 points are computed (and a line is emitted to
each
one of them).
I appreciate any feedback.
Regards,
Denis Lila.
