[OpenJDK 2D-Dev] Fix for drawing round endcaps on scaled lines.

[Jim Graham]

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.graham at oracle.com>
> To: "Denis Lila" <dlila at redhat.com>
> Cc: 2d-dev at 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.
>>