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

[Jim Graham]

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.
>