It's been a while since I went through that code, but the *mxy numbers
tend to be the perpendicular vectors at the vertices (multiplied by the
line width).
omx*mx + omy*my looks like the dot product of two vectors which produces
"len(v1) * len(v2) * cos(angle v1,v2)", so dividing it by lineWidth2
twice reduces it to the cosine of the two vectors and the extra factor
of 2 in the denominator means it is actually half of the cosine of the
angles at the start and end of the arc - i.e. cos(ext)/2.
It should be in the indicated range, but rounding error could mean it
may be occasionally outside of that range. I can see where very long
line widths might cause problems.
Since cv is a function only of cosext2 it might be better to simply
assign the value of cv directly, as in:
if (cosext2 <= -0.5f) {
cv = the answer for -0.5
// 4/3?
} else if (cosext >= 0.5f) {
cv = the answer for +0.5
// 0.0?
} else {
cv = current formula
}
Note that a cv value of 0.0 would insert an empty cubic so we could
probably just return right there instead of setting cv to 0.0 and
computing a bunch of useless values.
Also, the function should only ever be called with a maximum of a right
angle so we should never see negative numbers in any case - are you
seeing -0.5 values or just +0.5 values?
The fix could be as simple as "if (cosext2 >= 0.5) return;"
...jim
On 12/3/15 12:49 PM, Laurent Bourgès wrote:
Jim,
I should create a new bug concerning both Marlin & Pisces but I prefer
discussing the problem first.
A Marlin user reported me an issue with (text outline) rendering
artefacts (due to partial cleanup in arrays).
Using Marlin with -Dsun.java2d.renderer.doChecks=true (logs re-enabled),
we detected that edgeBucketCounts arrays were not properly zero-filled
due to NaN coordinates ie array[0] > 0 !
As it only happens with very large coordinates and round joins, we
finally got a reproducer test class.
However, we tracked the problem down into the
Stroker.drawBezApproxForArc() method (from Pisces):
cv = NaN.
I am not very good at curve maths but I figured out that cosext2 means
cos(ext)^2 as there is below sqrt(0.5 +/- cosext2) !
Of course, the problem is sqrt(negative) gives NaN !
Moreover, it only happens with very large out-of-clip coordinates (2M),
see the test class !
It probably means that float values have not enough precision in
previous math operations and it finally overflows 0.5 !
Is it correct to clamp cosext2 in [-0.5, 0.5] range as I propose ?
// the input arc defined by omx,omy and mx,my must span <= 90 degrees.
private void drawBezApproxForArc(final float cx, final float cy,
final float omx, final float omy,
final float mx, final float my,
boolean rev)
{
float cosext2 = (omx * mx + omy * my) / (2f * lineWidth2 *
lineWidth2);
// PROPOSED FIX TO BE CONFIRMED:
// clamp value within [-0.5, 0.5] range:
if (cosext2 < -0.5f) {
cosext2 = -0.5f;
} else if (cosext2 > 0.5f) {
cosext2 = 0.5f;
}
// cv is the length of P1-P0 and P2-P3 divided by the radius of
the arc
// (so, cv assumes the arc has radius 1). P0, P1, P2, P3 are
the points that
// define the bezier curve we're computing.
// It is computed using the constraints that P1-P0 and P3-P2
are parallel
// to the arc tangents at the endpoints, and that |P1-P0|=|P3-P2|.
float cv = (float) ((4.0 / 3.0) * sqrt(0.5 - cosext2) /
(1.0 + sqrt(cosext2 + 0.5)));
If you have any explanations, please tell me !
PS: Anyway NaN handling must be properly tested and filtered in Marlin's
pipeline (like DuctusRenderingEngine does) ...
but here it concerns intermediate points (not inputs).
Test code:
/*
* Copyright (c) 2015, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License
version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com <http://www.oracle.com> if you need
additional information or have any
* questions.
*/
import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Font;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.font.FontRenderContext;
import java.awt.font.GlyphVector;
import java.awt.geom.AffineTransform;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import javax.imageio.ImageIO;
/**
* @test
* @summary Check the Stroker.drawBezApproxForArc() bug:
* abs(cosext2) > 0.5 generates curves with NaN coordinates
* @run main TextClipErrorTest
*/
public class TextClipErrorTest {
public static void main(String[] args) {
BufferedImage image = new BufferedImage(256, 256,
BufferedImage.TYPE_INT_ARGB);
Graphics2D g2d = image.createGraphics();
g2d.setColor(Color.red);
try {
g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
Font font = g2d.getFont();
FontRenderContext frc = new FontRenderContext(
new AffineTransform(), true, true);
GlyphVector gv1 = font.createGlyphVector(frc, "\u00d6");
g2d.setStroke(new BasicStroke(4.0f,
BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
AffineTransform at1 = AffineTransform.getTranslateInstance(
-2091202.554154681, 5548.601436981691);
g2d.draw(at1.createTransformedShape(gv1.getOutline()));
GlyphVector gv2 = font.createGlyphVector(frc, "Test 2");
AffineTransform at2 = AffineTransform.getTranslateInstance(
// -218.1810476789251, 85.12774919422463);
10, 50);
g2d.draw(at2.createTransformedShape(gv2.getOutline()));
final File file = new File("TextClipErrorTest.png");
System.out.println("Writing file: " + file.getAbsolutePath());
ImageIO.write(image, "PNG", file);
} catch (IOException ex) {
ex.printStackTrace();
}
finally {
g2d.dispose();
}
}
}
Cheers,
Laurent
