6829673: ThinLineTest: A line < 1 pixel disappears.

Reviewed-by: igor, prr
Contributed-by: Nrkennke <roman.kennke@sun.com>

src/share/classes/sun/java2d/pisces/PiscesRenderingEngine.java

@@ -171,9 +171,9 @@ public class PiscesRenderingEngine extends RenderingEngine {
         float lw;
         if (thin) {
             if (antialias) {
-                lw = 0.5f;
+                lw = userSpaceLineWidth(at, 0.5f);
             } else {
-                lw = 1.0f;
+                lw = userSpaceLineWidth(at, 1.0f);
             }
         } else {
             lw = bs.getLineWidth();
@@ -189,6 +189,72 @@ public class PiscesRenderingEngine extends RenderingEngine {
                  lsink);
     }
 
+    private float userSpaceLineWidth(AffineTransform at, float lw) {
+
+        double widthScale;
+
+        if ((at.getType() & (AffineTransform.TYPE_GENERAL_TRANSFORM |
+                            AffineTransform.TYPE_GENERAL_SCALE)) != 0) {
+            widthScale = Math.sqrt(at.getDeterminant());
+        } else {
+            /* First calculate the "maximum scale" of this transform. */
+            double A = at.getScaleX();       // m00
+            double C = at.getShearX();       // m01
+            double B = at.getShearY();       // m10
+            double D = at.getScaleY();       // m11
+
+            /*
+             * Given a 2 x 2 affine matrix [ A B ] such that
+             *                             [ C D ]
+             * v' = [x' y'] = [Ax + Cy, Bx + Dy], we want to
+             * find the maximum magnitude (norm) of the vector v'
+             * with the constraint (x^2 + y^2 = 1).
+             * The equation to maximize is
+             *     |v'| = sqrt((Ax+Cy)^2+(Bx+Dy)^2)
+             * or  |v'| = sqrt((AA+BB)x^2 + 2(AC+BD)xy + (CC+DD)y^2).
+             * Since sqrt is monotonic we can maximize |v'|^2
+             * instead and plug in the substitution y = sqrt(1 - x^2).
+             * Trigonometric equalities can then be used to get
+             * rid of most of the sqrt terms.
+             */
+
+            double EA = A*A + B*B;          // x^2 coefficient
+            double EB = 2*(A*C + B*D);      // xy coefficient
+            double EC = C*C + D*D;          // y^2 coefficient
+
+            /*
+             * There is a lot of calculus omitted here.
+             *
+             * Conceptually, in the interests of understanding the
+             * terms that the calculus produced we can consider
+             * that EA and EC end up providing the lengths along
+             * the major axes and the hypot term ends up being an
+             * adjustment for the additional length along the off-axis
+             * angle of rotated or sheared ellipses as well as an
+             * adjustment for the fact that the equation below
+             * averages the two major axis lengths.  (Notice that
+             * the hypot term contains a part which resolves to the
+             * difference of these two axis lengths in the absence
+             * of rotation.)
+             *
+             * In the calculus, the ratio of the EB and (EA-EC) terms
+             * ends up being the tangent of 2*theta where theta is
+             * the angle that the long axis of the ellipse makes
+             * with the horizontal axis.  Thus, this equation is
+             * calculating the length of the hypotenuse of a triangle
+             * along that axis.
+             */
+
+            double hypot = Math.sqrt(EB*EB + (EA-EC)*(EA-EC));
+            /* sqrt omitted, compare to squared limits below. */
+            double widthsquared = ((EA + EC + hypot)/2.0);
+
+            widthScale = Math.sqrt(widthsquared);
+        }
+
+        return (float) (lw / widthScale);
+    }
+
     void strokeTo(Shape src,
                   AffineTransform at,
                   float width,

test/sun/pisces/ThinLineTest.java

+/*
+ * Copyright 2009 Sun Microsystems, Inc.  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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
+ * CA 95054 USA or visit www.sun.com if you need additional information or
+ * have any questions.
+ */
+import java.awt.*;
+import java.awt.geom.Ellipse2D;
+import java.awt.image.BufferedImage;
+import java.io.File;
+import javax.imageio.ImageIO;
+
+/**
+ * @author chrisn@google.com (Chris Nokleberg)
+ * @author yamauchi@google.com (Hiroshi Yamauchi)
+ */
+public class ThinLineTest {
+  private static final int PIXEL = 381;
+
+  public static void main(String[] args) throws Exception {
+    BufferedImage image = new BufferedImage(200, 200, BufferedImage.TYPE_INT_RGB);
+    Graphics2D g = image.createGraphics();
+
+    g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
+    g.setPaint(Color.WHITE);
+    g.fill(new Rectangle(image.getWidth(), image.getHeight()));
+
+    g.scale(0.5 / PIXEL, 0.5 / PIXEL);
+    g.setPaint(Color.BLACK);
+    g.setStroke(new BasicStroke(PIXEL));
+    g.draw(new Ellipse2D.Double(PIXEL * 50, PIXEL * 50, PIXEL * 300, PIXEL * 300));
+
+    // To visually check it
+    //ImageIO.write(image, "PNG", new File(args[0]));
+
+    boolean nonWhitePixelFound = false;
+    for (int x = 0; x < 200; ++x) {
+      if (image.getRGB(x, 100) != Color.WHITE.getRGB()) {
+        nonWhitePixelFound = true;
+        break;
+      }
+    }
+    if (!nonWhitePixelFound) {
+      throw new RuntimeException("The thin line disappeared.");
+    }
+  }
+}