--- a/jdk/src/share/classes/sun/java2d/pisces/PiscesRenderingEngine.java Thu Jul 30 12:25:39 2009 -0700
+++ b/jdk/src/share/classes/sun/java2d/pisces/PiscesRenderingEngine.java Tue Aug 04 17:25:36 2009 -0700
@@ -171,9 +171,9 @@
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 @@
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,