diff -r 2b6a7dc567ba -r d717df90e151 jdk/src/share/classes/sun/java2d/pisces/PiscesRenderingEngine.java --- 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,