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 * 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).

 *

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package sun.java2d.marlin;

final class Curve {

    float ax, ay, bx, by, cx, cy, dx, dy;

    float dax, day, dbx, dby;

    Curve() {

    }

            set(points[0], points[1],

                points[2], points[3],

                points[4], points[5],

                points[6], points[7]);

            set(points[0], points[1],

                points[2], points[3],

                points[4], points[5]);

        }

    }

    {

        final float dx32 = 3.0f * (x3 - x2);

        final float dy32 = 3.0f * (y3 - y2);

        final float dx21 = 3.0f * (x2 - x1);

        final float dy21 = 3.0f * (y2 - y1);

        ay = (y4 - y1) - dy32;

        by = (dy32 - dy21);

        cy = dy21;

        dy = y1;

    }

    {

        final float dx21 = (x2 - x1);

        final float dy21 = (y2 - y1);

        by = (y3 - y2) - dy21;

        cy = 2.0f * dy21;

        dy = y1;

    }

    }

        return Helpers.quadraticRoots(dax, dbx, cx, roots, off);

    }

        return Helpers.quadraticRoots(day, dby, cy, roots, off);

    }

        // inflection point at t if -f'(t)x*f''(t)y + f'(t)y*f''(t)x == 0

        // Fortunately, this turns out to be quadratic, so there are at

        // most 2 inflection points.

        final float a = dax * dby - dbx * day;

        final float b = 2.0f * (cy * dax - day * cx);

        final float c = cy * dbx - cx * dby;

        return Helpers.quadraticRoots(a, b, c, pts, off);

    }

    // finds points where the first and second derivative are

    // perpendicular. This happens when g(t) = f'(t)*f''(t) == 0 (where

    // * is a dot product). Unfortunately, we have to solve a cubic.

        assert pts.length >= off + 4;

        // these are the coefficients of some multiple of g(t) (not g(t),

        // because the roots of a polynomial are not changed after multiplication

        // by a constant, and this way we save a few multiplications).

        return Helpers.cubicRootsInAB(a, b, c, d, pts, off, 0.0f, 1.0f);

    }

    // Tries to find the roots of the function ROC(t)-w in [0, 1). It uses

    // a variant of the false position algorithm to find the roots. False

    // position requires that 2 initial values x0,x1 be given, and that the

    // function must have opposite signs at those values. To find such

    // values, we need the local extrema of the ROC function, for which we

    // need the roots of its derivative; however, it's harder to find the

    // roots of the derivative in this case than it is to find the roots

    // of the original function. So, we find all points where this curve's

    // first and second derivative are perpendicular, and we pretend these

    // are our local extrema. There are at most 3 of these, so we will check

    // at most 4 sub-intervals of (0,1). ROC has asymptotes at inflection

    // points, so roc-w can have at least 6 roots. This shouldn't be a

    // problem for what we're trying to do (draw a nice looking curve).

        // no OOB exception, because by now off<=6, and roots.length >= 10

        assert off <= 6 && roots.length >= 10;

        int ret = off;

            if (ft0 == 0.0f) {

                roots[ret++] = t0;

            } else if (ft1 * ft0 < 0.0f) { // have opposite signs

                // (ROC(t)^2 == w^2) == (ROC(t) == w) is true because

                // ROC(t) >= 0 for all t.

            }

            t0 = t1;

            ft0 = ft1;

        }

        return ret - off;

    }

        return (x == Float.POSITIVE_INFINITY ? Float.MAX_VALUE :

    }

    // A slight modification of the false position algorithm on wikipedia.

    // This only works for the ROCsq-x functions. It might be nice to have

    // the function as an argument, but that would be awkward in java6.

    // TODO: It is something to consider for java8 (or whenever lambda

    // expressions make it into the language), depending on how closures

    // and turn out. Same goes for the newton's method

    // algorithm in Helpers.java

    {

        final int iterLimit = 100;

        int side = 0;

        float r = s, fr;

        for (int i = 0; i < iterLimit && Math.abs(t - s) > err * Math.abs(t + s); i++) {

            r = (fs * t - ft * s) / (fs - ft);

            if (sameSign(fr, ft)) {

                ft = fr; t = r;

                if (side < 0) {

                    fs /= (1 << (-side));

                    side--;

                } else {

                    side = -1;

                }

                fs = fr; s = r;

                if (side > 0) {

                    ft /= (1 << side);

                    side++;

                } else {

                    side = 1;

                }

            } else {

                break;

            }

        }

        return r;

    }

        // another way is to test if x*y > 0. This is bad for small x, y.

        return (x < 0.0f && y < 0.0f) || (x > 0.0f && y > 0.0f);

    }

    // returns the radius of curvature squared at t of this curve

    // see http://en.wikipedia.org/wiki/Radius_of_curvature_(applications)

    private float ROCsq(final float t) {

        final float dx = t * (t * dax + dbx) + cx;

        final float dy = t * (t * day + dby) + cy;

        final float ddx = 2.0f * dax * t + dbx;

        final float ddy = 2.0f * day * t + dby;

    }

}