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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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 * 2 along with this work; if not, write to the Free Software Foundation,

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package sun.java2d.pisces;

import java.util.Iterator;

final class Curve {

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

    float dax, day, dbx, dby;

    Curve() {

    }

    void set(float[] points, int type) {

        switch(type) {

        case 8:

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

                points[2], points[3],

                points[4], points[5],

                points[6], points[7]);

            break;

        case 6:

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

                points[2], points[3],

                points[4], points[5]);

            break;

        default:

            throw new InternalError("Curves can only be cubic or quadratic");

        }

    }

    void set(float x1, float y1,

             float x2, float y2,

             float x3, float y3,

             float x4, float y4)

    {

        ax = 3 * (x2 - x3) + x4 - x1;

        ay = 3 * (y2 - y3) + y4 - y1;

        bx = 3 * (x1 - 2 * x2 + x3);

        by = 3 * (y1 - 2 * y2 + y3);

        cx = 3 * (x2 - x1);

        cy = 3 * (y2 - y1);

        dx = x1;

        dy = y1;

        dax = 3 * ax; day = 3 * ay;

        dbx = 2 * bx; dby = 2 * by;

    }

    void set(float x1, float y1,

             float x2, float y2,

             float x3, float y3)

    {

        ax = ay = 0f;

        bx = x1 - 2 * x2 + x3;

        by = y1 - 2 * y2 + y3;

        cx = 2 * (x2 - x1);

        cy = 2 * (y2 - y1);

        dx = x1;

        dy = y1;

        dax = 0; day = 0;

        dbx = 2 * bx; dby = 2 * by;

    }

    float xat(float t) {

        return t * (t * (t * ax + bx) + cx) + dx;

    }

    float yat(float t) {

        return t * (t * (t * ay + by) + cy) + dy;

    }

    float dxat(float t) {

        return t * (t * dax + dbx) + cx;

    }

    float dyat(float t) {

        return t * (t * day + dby) + cy;

    }

    int dxRoots(float[] roots, int off) {

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

    }

    int dyRoots(float[] roots, int off) {

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

    }

    int infPoints(float[] pts, int 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 * (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.

    private int perpendiculardfddf(float[] pts, int off) {

        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).

        final float a = 2*(dax*dax + day*day);

        final float b = 3*(dax*dbx + day*dby);

        final float c = 2*(dax*cx + day*cy) + dbx*dbx + dby*dby;

        final float d = dbx*cx + dby*cy;

        return Helpers.cubicRootsInAB(a, b, c, d, pts, off, 0f, 1f);

    }

    // 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).

    int rootsOfROCMinusW(float[] roots, int off, final float w, final float err) {

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

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

        int ret = off;

        int numPerpdfddf = perpendiculardfddf(roots, off);

        float t0 = 0, ft0 = ROCsq(t0) - w*w;

        roots[off + numPerpdfddf] = 1f; // always check interval end points

        numPerpdfddf++;

        for (int i = off; i < off + numPerpdfddf; i++) {

            float t1 = roots[i], ft1 = ROCsq(t1) - w*w;

            if (ft0 == 0f) {

                roots[ret++] = t0;

            } else if (ft1 * ft0 < 0f) { // have opposite signs

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

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

                roots[ret++] = falsePositionROCsqMinusX(t0, t1, w*w, err);

            }

            t0 = t1;

            ft0 = ft1;

        }

        return ret - off;

    }

    private static float eliminateInf(float x) {

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

            (x == Float.NEGATIVE_INFINITY ? Float.MIN_VALUE : x));

    }

    // 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

    private float falsePositionROCsqMinusX(float x0, float x1,

                                           final float x, final float err)

    {

        final int iterLimit = 100;

        int side = 0;

        float t = x1, ft = eliminateInf(ROCsq(t) - x);

        float s = x0, fs = eliminateInf(ROCsq(s) - x);

        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);

            fr = ROCsq(r) - x;

            if (sameSign(fr, ft)) {

                ft = fr; t = r;

                if (side < 0) {

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

                    side--;

                } else {

                    side = -1;

                }

            } else if (fr * fs > 0) {

                fs = fr; s = r;

                if (side > 0) {

                    ft /= (1 << side);

                    side++;

                } else {

                    side = 1;

                }

            } else {

                break;

            }

        }

        return r;

    }

    private static boolean sameSign(double x, double y) {

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

        return (x < 0 && y < 0) || (x > 0 && y > 0);

    }

    // 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) {

        // dx=xat(t) and dy=yat(t). These calls have been inlined for efficiency

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

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

        final float ddx = 2 * dax * t + dbx;

        final float ddy = 2 * day * t + dby;

        final float dx2dy2 = dx*dx + dy*dy;

        final float ddx2ddy2 = ddx*ddx + ddy*ddy;

        final float ddxdxddydy = ddx*dx + ddy*dy;

        return dx2dy2*((dx2dy2*dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy*ddxdxddydy));

    }

    // curve to be broken should be in pts

    // this will change the contents of pts but not Ts

    // TODO: There's no reason for Ts to be an array. All we need is a sequence

    // of t values at which to subdivide. An array statisfies this condition,

    // but is unnecessarily restrictive. Ts should be an Iterator<Float> instead.

    // Doing this will also make dashing easier, since we could easily make

    // LengthIterator an Iterator<Float> and feed it to this function to simplify

    // the loop in Dasher.somethingTo.

    static Iterator<Integer> breakPtsAtTs(final float[] pts, final int type,

                                          final float[] Ts, final int numTs)

    {

        assert pts.length >= 2*type && numTs <= Ts.length;

        return new Iterator<Integer>() {

            // these prevent object creation and destruction during autoboxing.

            // Because of this, the compiler should be able to completely

            // eliminate the boxing costs.

            final Integer i0 = 0;

            final Integer itype = type;

            int nextCurveIdx = 0;

            Integer curCurveOff = i0;

            float prevT = 0;

            @Override public boolean hasNext() {

                return nextCurveIdx < numTs + 1;

            }

            @Override public Integer next() {

                Integer ret;

                if (nextCurveIdx < numTs) {

                    float curT = Ts[nextCurveIdx];

                    float splitT = (curT - prevT) / (1 - prevT);

                    Helpers.subdivideAt(splitT,

                                        pts, curCurveOff,

                                        pts, 0,

                                        pts, type, type);

                    prevT = curT;

                    ret = i0;

                    curCurveOff = itype;

                } else {

                    ret = curCurveOff;

                }

                nextCurveIdx++;

                return ret;

            }

            @Override public void remove() {}

        };

    }

}