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#include "qbezier_p.h"

#include <qdebug.h>

#include <qline.h>

#include <qpolygon.h>

#include <qvector.h>

#include <qlist.h>

#include <qmath.h>

#include <private/qnumeric_p.h>

#include <private/qmath_p.h>

QT_BEGIN_NAMESPACE

//#define QDEBUG_BEZIER

#ifdef FLOAT_ACCURACY

#define INV_EPS (1L<<23)

#else

/* The value of 1.0 / (1L<<14) is enough for most applications */

#define INV_EPS (1L<<14)

#endif

#ifndef M_SQRT2

#define M_SQRT2	1.41421356237309504880

#endif

#define log2(x) (qLn(x)/qLn(2.))

static inline qreal log4(qreal x)

{

    return qreal(0.5) * log2(x);

}

/*!

  \internal

*/

QBezier QBezier::fromPoints(const QPointF &p1, const QPointF &p2,

                            const QPointF &p3, const QPointF &p4)

{

    QBezier b;

    b.x1 = p1.x();

    b.y1 = p1.y();

    b.x2 = p2.x();

    b.y2 = p2.y();

    b.x3 = p3.x();

    b.y3 = p3.y();

    b.x4 = p4.x();

    b.y4 = p4.y();

    return b;

}

/*!

  \internal

*/

QPolygonF QBezier::toPolygon() const

{

    // flattening is done by splitting the bezier until we can replace the segment by a straight

    // line. We split further until the control points are close enough to the line connecting the

    // boundary points.

    //

    // the Distance of a point p from a line given by the points (a,b) is given by:

    //

    // d = abs( (bx - ax)(ay - py) - (by - ay)(ax - px) ) / line_length

    //

    // We can stop splitting if both control points are close enough to the line.

    // To make the algorithm faster we use the manhattan length of the line.

    QPolygonF polygon;

    polygon.append(QPointF(x1, y1));

    addToPolygon(&polygon);

    return polygon;

}

//0.5 is really low

static const qreal flatness = 0.5;

//based on "Fast, precise flattening of cubic Bezier path and offset curves"

//      by T. F. Hain, A. L. Ahmad, S. V. R. Racherla and D. D. Langan

static inline void flattenBezierWithoutInflections(QBezier &bez,

                                                   QPolygonF *&p)

{

    QBezier left;

    while (1) {

        qreal dx = bez.x2 - bez.x1;

        qreal dy = bez.y2 - bez.y1;

        qreal normalized = qSqrt(dx * dx + dy * dy);

        if (qFuzzyIsNull(normalized))

           break;

        qreal d = qAbs(dx * (bez.y3 - bez.y2) - dy * (bez.x3 - bez.x2));

        qreal t = qSqrt(4. / 3. * normalized * flatness / d);

        if (t > 1 || qFuzzyIsNull(t - (qreal)1.))

            break;

        bez.parameterSplitLeft(t, &left);

        p->append(bez.pt1());

    }

}

static inline int quadraticRoots(qreal a, qreal b, qreal c,

                                 qreal *x1, qreal *x2)

{

    if (qFuzzyIsNull(a)) {

        if (qFuzzyIsNull(b))

            return 0;

        *x1 = *x2 = (-c / b);

        return 1;

    } else {

        const qreal det = b * b - 4 * a * c;

        if (qFuzzyIsNull(det)) {

            *x1 = *x2 = -b / (2 * a);

            return 1;

        }

        if (det > 0) {

            if (qFuzzyIsNull(b)) {

                *x2 = qSqrt(-c / a);

                *x1 = -(*x2);

                return 2;

            }

            const qreal stableA = b / (2 * a);

            const qreal stableB = c / (a * stableA * stableA);

            const qreal stableC = -1 - qSqrt(1 - stableB);

            *x2 = stableA * stableC;

            *x1 = (stableA * stableB) / stableC;

            return 2;

        } else

            return 0;

    }

}

static inline bool findInflections(qreal a, qreal b, qreal c,

                                   qreal *t1 , qreal *t2, qreal *tCups)

{

    qreal r1 = 0, r2 = 0;

    short rootsCount = quadraticRoots(a, b, c, &r1, &r2);

    if (rootsCount >= 1) {

        if (r1 < r2) {

            *t1 = r1;

            *t2 = r2;

        } else {

            *t1 = r2;

            *t2 = r1;

        }

        if (!qFuzzyIsNull(a))

            *tCups = 0.5 * (-b / a);

        else

            *tCups = 2;

        return true;

    }

    return false;

}

void QBezier::addToPolygon(QPolygonF *polygon) const

{

    QBezier beziers[32];

    beziers[0] = *this;

    QBezier *b = beziers;

    while (b >= beziers) {

        // check if we can pop the top bezier curve from the stack

        qreal y4y1 = b->y4 - b->y1;

        qreal x4x1 = b->x4 - b->x1;

        qreal l = qAbs(x4x1) + qAbs(y4y1);

        qreal d;

        if (l > 1.) {

            d = qAbs( (x4x1)*(b->y1 - b->y2) - (y4y1)*(b->x1 - b->x2) )

                + qAbs( (x4x1)*(b->y1 - b->y3) - (y4y1)*(b->x1 - b->x3) );

        } else {

            d = qAbs(b->x1 - b->x2) + qAbs(b->y1 - b->y2) +

                qAbs(b->x1 - b->x3) + qAbs(b->y1 - b->y3);

            l = 1.;

        }

        if (d < flatness*l || b == beziers + 31) {

            // good enough, we pop it off and add the endpoint

            polygon->append(QPointF(b->x4, b->y4));

            --b;

        } else {

            // split, second half of the polygon goes lower into the stack

            b->split(b+1, b);

            ++b;

        }

    }

}

void QBezier::addToPolygonMixed(QPolygonF *polygon) const

{

    qreal ax = -x1 + 3*x2 - 3*x3 + x4;

    qreal ay = -y1 + 3*y2 - 3*y3 + y4;

    qreal bx = 3*x1 - 6*x2 + 3*x3;

    qreal by = 3*y1 - 6*y2 + 3*y3;

    qreal cx = -3*x1 + 3*x2;

    qreal cy = -3*y1 + 2*y2;

    qreal a = 6 * (ay * bx - ax * by);

    qreal b = 6 * (ay * cx - ax * cy);

    qreal c = 2 * (by * cx - bx * cy);

    if ((qFuzzyIsNull(a) && qFuzzyIsNull(b)) ||

        (b * b - 4 * a *c) < 0) {

        QBezier bez(*this);

        flattenBezierWithoutInflections(bez, polygon);

        polygon->append(QPointF(x4, y4));

    } else {

        QBezier beziers[32];

        beziers[0] = *this;

        QBezier *b = beziers;

        while (b >= beziers) {

            // check if we can pop the top bezier curve from the stack

            qreal y4y1 = b->y4 - b->y1;

            qreal x4x1 = b->x4 - b->x1;

            qreal l = qAbs(x4x1) + qAbs(y4y1);

            qreal d;

            if (l > 1.) {

                d = qAbs( (x4x1)*(b->y1 - b->y2) - (y4y1)*(b->x1 - b->x2) )

                    + qAbs( (x4x1)*(b->y1 - b->y3) - (y4y1)*(b->x1 - b->x3) );

            } else {

                d = qAbs(b->x1 - b->x2) + qAbs(b->y1 - b->y2) +

                    qAbs(b->x1 - b->x3) + qAbs(b->y1 - b->y3);

                l = 1.;

            }

            if (d < .5*l || b == beziers + 31) {

                // good enough, we pop it off and add the endpoint

                polygon->append(QPointF(b->x4, b->y4));

                --b;

            } else {

                // split, second half of the polygon goes lower into the stack

                b->split(b+1, b);

                ++b;

            }

        }

    }

}

QRectF QBezier::bounds() const

{

    qreal xmin = x1;

    qreal xmax = x1;

    if (x2 < xmin)

        xmin = x2;

    else if (x2 > xmax)

        xmax = x2;

    if (x3 < xmin)

        xmin = x3;

    else if (x3 > xmax)

        xmax = x3;

    if (x4 < xmin)

        xmin = x4;

    else if (x4 > xmax)

        xmax = x4;

    qreal ymin = y1;

    qreal ymax = y1;

    if (y2 < ymin)

        ymin = y2;

    else if (y2 > ymax)

        ymax = y2;

    if (y3 < ymin)

        ymin = y3;

    else if (y3 > ymax)

        ymax = y3;

    if (y4 < ymin)

        ymin = y4;

    else if (y4 > ymax)

        ymax = y4;

    return QRectF(xmin, ymin, xmax-xmin, ymax-ymin);

}

enum ShiftResult {

    Ok,

    Discard,

    Split,

    Circle

};

static ShiftResult good_offset(const QBezier *b1, const QBezier *b2, qreal offset, qreal threshold)

{

    const qreal o2 = offset*offset;

    const qreal max_dist_line = threshold*offset*offset;

    const qreal max_dist_normal = threshold*offset;

    const qreal spacing = 0.25;

    for (qreal i = spacing; i < 0.99; i += spacing) {

        QPointF p1 = b1->pointAt(i);

        QPointF p2 = b2->pointAt(i);

        qreal d = (p1.x() - p2.x())*(p1.x() - p2.x()) + (p1.y() - p2.y())*(p1.y() - p2.y());

        if (qAbs(d - o2) > max_dist_line)

            return Split;

        QPointF normalPoint = b1->normalVector(i);

        qreal l = qAbs(normalPoint.x()) + qAbs(normalPoint.y());

        if (l != 0.) {

            d = qAbs( normalPoint.x()*(p1.y() - p2.y()) - normalPoint.y()*(p1.x() - p2.x()) ) / l;

            if (d > max_dist_normal)

                return Split;

        }

    }

    return Ok;

}

static inline QLineF qline_shifted(const QPointF &p1, const QPointF &p2, qreal offset)

{

    QLineF l(p1, p2);

    QLineF ln = l.normalVector().unitVector();

    l.translate(ln.dx() * offset, ln.dy() * offset);

    return l;

}

static bool qbezier_is_line(QPointF *points, int pointCount)

{

    Q_ASSERT(pointCount > 2);

    qreal dx13 = points[2].x() - points[0].x();

    qreal dy13 = points[2].y() - points[0].y();

    qreal dx12 = points[1].x() - points[0].x();

    qreal dy12 = points[1].y() - points[0].y();

    if (pointCount == 3) {

        return qFuzzyCompare(dx12 * dy13, dx13 * dy12);

    } else if (pointCount == 4) {

        qreal dx14 = points[3].x() - points[0].x();

        qreal dy14 = points[3].y() - points[0].y();

        return (qFuzzyCompare(dx12 * dy13, dx13 * dy12) && qFuzzyCompare(dx12 * dy14, dx14 * dy12));

    }

    return false;

}

static ShiftResult shift(const QBezier *orig, QBezier *shifted, qreal offset, qreal threshold)

{

    int map[4];

    bool p1_p2_equal = (orig->x1 == orig->x2 && orig->y1 == orig->y2);

    bool p2_p3_equal = (orig->x2 == orig->x3 && orig->y2 == orig->y3);

    bool p3_p4_equal = (orig->x3 == orig->x4 && orig->y3 == orig->y4);

    QPointF points[4];

    int np = 0;

    points[np] = QPointF(orig->x1, orig->y1);

    map[0] = 0;

    ++np;

    if (!p1_p2_equal) {

        points[np] = QPointF(orig->x2, orig->y2);

        ++np;

    }

    map[1] = np - 1;

    if (!p2_p3_equal) {

        points[np] = QPointF(orig->x3, orig->y3);

        ++np;

    }

    map[2] = np - 1;

    if (!p3_p4_equal) {

        points[np] = QPointF(orig->x4, orig->y4);

        ++np;

    }

    map[3] = np - 1;

    if (np == 1)

        return Discard;

    // We need to specialcase lines of 3 or 4 points due to numerical

    // instability in intersections below

    if (np > 2 && qbezier_is_line(points, np)) {

        if (points[0] == points[np-1])

            return Discard;

        QLineF l = qline_shifted(points[0], points[np-1], offset);

        *shifted = QBezier::fromPoints(l.p1(), l.pointAt(qreal(0.33)), l.pointAt(qreal(0.66)), l.p2());

        return Ok;

    }

    QRectF b = orig->bounds();

    if (np == 4 && b.width() < .1*offset && b.height() < .1*offset) {

        qreal l = (orig->x1 - orig->x2)*(orig->x1 - orig->x2) +

                  (orig->y1 - orig->y2)*(orig->y1 - orig->y1) *

                  (orig->x3 - orig->x4)*(orig->x3 - orig->x4) +

                  (orig->y3 - orig->y4)*(orig->y3 - orig->y4);

        qreal dot = (orig->x1 - orig->x2)*(orig->x3 - orig->x4) +

                    (orig->y1 - orig->y2)*(orig->y3 - orig->y4);

        if (dot < 0 && dot*dot < 0.8*l)

            // the points are close and reverse dirction. Approximate the whole

            // thing by a semi circle

            return Circle;

    }

    QPointF points_shifted[4];

    QLineF prev = QLineF(QPointF(), points[1] - points[0]);

    QPointF prev_normal = prev.normalVector().unitVector().p2();

    points_shifted[0] = points[0] + offset * prev_normal;

    for (int i = 1; i < np - 1; ++i) {

        QLineF next = QLineF(QPointF(), points[i + 1] - points[i]);

        QPointF next_normal = next.normalVector().unitVector().p2();

        QPointF normal_sum = prev_normal + next_normal;

        qreal r = 1.0 + prev_normal.x() * next_normal.x()

                  + prev_normal.y() * next_normal.y();

        if (qFuzzyIsNull(r)) {

            points_shifted[i] = points[i] + offset * prev_normal;

        } else {

            qreal k = offset / r;

            points_shifted[i] = points[i] + k * normal_sum;

        }

        prev_normal = next_normal;

    }

    points_shifted[np - 1] = points[np - 1] + offset * prev_normal;

    *shifted = QBezier::fromPoints(points_shifted[map[0]], points_shifted[map[1]],

                                   points_shifted[map[2]], points_shifted[map[3]]);

    return good_offset(orig, shifted, offset, threshold);

}

// This value is used to determine the length of control point vectors

// when approximating arc segments as curves. The factor is multiplied

// with the radius of the circle.

#define KAPPA 0.5522847498

static bool addCircle(const QBezier *b, qreal offset, QBezier *o)

{

    QPointF normals[3];

    normals[0] = QPointF(b->y2 - b->y1, b->x1 - b->x2);

    qreal dist = qSqrt(normals[0].x()*normals[0].x() + normals[0].y()*normals[0].y());

    if (qFuzzyIsNull(dist))

        return false;

    normals[0] /= dist;

    normals[2] = QPointF(b->y4 - b->y3, b->x3 - b->x4);

    dist = qSqrt(normals[2].x()*normals[2].x() + normals[2].y()*normals[2].y());

    if (qFuzzyIsNull(dist))

        return false;

    normals[2] /= dist;

    normals[1] = QPointF(b->x1 - b->x2 - b->x3 + b->x4, b->y1 - b->y2 - b->y3 + b->y4);

    normals[1] /= -1*qSqrt(normals[1].x()*normals[1].x() + normals[1].y()*normals[1].y());

    qreal angles[2];

    qreal sign = 1.;

    for (int i = 0; i < 2; ++i) {

        qreal cos_a = normals[i].x()*normals[i+1].x() + normals[i].y()*normals[i+1].y();

        if (cos_a > 1.)

            cos_a = 1.;

        if (cos_a < -1.)

            cos_a = -1;

        angles[i] = acos(cos_a)/Q_PI;

    }

    if (angles[0] + angles[1] > 1.) {

        // more than 180 degrees

        normals[1] = -normals[1];

        angles[0] = 1. - angles[0];

        angles[1] = 1. - angles[1];

        sign = -1.;

    }

    QPointF circle[3];

    circle[0] = QPointF(b->x1, b->y1) + normals[0]*offset;

    circle[1] = QPointF(0.5*(b->x1 + b->x4), 0.5*(b->y1 + b->y4)) + normals[1]*offset;

    circle[2] = QPointF(b->x4, b->y4) + normals[2]*offset;

    for (int i = 0; i < 2; ++i) {

        qreal kappa = 2.*KAPPA * sign * offset * angles[i];

        o->x1 = circle[i].x();

        o->y1 = circle[i].y();

        o->x2 = circle[i].x() - normals[i].y()*kappa;

        o->y2 = circle[i].y() + normals[i].x()*kappa;

        o->x3 = circle[i+1].x() + normals[i+1].y()*kappa;

        o->y3 = circle[i+1].y() - normals[i+1].x()*kappa;

        o->x4 = circle[i+1].x();

        o->y4 = circle[i+1].y();