qbezier.cpp File Reference

#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>

Go to the source code of this file.

Macros
#define	INV_EPS   (1L<<14)
#define	KAPPA   qreal(0.5522847498)
#define	M_SQRT2   1.41421356237309504880

Enumerations
enum	ShiftResult { Ok, Discard, Split, Circle }

Functions
static bool	addCircle (const QBezier *b, qreal offset, QBezier *o)
static bool	findInflections (qreal a, qreal b, qreal c, qreal *t1, qreal *t2, qreal *tCups)
static ShiftResult	good_offset (const QBezier *b1, const QBezier *b2, qreal offset, qreal threshold)
static int	quadraticRoots (qreal a, qreal b, qreal c, qreal *x1, qreal *x2)
static ShiftResult	shift (const QBezier *orig, QBezier *shifted, qreal offset, qreal threshold)
static void	splitBezierAt (const QBezier &bez, qreal t, QBezier *left, QBezier *right)

Macro Definition Documentation

INV_EPS

#define INV_EPS   (1L<<14)

Definition at line 61 of file qbezier.cpp.

KAPPA

#define KAPPA   qreal(0.5522847498)

Definition at line 370 of file qbezier.cpp.

Referenced by addCircle(), QPaintEngineEx::drawRoundedRect(), and QVGPaintEnginePrivate::roundedRectPath().

M_SQRT2

#define M_SQRT2   1.41421356237309504880

Definition at line 65 of file qbezier.cpp.

Enumeration Type Documentation

ShiftResult

enum ShiftResult

Enumerator
Ok
Discard
Split
Circle

Definition at line 258 of file qbezier.cpp.

                 {
    Ok,
    Discard,
    Split,
    Circle
};

Function Documentation

addCircle()

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

static

Definition at line 373 of file qbezier.cpp.

Referenced by QBezier::shifted().

{
    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] = qAcos(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(qreal(0.5)*(b->x1 + b->x4), qreal(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 = qreal(2.0) * 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();

        ++o;
    }
    return true;
}

findInflections()

static bool findInflections ( qreal  a, qreal  b, qreal  c, qreal *  t1, qreal *  t2, qreal *  tCups  )

inlinestatic

Definition at line 164 of file qbezier.cpp.

{
    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 = qreal(0.5) * (-b / a);
        else
            *tCups = 2;

        return true;
    }

    return false;
}

good_offset()

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

static

Definition at line 265 of file qbezier.cpp.

Referenced by shift().

{
    const qreal o2 = offset*offset;
    const qreal max_dist_line = threshold*offset*offset;
    const qreal max_dist_normal = threshold*offset;
    const qreal spacing = qreal(0.25);
    for (qreal i = spacing; i < qreal(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 != qreal(0.0)) {
            d = qAbs( normalPoint.x()*(p1.y() - p2.y()) - normalPoint.y()*(p1.x() - p2.x()) ) / l;
            if (d > max_dist_normal)
                return Split;
        }
    }
    return Ok;
}

quadraticRoots()

static int quadraticRoots ( qreal  a, qreal  b, qreal  c, qreal *  x1, qreal *  x2  )

inlinestatic

Definition at line 133 of file qbezier.cpp.

Referenced by findInflections().

{
    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;
    }
}

shift()

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

static

Definition at line 289 of file qbezier.cpp.

Referenced by qrgb444::byte_mul(), QWSCalibratedMouseHandler::calibrate(), checksum(), QImage::mirrored(), qt_memrotate270_tiled(), qt_memrotate90_tiled(), qt_static_shift(), QBezier::shifted(), and QAxServerBase::TranslateAcceleratorW().

{
    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;

    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 = qreal(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);
}

splitBezierAt()

static void splitBezierAt ( const QBezier &  bez, qreal  t, QBezier *  left, QBezier *  right  )

inlinestatic

Definition at line 501 of file qbezier.cpp.

{
    left->x1 = bez.x1;
    left->y1 = bez.y1;

    left->x2 = bez.x1 + t * ( bez.x2 - bez.x1 );
    left->y2 = bez.y1 + t * ( bez.y2 - bez.y1 );

    left->x3 = bez.x2 + t * ( bez.x3 - bez.x2 ); // temporary holding spot
    left->y3 = bez.y2 + t * ( bez.y3 - bez.y2 ); // temporary holding spot

    right->x3 = bez.x3 + t * ( bez.x4 - bez.x3 );
    right->y3 = bez.y3 + t * ( bez.y4 - bez.y3 );

    right->x2 = left->x3 + t * ( right->x3 - left->x3);
    right->y2 = left->y3 + t * ( right->y3 - left->y3);

    left->x3 = left->x2 + t * ( left->x3 - left->x2 );
    left->y3 = left->y2 + t * ( left->y3 - left->y2 );

    left->x4 = right->x1 = left->x3 + t * (right->x2 - left->x3);
    left->y4 = right->y1 = left->y3 + t * (right->y2 - left->y3);

    right->x4 = bez.x4;
    right->y4 = bez.y4;
}