qstroker.cpp File Reference

#include "private/qstroker_p.h"
#include "private/qbezier_p.h"
#include "private/qmath_p.h"
#include "qline.h"
#include "qtransform.h"
#include <qmath.h>

Go to the source code of this file.

Classes
class	QSubpathBackwardIterator
class	QSubpathFlatIterator
class	QSubpathForwardIterator

Functions
static qreal	adapted_angle_on_x (const QLineF &line)
static bool	lineIntersectsRect (qfixed2d p1, qfixed2d p2, const qfixed2d &tl, const qfixed2d &br)
static bool	lineRectIntersectsRect (qfixed2d p1, qfixed2d p2, const qfixed2d &tl, const qfixed2d &br)
static void	qdashstroker_cubicTo (qfixed, qfixed, qfixed, qfixed, qfixed, qfixed, void *)
static void	qdashstroker_lineTo (qfixed x, qfixed y, void *data)
static void	qdashstroker_moveTo (qfixed x, qfixed y, void *data)
QPointF	qt_curves_for_arc (const QRectF &rect, qreal startAngle, qreal sweepLength, QPointF *curves, int *point_count)
	Creates a number of curves for a given arc definition. More...
Q_GUI_EXPORT void	qt_find_ellipse_coords (const QRectF &r, qreal angle, qreal length, QPointF *startPoint, QPointF *endPoint)
template<class Iterator >
bool	qt_stroke_side (Iterator *it, QStroker *stroker, bool capFirst, QLineF *startTangent)
qreal	qt_t_for_arc_angle (qreal angle)

Function Documentation

adapted_angle_on_x()

static qreal adapted_angle_on_x ( const QLineF &  line )

inlinestatic

Definition at line 182 of file qstroker.cpp.

Referenced by QStroker::joinPoints().

{
    qreal angle = line.angle(QLineF(0, 0, 1, 0));
    if (line.dy() > 0)
        angle = 360 - angle;
    return angle;
}

lineIntersectsRect()

static bool lineIntersectsRect ( qfixed2d  p1, qfixed2d  p2, const qfixed2d &  tl, const qfixed2d &  br  )

static

Definition at line 1069 of file qstroker.cpp.

Referenced by QDashStroker::processCurrentSubpath().

{
    if (!lineRectIntersectsRect(p1, p2, tl, br))
        return false;
    if (p1.x == p2.x || p1.y == p2.y)
        return true;

    if (p1.y > p2.y)
        qSwap(p1, p2); // make p1 above p2
    qfixed2d u;
    qfixed2d v;
    qfixed2d w = {p2.x - p1.x, p2.y - p1.y};
    if (p1.x < p2.x) {
        // backslash
        u.x = tl.x - p1.x; u.y = br.y - p1.y;
        v.x = br.x - p1.x; v.y = tl.y - p1.y;
    } else {
        // slash
        u.x = tl.x - p1.x; u.y = tl.y - p1.y;
        v.x = br.x - p1.x; v.y = br.y - p1.y;
    }
#if defined(QFIXED_IS_26_6) || defined(QFIXED_IS_16_16)
    qint64 val1 = qint64(u.x) * qint64(w.y) - qint64(u.y) * qint64(w.x);
    qint64 val2 = qint64(v.x) * qint64(w.y) - qint64(v.y) * qint64(w.x);
    return (val1 < 0 && val2 > 0) || (val1 > 0 && val2 < 0);
#elif defined(QFIXED_IS_32_32)
    // Cannot do proper test because it may overflow.
    return true;
#else
    qreal val1 = u.x * w.y - u.y * w.x;
    qreal val2 = v.x * w.y - v.y * w.x;
    return (val1 < 0 && val2 > 0) || (val1 > 0 && val2 < 0);
#endif
}

lineRectIntersectsRect()

static bool lineRectIntersectsRect ( qfixed2d  p1, qfixed2d  p2, const qfixed2d &  tl, const qfixed2d &  br  )

inlinestatic

Definition at line 1062 of file qstroker.cpp.

Referenced by lineIntersectsRect(), and QDashStroker::processCurrentSubpath().

{
    return ((p1.x > tl.x || p2.x > tl.x) && (p1.x < br.x || p2.x < br.x)
        && (p1.y > tl.y || p2.y > tl.y) && (p1.y < br.y || p2.y < br.y));
}

qdashstroker_cubicTo()

static void qdashstroker_cubicTo ( qfixed  , qfixed  , qfixed  , qfixed  , qfixed  , qfixed  , void *    )

inlinestatic

Definition at line 1015 of file qstroker.cpp.

Referenced by QDashStroker::QDashStroker().

                                                                                                {
    Q_ASSERT(0);
//     ((QStroker *) data)->cubicTo(c1x, c1y, c2x, c2y, ex, ey);
}

qdashstroker_lineTo()

static void qdashstroker_lineTo ( qfixed  x, qfixed  y, void *  data  )

inlinestatic

Definition at line 1011 of file qstroker.cpp.

Referenced by QDashStroker::QDashStroker().

                                                                       {
    ((QStroker *) data)->lineTo(x, y);
}

qdashstroker_moveTo()

static void qdashstroker_moveTo ( qfixed  x, qfixed  y, void *  data  )

inlinestatic

Definition at line 1007 of file qstroker.cpp.

Referenced by QDashStroker::QDashStroker().

                                                                       {
    ((QStroker *) data)->moveTo(x, y);
}

qt_curves_for_arc()

QPointF qt_curves_for_arc	(	const QRectF &	rect,
		qreal	startAngle,
		qreal	sweepLength,
		QPointF *	curves,
		int *	point_count
	)

Creates a number of curves for a given arc definition.

Warning

This function is not part of the public interface.

The arc is defined an arc along the ellipses that fits into rect starting at startAngle and an arc length of sweepLength.

The function has three out parameters. The return value is the starting point of the arc. The curves array represents the list of cubicTo elements up to a maximum of point_count. There are of course 3 points pr curve.

Definition at line 859 of file qstroker.cpp.

Referenced by QPainterPath::addEllipse(), QPainterPath::arcTo(), QPaintEngineEx::drawEllipse(), QStroker::joinPoints(), and QStrokerOps::strokeEllipse().

{
    Q_ASSERT(point_count);
    Q_ASSERT(curves);

    *point_count = 0;
    if (qt_is_nan(rect.x()) || qt_is_nan(rect.y()) || qt_is_nan(rect.width()) || qt_is_nan(rect.height())
        || qt_is_nan(startAngle) || qt_is_nan(sweepLength)) {
        qWarning("QPainterPath::arcTo: Adding arc where a parameter is NaN, results are undefined");
        return QPointF();
    }

    if (rect.isNull()) {
        return QPointF();
    }

    qreal x = rect.x();
    qreal y = rect.y();

    qreal w = rect.width();
    qreal w2 = rect.width() / 2;
    qreal w2k = w2 * QT_PATH_KAPPA;

    qreal h = rect.height();
    qreal h2 = rect.height() / 2;
    qreal h2k = h2 * QT_PATH_KAPPA;

    QPointF points[16] =
    {
        // start point
        QPointF(x + w, y + h2),

        // 0 -> 270 degrees
        QPointF(x + w, y + h2 + h2k),
        QPointF(x + w2 + w2k, y + h),
        QPointF(x + w2, y + h),

        // 270 -> 180 degrees
        QPointF(x + w2 - w2k, y + h),
        QPointF(x, y + h2 + h2k),
        QPointF(x, y + h2),

        // 180 -> 90 degrees
        QPointF(x, y + h2 - h2k),
        QPointF(x + w2 - w2k, y),
        QPointF(x + w2, y),

        // 90 -> 0 degrees
        QPointF(x + w2 + w2k, y),
        QPointF(x + w, y + h2 - h2k),
        QPointF(x + w, y + h2)
    };

    if (sweepLength > 360) sweepLength = 360;
    else if (sweepLength < -360) sweepLength = -360;

    // Special case fast paths
    if (startAngle == 0.0) {
        if (sweepLength == 360.0) {
            for (int i = 11; i >= 0; --i)
                curves[(*point_count)++] = points[i];
            return points[12];
        } else if (sweepLength == -360.0) {
            for (int i = 1; i <= 12; ++i)
                curves[(*point_count)++] = points[i];
            return points[0];
        }
    }

    int startSegment = int(qFloor(startAngle / 90));
    int endSegment = int(qFloor((startAngle + sweepLength) / 90));

    qreal startT = (startAngle - startSegment * 90) / 90;
    qreal endT = (startAngle + sweepLength - endSegment * 90) / 90;

    int delta = sweepLength > 0 ? 1 : -1;
    if (delta < 0) {
        startT = 1 - startT;
        endT = 1 - endT;
    }

    // avoid empty start segment
    if (qFuzzyIsNull(startT - qreal(1))) {
        startT = 0;
        startSegment += delta;
    }

    // avoid empty end segment
    if (qFuzzyIsNull(endT)) {
        endT = 1;
        endSegment -= delta;
    }

    startT = qt_t_for_arc_angle(startT * 90);
    endT = qt_t_for_arc_angle(endT * 90);

    const bool splitAtStart = !qFuzzyIsNull(startT);
    const bool splitAtEnd = !qFuzzyIsNull(endT - qreal(1));

    const int end = endSegment + delta;

    // empty arc?
    if (startSegment == end) {
        const int quadrant = 3 - ((startSegment % 4) + 4) % 4;
        const int j = 3 * quadrant;
        return delta > 0 ? points[j + 3] : points[j];
    }

    QPointF startPoint, endPoint;
    qt_find_ellipse_coords(rect, startAngle, sweepLength, &startPoint, &endPoint);

    for (int i = startSegment; i != end; i += delta) {
        const int quadrant = 3 - ((i % 4) + 4) % 4;
        const int j = 3 * quadrant;

        QBezier b;
        if (delta > 0)
            b = QBezier::fromPoints(points[j + 3], points[j + 2], points[j + 1], points[j]);
        else
            b = QBezier::fromPoints(points[j], points[j + 1], points[j + 2], points[j + 3]);

        // empty arc?
        if (startSegment == endSegment && qFuzzyCompare(startT, endT))
            return startPoint;

        if (i == startSegment) {
            if (i == endSegment && splitAtEnd)
                b = b.bezierOnInterval(startT, endT);
            else if (splitAtStart)
                b = b.bezierOnInterval(startT, 1);
        } else if (i == endSegment && splitAtEnd) {
            b = b.bezierOnInterval(0, endT);
        }

        // push control points
        curves[(*point_count)++] = b.pt2();
        curves[(*point_count)++] = b.pt3();
        curves[(*point_count)++] = b.pt4();
    }

    Q_ASSERT(*point_count > 0);
    curves[*(point_count)-1] = endPoint;

    return startPoint;
}

qt_find_ellipse_coords()

Q_GUI_EXPORT void qt_find_ellipse_coords	(	const QRectF &	r,
		qreal	angle,
		qreal	length,
		QPointF *	startPoint,
		QPointF *	endPoint
	)

Definition at line 97 of file qpainterpath.cpp.

Referenced by QPainterPath::arcMoveTo(), qt_curves_for_arc(), and qt_t_for_arc_angle().

{
    if (r.isNull()) {
        if (startPoint)
            *startPoint = QPointF();
        if (endPoint)
            *endPoint = QPointF();
        return;
    }

    qreal w2 = r.width() / 2;
    qreal h2 = r.height() / 2;

    qreal angles[2] = { angle, angle + length };
    QPointF *points[2] = { startPoint, endPoint };

    for (int i = 0; i < 2; ++i) {
        if (!points[i])
            continue;

        qreal theta = angles[i] - 360 * qFloor(angles[i] / 360);
        qreal t = theta / 90;
        // truncate
        int quadrant = int(t);
        t -= quadrant;

        t = qt_t_for_arc_angle(90 * t);

        // swap x and y?
        if (quadrant & 1)
            t = 1 - t;

        qreal a, b, c, d;
        QBezier::coefficients(t, a, b, c, d);
        QPointF p(a + b + c*QT_PATH_KAPPA, d + c + b*QT_PATH_KAPPA);

        // left quadrants
        if (quadrant == 1 || quadrant == 2)
            p.rx() = -p.x();

        // top quadrants
        if (quadrant == 0 || quadrant == 1)
            p.ry() = -p.y();

        *points[i] = r.center() + QPointF(w2 * p.x(), h2 * p.y());
    }
}

qt_stroke_side()

template<class Iterator >

bool qt_stroke_side	(	Iterator *	it,
		QStroker *	stroker,
		bool	capFirst,
		QLineF *	startTangent
	)

Definition at line 635 of file qstroker.cpp.

Referenced by QStroker::processCurrentSubpath().

{
    // Used in CurveToElement section below.
    const int MAX_OFFSET = 16;
    QBezier offsetCurves[MAX_OFFSET];

    Q_ASSERT(it->hasNext()); // The initaial move to
    QStrokerOps::Element first_element = it->next();
    Q_ASSERT(first_element.isMoveTo());

    qfixed2d start = first_element;

#ifdef QPP_STROKE_DEBUG
    qDebug(" -> (side) [%.2f, %.2f], startPos=%d",
           qt_fixed_to_real(start.x),
           qt_fixed_to_real(start.y));
#endif

    qfixed2d prev = start;

    bool first = true;

    qfixed offset = stroker->strokeWidth() / 2;

    while (it->hasNext()) {
        QStrokerOps::Element e = it->next();

        // LineToElement
        if (e.isLineTo()) {
#ifdef QPP_STROKE_DEBUG
            qDebug("\n ---> (side) lineto [%.2f, %.2f]", e.x, e.y);
#endif
            QLineF line(qt_fixed_to_real(prev.x), qt_fixed_to_real(prev.y),
                        qt_fixed_to_real(e.x), qt_fixed_to_real(e.y));
            if (line.p1() != line.p2()) {
                QLineF normal = line.normalVector();
                normal.setLength(offset);
                line.translate(normal.dx(), normal.dy());

                // If we are starting a new subpath, move to correct starting point.
                if (first) {
                    if (capFirst)
                        stroker->joinPoints(prev.x, prev.y, line, stroker->capStyleMode());
                    else
                        stroker->emitMoveTo(qt_real_to_fixed(line.x1()), qt_real_to_fixed(line.y1()));
                    *startTangent = line;
                    first = false;
                } else {
                    stroker->joinPoints(prev.x, prev.y, line, stroker->joinStyleMode());
                }

                // Add the stroke for this line.
                stroker->emitLineTo(qt_real_to_fixed(line.x2()),
                                    qt_real_to_fixed(line.y2()));
                prev = e;
            }

        // CurveToElement
        } else if (e.isCurveTo()) {
            QStrokerOps::Element cp2 = it->next(); // control point 2
            QStrokerOps::Element ep = it->next();  // end point

#ifdef QPP_STROKE_DEBUG
            qDebug("\n ---> (side) cubicTo [%.2f, %.2f]",
                   qt_fixed_to_real(ep.x),
                   qt_fixed_to_real(ep.y));
#endif

            QBezier bezier =
                QBezier::fromPoints(QPointF(qt_fixed_to_real(prev.x), qt_fixed_to_real(prev.y)),
                                    QPointF(qt_fixed_to_real(e.x), qt_fixed_to_real(e.y)),
                                    QPointF(qt_fixed_to_real(cp2.x), qt_fixed_to_real(cp2.y)),
                                    QPointF(qt_fixed_to_real(ep.x), qt_fixed_to_real(ep.y)));

            int count = bezier.shifted(offsetCurves,
                                       MAX_OFFSET,
                                       offset,
                                       stroker->curveThreshold());

            if (count) {
                // If we are starting a new subpath, move to correct starting point
                QLineF tangent = bezier.startTangent();
                tangent.translate(offsetCurves[0].pt1() - bezier.pt1());
                if (first) {
                    QPointF pt = offsetCurves[0].pt1();
                    if (capFirst) {
                        stroker->joinPoints(prev.x, prev.y,
                                            tangent,
                                            stroker->capStyleMode());
                    } else {
                        stroker->emitMoveTo(qt_real_to_fixed(pt.x()),
                                            qt_real_to_fixed(pt.y()));
                    }
                    *startTangent = tangent;
                    first = false;
                } else {
                    stroker->joinPoints(prev.x, prev.y,
                                        tangent,
                                        stroker->joinStyleMode());
                }

                // Add these beziers
                for (int i=0; i<count; ++i) {
                    QPointF cp1 = offsetCurves[i].pt2();
                    QPointF cp2 = offsetCurves[i].pt3();
                    QPointF ep = offsetCurves[i].pt4();
                    stroker->emitCubicTo(qt_real_to_fixed(cp1.x()), qt_real_to_fixed(cp1.y()),
                                         qt_real_to_fixed(cp2.x()), qt_real_to_fixed(cp2.y()),
                                         qt_real_to_fixed(ep.x()), qt_real_to_fixed(ep.y()));
                }
            }

            prev = ep;
        }
    }

    if (start == prev) {
        // closed subpath, join first and last point
#ifdef QPP_STROKE_DEBUG
        qDebug("\n ---> (side) closed subpath");
#endif
        // don't join empty subpaths
        if (!first)
            stroker->joinPoints(prev.x, prev.y, *startTangent, stroker->joinStyleMode());
        return true;
    } else {
#ifdef QPP_STROKE_DEBUG
        qDebug("\n ---> (side) open subpath");
#endif
        return false;
    }
}

qt_t_for_arc_angle()

qreal qt_t_for_arc_angle

(

qreal

angle

)

Warning

This function is not part of the public interface.

For a given angle in the range [0 .. 90], finds the corresponding parameter t of the prototype cubic bezier arc segment b = fromPoints(QPointF(1, 0), QPointF(1, KAPPA), QPointF(KAPPA, 1), QPointF(0, 1));

From the bezier equation: b.pointAt(t).x() = (1-t)^3 + t*(1-t)^2 + t^2*(1-t)*KAPPA b.pointAt(t).y() = t*(1-t)^2 * KAPPA + t^2*(1-t) + t^3

Third degree coefficients: b.pointAt(t).x() = at^3 + bt^2 + ct + d where a = 2-3*KAPPA, b = 3*(KAPPA-1), c = 0, d = 1

b.pointAt(t).y() = at^3 + bt^2 + ct + d where a = 3*KAPPA-2, b = 6*KAPPA+3, c = 3*KAPPA, d = 0

Newton's method to find the zero of a function: given a function f(x) and initial guess x_0 x_1 = f(x_0) / f'(x_0) x_2 = f(x_1) / f'(x_1) etc...

Definition at line 796 of file qstroker.cpp.

Referenced by qt_curves_for_arc(), and qt_find_ellipse_coords().

{
    if (qFuzzyIsNull(angle))
        return 0;

    if (qFuzzyCompare(angle, qreal(90)))
        return 1;

    qreal radians = Q_PI * angle / 180;
    qreal cosAngle = qCos(radians);
    qreal sinAngle = qSin(radians);

    // initial guess
    qreal tc = angle / 90;
    // do some iterations of newton's method to approximate cosAngle
    // finds the zero of the function b.pointAt(tc).x() - cosAngle
    tc -= ((((2-3*QT_PATH_KAPPA) * tc + 3*(QT_PATH_KAPPA-1)) * tc) * tc + 1 - cosAngle) // value
         / (((6-9*QT_PATH_KAPPA) * tc + 6*(QT_PATH_KAPPA-1)) * tc); // derivative
    tc -= ((((2-3*QT_PATH_KAPPA) * tc + 3*(QT_PATH_KAPPA-1)) * tc) * tc + 1 - cosAngle) // value
         / (((6-9*QT_PATH_KAPPA) * tc + 6*(QT_PATH_KAPPA-1)) * tc); // derivative

    // initial guess
    qreal ts = tc;
    // do some iterations of newton's method to approximate sinAngle
    // finds the zero of the function b.pointAt(tc).y() - sinAngle
    ts -= ((((3*QT_PATH_KAPPA-2) * ts -  6*QT_PATH_KAPPA + 3) * ts + 3*QT_PATH_KAPPA) * ts - sinAngle)
         / (((9*QT_PATH_KAPPA-6) * ts + 12*QT_PATH_KAPPA - 6) * ts + 3*QT_PATH_KAPPA);
    ts -= ((((3*QT_PATH_KAPPA-2) * ts -  6*QT_PATH_KAPPA + 3) * ts + 3*QT_PATH_KAPPA) * ts - sinAngle)
         / (((9*QT_PATH_KAPPA-6) * ts + 12*QT_PATH_KAPPA - 6) * ts + 3*QT_PATH_KAPPA);

    // use the average of the t that best approximates cosAngle
    // and the t that best approximates sinAngle
    qreal t = 0.5 * (tc + ts);

#if 0
    printf("angle: %f, t: %f\n", angle, t);
    qreal a, b, c, d;
    bezierCoefficients(t, a, b, c, d);
    printf("cosAngle: %.10f, value: %.10f\n", cosAngle, a + b + c * QT_PATH_KAPPA);
    printf("sinAngle: %.10f, value: %.10f\n", sinAngle, b * QT_PATH_KAPPA + c + d);
#endif

    return t;
}