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Diffstat (limited to 'src/gui/painting/qbezier_p.h')
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1 files changed, 280 insertions, 0 deletions
diff --git a/src/gui/painting/qbezier_p.h b/src/gui/painting/qbezier_p.h new file mode 100644 index 0000000..5c2ad5e --- /dev/null +++ b/src/gui/painting/qbezier_p.h @@ -0,0 +1,280 @@ +/**************************************************************************** +** +** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies). +** Contact: Qt Software Information (qt-info@nokia.com) +** +** This file is part of the QtGui module of the Qt Toolkit. +** +** $QT_BEGIN_LICENSE:LGPL$ +** No Commercial Usage +** This file contains pre-release code and may not be distributed. +** You may use this file in accordance with the terms and conditions +** contained in the either Technology Preview License Agreement or the +** Beta Release License Agreement. +** +** GNU Lesser General Public License Usage +** Alternatively, this file may be used under the terms of the GNU Lesser +** General Public License version 2.1 as published by the Free Software +** Foundation and appearing in the file LICENSE.LGPL included in the +** packaging of this file. Please review the following information to +** ensure the GNU Lesser General Public License version 2.1 requirements +** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html. +** +** In addition, as a special exception, Nokia gives you certain +** additional rights. These rights are described in the Nokia Qt LGPL +** Exception version 1.0, included in the file LGPL_EXCEPTION.txt in this +** package. +** +** GNU General Public License Usage +** Alternatively, this file may be used under the terms of the GNU +** General Public License version 3.0 as published by the Free Software +** Foundation and appearing in the file LICENSE.GPL included in the +** packaging of this file. Please review the following information to +** ensure the GNU General Public License version 3.0 requirements will be +** met: http://www.gnu.org/copyleft/gpl.html. +** +** If you are unsure which license is appropriate for your use, please +** contact the sales department at qt-sales@nokia.com. +** $QT_END_LICENSE$ +** +****************************************************************************/ + +#ifndef QBEZIER_P_H +#define QBEZIER_P_H + +// +// W A R N I N G +// ------------- +// +// This file is not part of the Qt API. It exists for the convenience +// of other Qt classes. This header file may change from version to +// version without notice, or even be removed. +// +// We mean it. +// + +#include "QtCore/qpoint.h" +#include "QtCore/qline.h" +#include "QtCore/qrect.h" +#include "QtCore/qvector.h" +#include "QtCore/qlist.h" +#include "QtCore/qpair.h" + +QT_BEGIN_NAMESPACE + +class QPolygonF; + +class Q_GUI_EXPORT QBezier +{ +public: + static QBezier fromPoints(const QPointF &p1, const QPointF &p2, + const QPointF &p3, const QPointF &p4); + + static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d); + + inline QPointF pointAt(qreal t) const; + inline QPointF normalVector(qreal t) const; + + inline QPointF derivedAt(qreal t) const; + inline QPointF secondDerivedAt(qreal t) const; + + QPolygonF toPolygon() const; + void addToPolygon(QPolygonF *p) const; + void addToPolygonIterative(QPolygonF *p) const; + void addToPolygonMixed(QPolygonF *p) const; + QRectF bounds() const; + qreal length(qreal error = 0.01) const; + void addIfClose(qreal *length, qreal error) const; + + qreal tAtLength(qreal len) const; + + int stationaryYPoints(qreal &t0, qreal &t1) const; + qreal tForY(qreal t0, qreal t1, qreal y) const; + + QPointF pt1() const { return QPointF(x1, y1); } + QPointF pt2() const { return QPointF(x2, y2); } + QPointF pt3() const { return QPointF(x3, y3); } + QPointF pt4() const { return QPointF(x4, y4); } + + inline QPointF midPoint() const; + inline QLineF midTangent() const; + + inline QLineF startTangent() const; + inline QLineF endTangent() const; + + inline void parameterSplitLeft(qreal t, QBezier *left); + inline void split(QBezier *firstHalf, QBezier *secondHalf) const; + int shifted(QBezier *curveSegments, int maxSegmets, + qreal offset, float threshold) const; + + QVector< QList<QBezier> > splitAtIntersections(QBezier &a); + + QBezier bezierOnInterval(qreal t0, qreal t1) const; + + static QVector< QPair<qreal, qreal> > findIntersections(const QBezier &a, + const QBezier &b); + + static bool findIntersections(const QBezier &a, const QBezier &b, + QVector<QPair<qreal, qreal> > *t); + + qreal x1, y1, x2, y2, x3, y3, x4, y4; +}; + +inline QPointF QBezier::midPoint() const +{ + return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.); +} + +inline QLineF QBezier::midTangent() const +{ + QPointF mid = midPoint(); + QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5)); + return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(), + mid.x() + dir.dx(), mid.y() + dir.dy()); +} + +inline QLineF QBezier::startTangent() const +{ + QLineF tangent(pt1(), pt2()); + if (tangent.isNull()) + tangent = QLineF(pt1(), pt3()); + if (tangent.isNull()) + tangent = QLineF(pt1(), pt4()); + return tangent; +} + +inline QLineF QBezier::endTangent() const +{ + QLineF tangent(pt4(), pt3()); + if (tangent.isNull()) + tangent = QLineF(pt4(), pt2()); + if (tangent.isNull()) + tangent = QLineF(pt4(), pt1()); + return tangent; +} + +inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d) +{ + qreal m_t = 1. - t; + b = m_t * m_t; + c = t * t; + d = c * t; + a = b * m_t; + b *= 3. * t; + c *= 3. * m_t; +} + +inline QPointF QBezier::pointAt(qreal t) const +{ + Q_ASSERT(t >= 0); + Q_ASSERT(t <= 1); +#if 1 + qreal a, b, c, d; + coefficients(t, a, b, c, d); + return QPointF(a*x1 + b*x2 + c*x3 + d*x4, a*y1 + b*y2 + c*y3 + d*y4); +#else + // numerically more stable: + qreal m_t = 1. - t; + qreal a = x1*m_t + x2*t; + qreal b = x2*m_t + x3*t; + qreal c = x3*m_t + x4*t; + a = a*m_t + b*t; + b = b*m_t + c*t; + qreal x = a*m_t + b*t; + qreal a = y1*m_t + y2*t; + qreal b = y2*m_t + y3*t; + qreal c = y3*m_t + y4*t; + a = a*m_t + b*t; + b = b*m_t + c*t; + qreal y = a*m_t + b*t; + return QPointF(x, y); +#endif +} + +inline QPointF QBezier::normalVector(qreal t) const +{ + qreal m_t = 1. - t; + qreal a = m_t * m_t; + qreal b = t * m_t; + qreal c = t * t; + + return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c); +} + +inline QPointF QBezier::derivedAt(qreal t) const +{ + // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3) + + qreal m_t = 1. - t; + + qreal d = t * t; + qreal a = -m_t * m_t; + qreal b = 1 - 4 * t + 3 * d; + qreal c = 2 * t - 3 * d; + + return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4, + a * y1 + b * y2 + c * y3 + d * y4); +} + +inline QPointF QBezier::secondDerivedAt(qreal t) const +{ + qreal a = 2. - 2. * t; + qreal b = -4 + 6 * t; + qreal c = 2 - 6 * t; + qreal d = 2 * t; + + return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4, + a * y1 + b * y2 + c * y3 + d * y4); +} + +inline void QBezier::split(QBezier *firstHalf, QBezier *secondHalf) const +{ + Q_ASSERT(firstHalf); + Q_ASSERT(secondHalf); + + qreal c = (x2 + x3)*.5; + firstHalf->x2 = (x1 + x2)*.5; + secondHalf->x3 = (x3 + x4)*.5; + firstHalf->x1 = x1; + secondHalf->x4 = x4; + firstHalf->x3 = (firstHalf->x2 + c)*.5; + secondHalf->x2 = (secondHalf->x3 + c)*.5; + firstHalf->x4 = secondHalf->x1 = (firstHalf->x3 + secondHalf->x2)*.5; + + c = (y2 + y3)/2; + firstHalf->y2 = (y1 + y2)*.5; + secondHalf->y3 = (y3 + y4)*.5; + firstHalf->y1 = y1; + secondHalf->y4 = y4; + firstHalf->y3 = (firstHalf->y2 + c)*.5; + secondHalf->y2 = (secondHalf->y3 + c)*.5; + firstHalf->y4 = secondHalf->y1 = (firstHalf->y3 + secondHalf->y2)*.5; +} + +inline void QBezier::parameterSplitLeft(qreal t, QBezier *left) +{ + left->x1 = x1; + left->y1 = y1; + + left->x2 = x1 + t * ( x2 - x1 ); + left->y2 = y1 + t * ( y2 - y1 ); + + left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot + left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot + + x3 = x3 + t * ( x4 - x3 ); + y3 = y3 + t * ( y4 - y3 ); + + x2 = left->x3 + t * ( x3 - left->x3); + y2 = left->y3 + t * ( y3 - left->y3); + + left->x3 = left->x2 + t * ( left->x3 - left->x2 ); + left->y3 = left->y2 + t * ( left->y3 - left->y2 ); + + left->x4 = x1 = left->x3 + t * (x2 - left->x3); + left->y4 = y1 = left->y3 + t * (y2 - left->y3); +} + +QT_END_NAMESPACE + +#endif // QBEZIER_P_H |