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+/****************************************************************************
+**
+** Copyright (C) 2010 Nokia Corporation and/or its subsidiary(-ies).
+** All rights reserved.
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the QtGui module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** Commercial Usage
+** Licensees holding valid Qt Commercial licenses may use this file in
+** accordance with the Qt Commercial License Agreement provided with the
+** Software or, alternatively, in accordance with the terms contained in
+** a written agreement between you and Nokia.
+**
+** 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 1.1, 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 have questions regarding the use of this file, please contact
+** Nokia at qt-info@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"
+#include "QtGui/qtransform.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(qreal bezier_flattening_threshold = 0.5) const;
+ void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) 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); }
+
+ QBezier mapBy(const QTransform &transform) const;
+
+ 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;
+
+ QBezier bezierOnInterval(qreal t0, qreal t1) const;
+ QBezier getSubRange(qreal t0, qreal t1) const;
+
+ 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
+{
+#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
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