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275 lines
8.0 KiB
275 lines
8.0 KiB
/****************************************************************************
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**
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** Copyright (C) 2010 Nokia Corporation and/or its subsidiary(-ies).
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** All rights reserved.
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** Contact: Nokia Corporation (qt-info@nokia.com)
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**
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** This file is part of the QtGui module of the Qt Toolkit.
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**
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** $QT_BEGIN_LICENSE:LGPL$
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** Commercial Usage
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** Licensees holding valid Qt Commercial licenses may use this file in
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** accordance with the Qt Commercial License Agreement provided with the
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** Software or, alternatively, in accordance with the terms contained in
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** a written agreement between you and Nokia.
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**
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** GNU Lesser General Public License Usage
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** Alternatively, this file may be used under the terms of the GNU Lesser
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** General Public License version 2.1 as published by the Free Software
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** Foundation and appearing in the file LICENSE.LGPL included in the
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** packaging of this file. Please review the following information to
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** ensure the GNU Lesser General Public License version 2.1 requirements
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** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
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**
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** In addition, as a special exception, Nokia gives you certain additional
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** rights. These rights are described in the Nokia Qt LGPL Exception
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** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
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**
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** GNU General Public License Usage
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** Alternatively, this file may be used under the terms of the GNU
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** General Public License version 3.0 as published by the Free Software
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** Foundation and appearing in the file LICENSE.GPL included in the
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** packaging of this file. Please review the following information to
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** ensure the GNU General Public License version 3.0 requirements will be
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** met: http://www.gnu.org/copyleft/gpl.html.
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**
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** If you have questions regarding the use of this file, please contact
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** Nokia at qt-info@nokia.com.
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** $QT_END_LICENSE$
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**
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****************************************************************************/
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#ifndef QBEZIER_P_H
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#define QBEZIER_P_H
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//
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// W A R N I N G
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// -------------
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//
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// This file is not part of the Qt API. It exists for the convenience
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// of other Qt classes. This header file may change from version to
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// version without notice, or even be removed.
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//
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// We mean it.
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//
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#include "QtCore/qpoint.h"
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#include "QtCore/qline.h"
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#include "QtCore/qrect.h"
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#include "QtCore/qvector.h"
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#include "QtCore/qlist.h"
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#include "QtCore/qpair.h"
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#include "QtGui/qtransform.h"
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QT_BEGIN_NAMESPACE
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class QPolygonF;
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class Q_GUI_EXPORT QBezier
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{
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public:
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static QBezier fromPoints(const QPointF &p1, const QPointF &p2,
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const QPointF &p3, const QPointF &p4);
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static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d);
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inline QPointF pointAt(qreal t) const;
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inline QPointF normalVector(qreal t) const;
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inline QPointF derivedAt(qreal t) const;
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inline QPointF secondDerivedAt(qreal t) const;
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QPolygonF toPolygon(qreal bezier_flattening_threshold = 0.5) const;
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void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) const;
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QRectF bounds() const;
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qreal length(qreal error = 0.01) const;
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void addIfClose(qreal *length, qreal error) const;
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qreal tAtLength(qreal len) const;
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int stationaryYPoints(qreal &t0, qreal &t1) const;
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qreal tForY(qreal t0, qreal t1, qreal y) const;
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QPointF pt1() const { return QPointF(x1, y1); }
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QPointF pt2() const { return QPointF(x2, y2); }
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QPointF pt3() const { return QPointF(x3, y3); }
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QPointF pt4() const { return QPointF(x4, y4); }
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QBezier mapBy(const QTransform &transform) const;
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inline QPointF midPoint() const;
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inline QLineF midTangent() const;
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inline QLineF startTangent() const;
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inline QLineF endTangent() const;
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inline void parameterSplitLeft(qreal t, QBezier *left);
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inline void split(QBezier *firstHalf, QBezier *secondHalf) const;
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int shifted(QBezier *curveSegments, int maxSegmets,
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qreal offset, float threshold) const;
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QBezier bezierOnInterval(qreal t0, qreal t1) const;
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QBezier getSubRange(qreal t0, qreal t1) const;
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qreal x1, y1, x2, y2, x3, y3, x4, y4;
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};
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inline QPointF QBezier::midPoint() const
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{
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return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.);
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}
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inline QLineF QBezier::midTangent() const
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{
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QPointF mid = midPoint();
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QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5));
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return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(),
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mid.x() + dir.dx(), mid.y() + dir.dy());
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}
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inline QLineF QBezier::startTangent() const
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{
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QLineF tangent(pt1(), pt2());
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if (tangent.isNull())
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tangent = QLineF(pt1(), pt3());
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if (tangent.isNull())
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tangent = QLineF(pt1(), pt4());
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return tangent;
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}
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inline QLineF QBezier::endTangent() const
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{
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QLineF tangent(pt4(), pt3());
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if (tangent.isNull())
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tangent = QLineF(pt4(), pt2());
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if (tangent.isNull())
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tangent = QLineF(pt4(), pt1());
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return tangent;
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}
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inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d)
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{
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qreal m_t = 1. - t;
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b = m_t * m_t;
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c = t * t;
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d = c * t;
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a = b * m_t;
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b *= 3. * t;
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c *= 3. * m_t;
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}
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inline QPointF QBezier::pointAt(qreal t) const
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{
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#if 1
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qreal a, b, c, d;
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coefficients(t, a, b, c, d);
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return QPointF(a*x1 + b*x2 + c*x3 + d*x4, a*y1 + b*y2 + c*y3 + d*y4);
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#else
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// numerically more stable:
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qreal m_t = 1. - t;
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qreal a = x1*m_t + x2*t;
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qreal b = x2*m_t + x3*t;
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qreal c = x3*m_t + x4*t;
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a = a*m_t + b*t;
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b = b*m_t + c*t;
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qreal x = a*m_t + b*t;
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qreal a = y1*m_t + y2*t;
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qreal b = y2*m_t + y3*t;
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qreal c = y3*m_t + y4*t;
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a = a*m_t + b*t;
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b = b*m_t + c*t;
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qreal y = a*m_t + b*t;
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return QPointF(x, y);
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#endif
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}
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inline QPointF QBezier::normalVector(qreal t) const
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{
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qreal m_t = 1. - t;
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qreal a = m_t * m_t;
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qreal b = t * m_t;
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qreal c = t * t;
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return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c);
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}
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inline QPointF QBezier::derivedAt(qreal t) const
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{
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// p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3)
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qreal m_t = 1. - t;
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qreal d = t * t;
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qreal a = -m_t * m_t;
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qreal b = 1 - 4 * t + 3 * d;
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qreal c = 2 * t - 3 * d;
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return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
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a * y1 + b * y2 + c * y3 + d * y4);
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}
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inline QPointF QBezier::secondDerivedAt(qreal t) const
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{
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qreal a = 2. - 2. * t;
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qreal b = -4 + 6 * t;
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qreal c = 2 - 6 * t;
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qreal d = 2 * t;
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return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
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a * y1 + b * y2 + c * y3 + d * y4);
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}
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inline void QBezier::split(QBezier *firstHalf, QBezier *secondHalf) const
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{
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Q_ASSERT(firstHalf);
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Q_ASSERT(secondHalf);
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qreal c = (x2 + x3)*.5;
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firstHalf->x2 = (x1 + x2)*.5;
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secondHalf->x3 = (x3 + x4)*.5;
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firstHalf->x1 = x1;
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secondHalf->x4 = x4;
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firstHalf->x3 = (firstHalf->x2 + c)*.5;
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secondHalf->x2 = (secondHalf->x3 + c)*.5;
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firstHalf->x4 = secondHalf->x1 = (firstHalf->x3 + secondHalf->x2)*.5;
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c = (y2 + y3)/2;
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firstHalf->y2 = (y1 + y2)*.5;
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secondHalf->y3 = (y3 + y4)*.5;
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firstHalf->y1 = y1;
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secondHalf->y4 = y4;
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firstHalf->y3 = (firstHalf->y2 + c)*.5;
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secondHalf->y2 = (secondHalf->y3 + c)*.5;
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firstHalf->y4 = secondHalf->y1 = (firstHalf->y3 + secondHalf->y2)*.5;
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}
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inline void QBezier::parameterSplitLeft(qreal t, QBezier *left)
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{
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left->x1 = x1;
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left->y1 = y1;
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left->x2 = x1 + t * ( x2 - x1 );
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left->y2 = y1 + t * ( y2 - y1 );
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left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot
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left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot
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x3 = x3 + t * ( x4 - x3 );
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y3 = y3 + t * ( y4 - y3 );
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x2 = left->x3 + t * ( x3 - left->x3);
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y2 = left->y3 + t * ( y3 - left->y3);
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left->x3 = left->x2 + t * ( left->x3 - left->x2 );
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left->y3 = left->y2 + t * ( left->y3 - left->y2 );
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left->x4 = x1 = left->x3 + t * (x2 - left->x3);
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left->y4 = y1 = left->y3 + t * (y2 - left->y3);
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}
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QT_END_NAMESPACE
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#endif // QBEZIER_P_H
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