1 /****************************************************************************
3 ** Copyright (C) 2011 Nokia Corporation and/or its subsidiary(-ies).
4 ** All rights reserved.
5 ** Contact: Nokia Corporation (qt-info@nokia.com)
7 ** This file is part of the QtGui module of the Qt Toolkit.
9 ** $QT_BEGIN_LICENSE:LGPL$
10 ** GNU Lesser General Public License Usage
11 ** This file may be used under the terms of the GNU Lesser General Public
12 ** License version 2.1 as published by the Free Software Foundation and
13 ** appearing in the file LICENSE.LGPL included in the packaging of this
14 ** file. Please review the following information to ensure the GNU Lesser
15 ** General Public License version 2.1 requirements will be met:
16 ** http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
18 ** In addition, as a special exception, Nokia gives you certain additional
19 ** rights. These rights are described in the Nokia Qt LGPL Exception
20 ** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
22 ** GNU General Public License Usage
23 ** Alternatively, this file may be used under the terms of the GNU General
24 ** Public License version 3.0 as published by the Free Software Foundation
25 ** and appearing in the file LICENSE.GPL included in the packaging of this
26 ** file. Please review the following information to ensure the GNU General
27 ** Public License version 3.0 requirements will be met:
28 ** http://www.gnu.org/copyleft/gpl.html.
31 ** Alternatively, this file may be used in accordance with the terms and
32 ** conditions contained in a signed written agreement between you and Nokia.
40 ****************************************************************************/
49 // This file is not part of the Qt API. It exists for the convenience
50 // of other Qt classes. This header file may change from version to
51 // version without notice, or even be removed.
56 #include "QtCore/qpoint.h"
57 #include "QtCore/qline.h"
58 #include "QtCore/qrect.h"
59 #include "QtCore/qvector.h"
60 #include "QtCore/qlist.h"
61 #include "QtCore/qpair.h"
62 #include "QtGui/qtransform.h"
68 class Q_GUI_EXPORT QBezier
71 static QBezier fromPoints(const QPointF &p1, const QPointF &p2,
72 const QPointF &p3, const QPointF &p4);
74 static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d);
76 inline QPointF pointAt(qreal t) const;
77 inline QPointF normalVector(qreal t) const;
79 inline QPointF derivedAt(qreal t) const;
80 inline QPointF secondDerivedAt(qreal t) const;
82 QPolygonF toPolygon(qreal bezier_flattening_threshold = 0.5) const;
83 void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) const;
85 QRectF bounds() const;
86 qreal length(qreal error = 0.01) const;
87 void addIfClose(qreal *length, qreal error) const;
89 qreal tAtLength(qreal len) const;
91 int stationaryYPoints(qreal &t0, qreal &t1) const;
92 qreal tForY(qreal t0, qreal t1, qreal y) const;
94 QPointF pt1() const { return QPointF(x1, y1); }
95 QPointF pt2() const { return QPointF(x2, y2); }
96 QPointF pt3() const { return QPointF(x3, y3); }
97 QPointF pt4() const { return QPointF(x4, y4); }
99 QBezier mapBy(const QTransform &transform) const;
101 inline QPointF midPoint() const;
102 inline QLineF midTangent() const;
104 inline QLineF startTangent() const;
105 inline QLineF endTangent() const;
107 inline void parameterSplitLeft(qreal t, QBezier *left);
108 inline void split(QBezier *firstHalf, QBezier *secondHalf) const;
110 int shifted(QBezier *curveSegments, int maxSegmets,
111 qreal offset, float threshold) const;
113 QBezier bezierOnInterval(qreal t0, qreal t1) const;
114 QBezier getSubRange(qreal t0, qreal t1) const;
116 qreal x1, y1, x2, y2, x3, y3, x4, y4;
119 inline QPointF QBezier::midPoint() const
121 return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.);
124 inline QLineF QBezier::midTangent() const
126 QPointF mid = midPoint();
127 QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5));
128 return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(),
129 mid.x() + dir.dx(), mid.y() + dir.dy());
132 inline QLineF QBezier::startTangent() const
134 QLineF tangent(pt1(), pt2());
135 if (tangent.isNull())
136 tangent = QLineF(pt1(), pt3());
137 if (tangent.isNull())
138 tangent = QLineF(pt1(), pt4());
142 inline QLineF QBezier::endTangent() const
144 QLineF tangent(pt4(), pt3());
145 if (tangent.isNull())
146 tangent = QLineF(pt4(), pt2());
147 if (tangent.isNull())
148 tangent = QLineF(pt4(), pt1());
152 inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d)
163 inline QPointF QBezier::pointAt(qreal t) const
165 // numerically more stable:
170 qreal a = x1*m_t + x2*t;
171 qreal b = x2*m_t + x3*t;
172 qreal c = x3*m_t + x4*t;
178 qreal a = y1*m_t + y2*t;
179 qreal b = y2*m_t + y3*t;
180 qreal c = y3*m_t + y4*t;
185 return QPointF(x, y);
188 inline QPointF QBezier::normalVector(qreal t) const
195 return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c);
198 inline QPointF QBezier::derivedAt(qreal t) const
200 // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3)
205 qreal a = -m_t * m_t;
206 qreal b = 1 - 4 * t + 3 * d;
207 qreal c = 2 * t - 3 * d;
209 return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
210 a * y1 + b * y2 + c * y3 + d * y4);
213 inline QPointF QBezier::secondDerivedAt(qreal t) const
215 qreal a = 2. - 2. * t;
216 qreal b = -4 + 6 * t;
220 return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
221 a * y1 + b * y2 + c * y3 + d * y4);
224 inline void QBezier::split(QBezier *firstHalf, QBezier *secondHalf) const
227 Q_ASSERT(secondHalf);
229 qreal c = (x2 + x3)*.5;
230 firstHalf->x2 = (x1 + x2)*.5;
231 secondHalf->x3 = (x3 + x4)*.5;
234 firstHalf->x3 = (firstHalf->x2 + c)*.5;
235 secondHalf->x2 = (secondHalf->x3 + c)*.5;
236 firstHalf->x4 = secondHalf->x1 = (firstHalf->x3 + secondHalf->x2)*.5;
239 firstHalf->y2 = (y1 + y2)*.5;
240 secondHalf->y3 = (y3 + y4)*.5;
243 firstHalf->y3 = (firstHalf->y2 + c)*.5;
244 secondHalf->y2 = (secondHalf->y3 + c)*.5;
245 firstHalf->y4 = secondHalf->y1 = (firstHalf->y3 + secondHalf->y2)*.5;
248 inline void QBezier::parameterSplitLeft(qreal t, QBezier *left)
253 left->x2 = x1 + t * ( x2 - x1 );
254 left->y2 = y1 + t * ( y2 - y1 );
256 left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot
257 left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot
259 x3 = x3 + t * ( x4 - x3 );
260 y3 = y3 + t * ( y4 - y3 );
262 x2 = left->x3 + t * ( x3 - left->x3);
263 y2 = left->y3 + t * ( y3 - left->y3);
265 left->x3 = left->x2 + t * ( left->x3 - left->x2 );
266 left->y3 = left->y2 + t * ( left->y3 - left->y2 );
268 left->x4 = x1 = left->x3 + t * (x2 - left->x3);
269 left->y4 = y1 = left->y3 + t * (y2 - left->y3);
274 #endif // QBEZIER_P_H