1// Copyright (C) 2016 The Qt Company Ltd.
2// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
3
4#ifndef QBEZIER_P_H
5#define QBEZIER_P_H
6
7//
8// W A R N I N G
9// -------------
10//
11// This file is not part of the Qt API. It exists for the convenience
12// of other Qt classes. This header file may change from version to
13// version without notice, or even be removed.
14//
15// We mean it.
16//
17
18#include <QtGui/private/qtguiglobal_p.h>
19#include "QtCore/qline.h"
20#include "QtCore/qlist.h"
21#include "QtCore/qpair.h"
22#include "QtCore/qpoint.h"
23#include "QtCore/qrect.h"
24#include "QtGui/qtransform.h"
25#include <private/qdatabuffer_p.h>
26
27QT_BEGIN_NAMESPACE
28
29class QPolygonF;
30
31class Q_GUI_EXPORT QBezier
32{
33public:
34 static QBezier fromPoints(const QPointF &p1, const QPointF &p2,
35 const QPointF &p3, const QPointF &p4)
36 { return {.x1: p1.x(), .y1: p1.y(), .x2: p2.x(), .y2: p2.y(), .x3: p3.x(), .y3: p3.y(), .x4: p4.x(), .y4: p4.y()}; }
37
38 static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d);
39
40 inline QPointF pointAt(qreal t) const;
41 inline QPointF normalVector(qreal t) const;
42
43 inline QPointF derivedAt(qreal t) const;
44 inline QPointF secondDerivedAt(qreal t) const;
45
46 QPolygonF toPolygon(qreal bezier_flattening_threshold = 0.5) const;
47 void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) const;
48 void addToPolygon(QDataBuffer<QPointF> &polygon, qreal bezier_flattening_threshold) const;
49
50 QRectF bounds() const;
51 qreal length(qreal error = 0.01) const;
52 void addIfClose(qreal *length, qreal error) const;
53
54 qreal tAtLength(qreal len) const;
55
56 int stationaryYPoints(qreal &t0, qreal &t1) const;
57 qreal tForY(qreal t0, qreal t1, qreal y) const;
58
59 QPointF pt1() const { return QPointF(x1, y1); }
60 QPointF pt2() const { return QPointF(x2, y2); }
61 QPointF pt3() const { return QPointF(x3, y3); }
62 QPointF pt4() const { return QPointF(x4, y4); }
63
64 QBezier mapBy(const QTransform &transform) const;
65
66 inline QPointF midPoint() const;
67 inline QLineF midTangent() const;
68
69 inline QLineF startTangent() const;
70 inline QLineF endTangent() const;
71
72 inline void parameterSplitLeft(qreal t, QBezier *left);
73 inline std::pair<QBezier, QBezier> split() const;
74
75 int shifted(QBezier *curveSegments, int maxSegmets,
76 qreal offset, float threshold) const;
77
78 QBezier bezierOnInterval(qreal t0, qreal t1) const;
79 QBezier getSubRange(qreal t0, qreal t1) const;
80
81 qreal x1, y1, x2, y2, x3, y3, x4, y4;
82};
83
84inline QPointF QBezier::midPoint() const
85{
86 return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.);
87}
88
89inline QLineF QBezier::midTangent() const
90{
91 QPointF mid = midPoint();
92 QLineF dir(QLineF(x1, y1, x2, y2).pointAt(t: 0.5), QLineF(x3, y3, x4, y4).pointAt(t: 0.5));
93 return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(),
94 mid.x() + dir.dx(), mid.y() + dir.dy());
95}
96
97inline QLineF QBezier::startTangent() const
98{
99 QLineF tangent(pt1(), pt2());
100 if (tangent.isNull())
101 tangent = QLineF(pt1(), pt3());
102 if (tangent.isNull())
103 tangent = QLineF(pt1(), pt4());
104 return tangent;
105}
106
107inline QLineF QBezier::endTangent() const
108{
109 QLineF tangent(pt4(), pt3());
110 if (tangent.isNull())
111 tangent = QLineF(pt4(), pt2());
112 if (tangent.isNull())
113 tangent = QLineF(pt4(), pt1());
114 return tangent;
115}
116
117inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d)
118{
119 qreal m_t = 1. - t;
120 b = m_t * m_t;
121 c = t * t;
122 d = c * t;
123 a = b * m_t;
124 b *= 3. * t;
125 c *= 3. * m_t;
126}
127
128inline QPointF QBezier::pointAt(qreal t) const
129{
130 // numerically more stable:
131 qreal x, y;
132
133 qreal m_t = 1. - t;
134 {
135 qreal a = x1*m_t + x2*t;
136 qreal b = x2*m_t + x3*t;
137 qreal c = x3*m_t + x4*t;
138 a = a*m_t + b*t;
139 b = b*m_t + c*t;
140 x = a*m_t + b*t;
141 }
142 {
143 qreal a = y1*m_t + y2*t;
144 qreal b = y2*m_t + y3*t;
145 qreal c = y3*m_t + y4*t;
146 a = a*m_t + b*t;
147 b = b*m_t + c*t;
148 y = a*m_t + b*t;
149 }
150 return QPointF(x, y);
151}
152
153inline QPointF QBezier::normalVector(qreal t) const
154{
155 qreal m_t = 1. - t;
156 qreal a = m_t * m_t;
157 qreal b = t * m_t;
158 qreal c = t * t;
159
160 return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c);
161}
162
163inline QPointF QBezier::derivedAt(qreal t) const
164{
165 // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3)
166
167 qreal m_t = 1. - t;
168
169 qreal d = t * t;
170 qreal a = -m_t * m_t;
171 qreal b = 1 - 4 * t + 3 * d;
172 qreal c = 2 * t - 3 * d;
173
174 return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
175 a * y1 + b * y2 + c * y3 + d * y4);
176}
177
178inline QPointF QBezier::secondDerivedAt(qreal t) const
179{
180 qreal a = 2. - 2. * t;
181 qreal b = -4 + 6 * t;
182 qreal c = 2 - 6 * t;
183 qreal d = 2 * t;
184
185 return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
186 a * y1 + b * y2 + c * y3 + d * y4);
187}
188
189std::pair<QBezier, QBezier> QBezier::split() const
190{
191 const auto mid = [](QPointF lhs, QPointF rhs) { return (lhs + rhs) * .5; };
192
193 const QPointF mid_12 = mid(pt1(), pt2());
194 const QPointF mid_23 = mid(pt2(), pt3());
195 const QPointF mid_34 = mid(pt3(), pt4());
196 const QPointF mid_12_23 = mid(mid_12, mid_23);
197 const QPointF mid_23_34 = mid(mid_23, mid_34);
198 const QPointF mid_12_23__23_34 = mid(mid_12_23, mid_23_34);
199
200 return {
201 fromPoints(p1: pt1(), p2: mid_12, p3: mid_12_23, p4: mid_12_23__23_34),
202 fromPoints(p1: mid_12_23__23_34, p2: mid_23_34, p3: mid_34, p4: pt4()),
203 };
204}
205
206inline void QBezier::parameterSplitLeft(qreal t, QBezier *left)
207{
208 left->x1 = x1;
209 left->y1 = y1;
210
211 left->x2 = x1 + t * ( x2 - x1 );
212 left->y2 = y1 + t * ( y2 - y1 );
213
214 left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot
215 left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot
216
217 x3 = x3 + t * ( x4 - x3 );
218 y3 = y3 + t * ( y4 - y3 );
219
220 x2 = left->x3 + t * ( x3 - left->x3);
221 y2 = left->y3 + t * ( y3 - left->y3);
222
223 left->x3 = left->x2 + t * ( left->x3 - left->x2 );
224 left->y3 = left->y2 + t * ( left->y3 - left->y2 );
225
226 left->x4 = x1 = left->x3 + t * (x2 - left->x3);
227 left->y4 = y1 = left->y3 + t * (y2 - left->y3);
228}
229
230QT_END_NAMESPACE
231
232#endif // QBEZIER_P_H
233

source code of qtbase/src/gui/painting/qbezier_p.h