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39
40 #ifndef QBEZIER_P_H
41 #define QBEZIER_P_H
42
43 //
44 // W A R N I N G
45 // -------------
46 //
47 // This file is not part of the Qt API. It exists for the convenience
48 // of other Qt classes. This header file may change from version to
49 // version without notice, or even be removed.
50 //
51 // We mean it.
52 //
53
54 #include <QtGui/private/qtguiglobal_p.h>
55 #include "QtCore/qpoint.h"
56 #include "QtCore/qline.h"
57 #include "QtCore/qrect.h"
58 #include "QtCore/qvector.h"
59 #include "QtCore/qlist.h"
60 #include "QtCore/qpair.h"
61 #include "QtGui/qtransform.h"
62 #include <private/qdatabuffer_p.h>
63
64 QT_BEGIN_NAMESPACE
65
66 class QPolygonF;
67
68 class Q_GUI_EXPORT QBezier
69 {
70 public:
fromPoints(const QPointF & p1,const QPointF & p2,const QPointF & p3,const QPointF & p4)71 static QBezier fromPoints(const QPointF &p1, const QPointF &p2,
72 const QPointF &p3, const QPointF &p4)
73 { return {p1.x(), p1.y(), p2.x(), p2.y(), p3.x(), p3.y(), p4.x(), p4.y()}; }
74
75 static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d);
76
77 inline QPointF pointAt(qreal t) const;
78 inline QPointF normalVector(qreal t) const;
79
80 inline QPointF derivedAt(qreal t) const;
81 inline QPointF secondDerivedAt(qreal t) const;
82
83 QPolygonF toPolygon(qreal bezier_flattening_threshold = 0.5) const;
84 void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) const;
85 void addToPolygon(QDataBuffer<QPointF> &polygon, qreal bezier_flattening_threshold) const;
86
87 QRectF bounds() const;
88 qreal length(qreal error = 0.01) const;
89 void addIfClose(qreal *length, qreal error) const;
90
91 qreal tAtLength(qreal len) const;
92
93 int stationaryYPoints(qreal &t0, qreal &t1) const;
94 qreal tForY(qreal t0, qreal t1, qreal y) const;
95
pt1()96 QPointF pt1() const { return QPointF(x1, y1); }
pt2()97 QPointF pt2() const { return QPointF(x2, y2); }
pt3()98 QPointF pt3() const { return QPointF(x3, y3); }
pt4()99 QPointF pt4() const { return QPointF(x4, y4); }
100
101 QBezier mapBy(const QTransform &transform) const;
102
103 inline QPointF midPoint() const;
104 inline QLineF midTangent() const;
105
106 inline QLineF startTangent() const;
107 inline QLineF endTangent() const;
108
109 inline void parameterSplitLeft(qreal t, QBezier *left);
110 inline std::pair<QBezier, QBezier> split() const;
111
112 int shifted(QBezier *curveSegments, int maxSegmets,
113 qreal offset, float threshold) const;
114
115 QBezier bezierOnInterval(qreal t0, qreal t1) const;
116 QBezier getSubRange(qreal t0, qreal t1) const;
117
118 qreal x1, y1, x2, y2, x3, y3, x4, y4;
119 };
120
midPoint()121 inline QPointF QBezier::midPoint() const
122 {
123 return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.);
124 }
125
midTangent()126 inline QLineF QBezier::midTangent() const
127 {
128 QPointF mid = midPoint();
129 QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5));
130 return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(),
131 mid.x() + dir.dx(), mid.y() + dir.dy());
132 }
133
startTangent()134 inline QLineF QBezier::startTangent() const
135 {
136 QLineF tangent(pt1(), pt2());
137 if (tangent.isNull())
138 tangent = QLineF(pt1(), pt3());
139 if (tangent.isNull())
140 tangent = QLineF(pt1(), pt4());
141 return tangent;
142 }
143
endTangent()144 inline QLineF QBezier::endTangent() const
145 {
146 QLineF tangent(pt4(), pt3());
147 if (tangent.isNull())
148 tangent = QLineF(pt4(), pt2());
149 if (tangent.isNull())
150 tangent = QLineF(pt4(), pt1());
151 return tangent;
152 }
153
coefficients(qreal t,qreal & a,qreal & b,qreal & c,qreal & d)154 inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d)
155 {
156 qreal m_t = 1. - t;
157 b = m_t * m_t;
158 c = t * t;
159 d = c * t;
160 a = b * m_t;
161 b *= 3. * t;
162 c *= 3. * m_t;
163 }
164
pointAt(qreal t)165 inline QPointF QBezier::pointAt(qreal t) const
166 {
167 // numerically more stable:
168 qreal x, y;
169
170 qreal m_t = 1. - t;
171 {
172 qreal a = x1*m_t + x2*t;
173 qreal b = x2*m_t + x3*t;
174 qreal c = x3*m_t + x4*t;
175 a = a*m_t + b*t;
176 b = b*m_t + c*t;
177 x = a*m_t + b*t;
178 }
179 {
180 qreal a = y1*m_t + y2*t;
181 qreal b = y2*m_t + y3*t;
182 qreal c = y3*m_t + y4*t;
183 a = a*m_t + b*t;
184 b = b*m_t + c*t;
185 y = a*m_t + b*t;
186 }
187 return QPointF(x, y);
188 }
189
normalVector(qreal t)190 inline QPointF QBezier::normalVector(qreal t) const
191 {
192 qreal m_t = 1. - t;
193 qreal a = m_t * m_t;
194 qreal b = t * m_t;
195 qreal c = t * t;
196
197 return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c);
198 }
199
derivedAt(qreal t)200 inline QPointF QBezier::derivedAt(qreal t) const
201 {
202 // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3)
203
204 qreal m_t = 1. - t;
205
206 qreal d = t * t;
207 qreal a = -m_t * m_t;
208 qreal b = 1 - 4 * t + 3 * d;
209 qreal c = 2 * t - 3 * d;
210
211 return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
212 a * y1 + b * y2 + c * y3 + d * y4);
213 }
214
secondDerivedAt(qreal t)215 inline QPointF QBezier::secondDerivedAt(qreal t) const
216 {
217 qreal a = 2. - 2. * t;
218 qreal b = -4 + 6 * t;
219 qreal c = 2 - 6 * t;
220 qreal d = 2 * t;
221
222 return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,
223 a * y1 + b * y2 + c * y3 + d * y4);
224 }
225
split()226 std::pair<QBezier, QBezier> QBezier::split() const
227 {
228 const auto mid = [](QPointF lhs, QPointF rhs) { return (lhs + rhs) * .5; };
229
230 const QPointF mid_12 = mid(pt1(), pt2());
231 const QPointF mid_23 = mid(pt2(), pt3());
232 const QPointF mid_34 = mid(pt3(), pt4());
233 const QPointF mid_12_23 = mid(mid_12, mid_23);
234 const QPointF mid_23_34 = mid(mid_23, mid_34);
235 const QPointF mid_12_23__23_34 = mid(mid_12_23, mid_23_34);
236
237 return {
238 fromPoints(pt1(), mid_12, mid_12_23, mid_12_23__23_34),
239 fromPoints(mid_12_23__23_34, mid_23_34, mid_34, pt4()),
240 };
241 }
242
parameterSplitLeft(qreal t,QBezier * left)243 inline void QBezier::parameterSplitLeft(qreal t, QBezier *left)
244 {
245 left->x1 = x1;
246 left->y1 = y1;
247
248 left->x2 = x1 + t * ( x2 - x1 );
249 left->y2 = y1 + t * ( y2 - y1 );
250
251 left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot
252 left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot
253
254 x3 = x3 + t * ( x4 - x3 );
255 y3 = y3 + t * ( y4 - y3 );
256
257 x2 = left->x3 + t * ( x3 - left->x3);
258 y2 = left->y3 + t * ( y3 - left->y3);
259
260 left->x3 = left->x2 + t * ( left->x3 - left->x2 );
261 left->y3 = left->y2 + t * ( left->y3 - left->y2 );
262
263 left->x4 = x1 = left->x3 + t * (x2 - left->x3);
264 left->y4 = y1 = left->y3 + t * (y2 - left->y3);
265 }
266
267 QT_END_NAMESPACE
268
269 #endif // QBEZIER_P_H
270