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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: |

71 | static QBezier fromPoints(const QPointF &p1, const QPointF &p2, |

72 | const QPointF &p3, const QPointF &p4); |

73 | |

74 | static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d); |

75 | |

76 | inline QPointF pointAt(qreal t) const; |

77 | inline QPointF normalVector(qreal t) const; |

78 | |

79 | inline QPointF derivedAt(qreal t) const; |

80 | inline QPointF secondDerivedAt(qreal t) const; |

81 | |

82 | QPolygonF toPolygon(qreal bezier_flattening_threshold = 0.5) const; |

83 | void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) const; |

84 | void addToPolygon(QDataBuffer<QPointF> &polygon, qreal bezier_flattening_threshold) const; |

85 | |

86 | QRectF bounds() const; |

87 | qreal length(qreal error = 0.01) const; |

88 | void addIfClose(qreal *length, qreal error) const; |

89 | |

90 | qreal tAtLength(qreal len) const; |

91 | |

92 | int stationaryYPoints(qreal &t0, qreal &t1) const; |

93 | qreal tForY(qreal t0, qreal t1, qreal y) const; |

94 | |

95 | QPointF pt1() const { return QPointF(x1, y1); } |

96 | QPointF pt2() const { return QPointF(x2, y2); } |

97 | QPointF pt3() const { return QPointF(x3, y3); } |

98 | QPointF pt4() const { return QPointF(x4, y4); } |

99 | |

100 | QBezier mapBy(const QTransform &transform) const; |

101 | |

102 | inline QPointF midPoint() const; |

103 | inline QLineF midTangent() const; |

104 | |

105 | inline QLineF startTangent() const; |

106 | inline QLineF endTangent() const; |

107 | |

108 | inline void parameterSplitLeft(qreal t, QBezier *left); |

109 | inline void split(QBezier *firstHalf, QBezier *secondHalf) const; |

110 | |

111 | int shifted(QBezier *curveSegments, int maxSegmets, |

112 | qreal offset, float threshold) const; |

113 | |

114 | QBezier bezierOnInterval(qreal t0, qreal t1) const; |

115 | QBezier getSubRange(qreal t0, qreal t1) const; |

116 | |

117 | qreal x1, y1, x2, y2, x3, y3, x4, y4; |

118 | }; |

119 | |

120 | inline QPointF QBezier::midPoint() const |

121 | { |

122 | return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.); |

123 | } |

124 | |

125 | inline QLineF QBezier::midTangent() const |

126 | { |

127 | QPointF mid = midPoint(); |

128 | QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5)); |

129 | return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(), |

130 | mid.x() + dir.dx(), mid.y() + dir.dy()); |

131 | } |

132 | |

133 | inline QLineF QBezier::startTangent() const |

134 | { |

135 | QLineF tangent(pt1(), pt2()); |

136 | if (tangent.isNull()) |

137 | tangent = QLineF(pt1(), pt3()); |

138 | if (tangent.isNull()) |

139 | tangent = QLineF(pt1(), pt4()); |

140 | return tangent; |

141 | } |

142 | |

143 | inline QLineF QBezier::endTangent() const |

144 | { |

145 | QLineF tangent(pt4(), pt3()); |

146 | if (tangent.isNull()) |

147 | tangent = QLineF(pt4(), pt2()); |

148 | if (tangent.isNull()) |

149 | tangent = QLineF(pt4(), pt1()); |

150 | return tangent; |

151 | } |

152 | |

153 | inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d) |

154 | { |

155 | qreal m_t = 1. - t; |

156 | b = m_t * m_t; |

157 | c = t * t; |

158 | d = c * t; |

159 | a = b * m_t; |

160 | b *= 3. * t; |

161 | c *= 3. * m_t; |

162 | } |

163 | |

164 | inline QPointF QBezier::pointAt(qreal t) const |

165 | { |

166 | // numerically more stable: |

167 | qreal x, y; |

168 | |

169 | qreal m_t = 1. - t; |

170 | { |

171 | qreal a = x1*m_t + x2*t; |

172 | qreal b = x2*m_t + x3*t; |

173 | qreal c = x3*m_t + x4*t; |

174 | a = a*m_t + b*t; |

175 | b = b*m_t + c*t; |

176 | x = a*m_t + b*t; |

177 | } |

178 | { |

179 | qreal a = y1*m_t + y2*t; |

180 | qreal b = y2*m_t + y3*t; |

181 | qreal c = y3*m_t + y4*t; |

182 | a = a*m_t + b*t; |

183 | b = b*m_t + c*t; |

184 | y = a*m_t + b*t; |

185 | } |

186 | return QPointF(x, y); |

187 | } |

188 | |

189 | inline QPointF QBezier::normalVector(qreal t) const |

190 | { |

191 | qreal m_t = 1. - t; |

192 | qreal a = m_t * m_t; |

193 | qreal b = t * m_t; |

194 | qreal c = t * t; |

195 | |

196 | return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c); |

197 | } |

198 | |

199 | inline QPointF QBezier::derivedAt(qreal t) const |

200 | { |

201 | // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3) |

202 | |

203 | qreal m_t = 1. - t; |

204 | |

205 | qreal d = t * t; |

206 | qreal a = -m_t * m_t; |

207 | qreal b = 1 - 4 * t + 3 * d; |

208 | qreal c = 2 * t - 3 * d; |

209 | |

210 | return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4, |

211 | a * y1 + b * y2 + c * y3 + d * y4); |

212 | } |

213 | |

214 | inline QPointF QBezier::secondDerivedAt(qreal t) const |

215 | { |

216 | qreal a = 2. - 2. * t; |

217 | qreal b = -4 + 6 * t; |

218 | qreal c = 2 - 6 * t; |

219 | qreal d = 2 * t; |

220 | |

221 | return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4, |

222 | a * y1 + b * y2 + c * y3 + d * y4); |

223 | } |

224 | |

225 | inline void QBezier::split(QBezier *firstHalf, QBezier *secondHalf) const |

226 | { |

227 | Q_ASSERT(firstHalf); |

228 | Q_ASSERT(secondHalf); |

229 | |

230 | qreal c = (x2 + x3)*.5; |

231 | firstHalf->x2 = (x1 + x2)*.5; |

232 | secondHalf->x3 = (x3 + x4)*.5; |

233 | firstHalf->x1 = x1; |

234 | secondHalf->x4 = x4; |

235 | firstHalf->x3 = (firstHalf->x2 + c)*.5; |

236 | secondHalf->x2 = (secondHalf->x3 + c)*.5; |

237 | firstHalf->x4 = secondHalf->x1 = (firstHalf->x3 + secondHalf->x2)*.5; |

238 | |

239 | c = (y2 + y3)/2; |

240 | firstHalf->y2 = (y1 + y2)*.5; |

241 | secondHalf->y3 = (y3 + y4)*.5; |

242 | firstHalf->y1 = y1; |

243 | secondHalf->y4 = y4; |

244 | firstHalf->y3 = (firstHalf->y2 + c)*.5; |

245 | secondHalf->y2 = (secondHalf->y3 + c)*.5; |

246 | firstHalf->y4 = secondHalf->y1 = (firstHalf->y3 + secondHalf->y2)*.5; |

247 | } |

248 | |

249 | inline void QBezier::parameterSplitLeft(qreal t, QBezier *left) |

250 | { |

251 | left->x1 = x1; |

252 | left->y1 = y1; |

253 | |

254 | left->x2 = x1 + t * ( x2 - x1 ); |

255 | left->y2 = y1 + t * ( y2 - y1 ); |

256 | |

257 | left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot |

258 | left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot |

259 | |

260 | x3 = x3 + t * ( x4 - x3 ); |

261 | y3 = y3 + t * ( y4 - y3 ); |

262 | |

263 | x2 = left->x3 + t * ( x3 - left->x3); |

264 | y2 = left->y3 + t * ( y3 - left->y3); |

265 | |

266 | left->x3 = left->x2 + t * ( left->x3 - left->x2 ); |

267 | left->y3 = left->y2 + t * ( left->y3 - left->y2 ); |

268 | |

269 | left->x4 = x1 = left->x3 + t * (x2 - left->x3); |

270 | left->y4 = y1 = left->y3 + t * (y2 - left->y3); |

271 | } |

272 | |

273 | QT_END_NAMESPACE |

274 | |

275 | #endif // QBEZIER_P_H |

276 |