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| |
| #ifndef QBEZIER_P_H |
| #define QBEZIER_P_H |
| |
| // |
| // W A R N I N G |
| // ------------- |
| // |
| // This file is not part of the Qt API. It exists for the convenience |
| // of other Qt classes. This header file may change from version to |
| // version without notice, or even be removed. |
| // |
| // We mean it. |
| // |
| |
| #include <QtGui/private/qtguiglobal_p.h> |
| #include "QtCore/qpoint.h" |
| #include "QtCore/qline.h" |
| #include "QtCore/qrect.h" |
| #include "QtCore/qvector.h" |
| #include "QtCore/qlist.h" |
| #include "QtCore/qpair.h" |
| #include "QtGui/qtransform.h" |
| #include <private/qdatabuffer_p.h> |
| |
| QT_BEGIN_NAMESPACE |
| |
| class QPolygonF; |
| |
| class Q_GUI_EXPORT QBezier |
| { |
| public: |
| static QBezier fromPoints(const QPointF &p1, const QPointF &p2, |
| const QPointF &p3, const QPointF &p4) |
| { return {p1.x(), p1.y(), p2.x(), p2.y(), p3.x(), p3.y(), p4.x(), p4.y()}; } |
| |
| static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d); |
| |
| inline QPointF pointAt(qreal t) const; |
| inline QPointF normalVector(qreal t) const; |
| |
| inline QPointF derivedAt(qreal t) const; |
| inline QPointF secondDerivedAt(qreal t) const; |
| |
| QPolygonF toPolygon(qreal bezier_flattening_threshold = 0.5) const; |
| void addToPolygon(QPolygonF *p, qreal bezier_flattening_threshold = 0.5) const; |
| void addToPolygon(QDataBuffer<QPointF> &polygon, qreal bezier_flattening_threshold) const; |
| |
| QRectF bounds() const; |
| qreal length(qreal error = 0.01) const; |
| void addIfClose(qreal *length, qreal error) const; |
| |
| qreal tAtLength(qreal len) const; |
| |
| int stationaryYPoints(qreal &t0, qreal &t1) const; |
| qreal tForY(qreal t0, qreal t1, qreal y) const; |
| |
| QPointF pt1() const { return QPointF(x1, y1); } |
| QPointF pt2() const { return QPointF(x2, y2); } |
| QPointF pt3() const { return QPointF(x3, y3); } |
| QPointF pt4() const { return QPointF(x4, y4); } |
| |
| QBezier mapBy(const QTransform &transform) const; |
| |
| inline QPointF midPoint() const; |
| inline QLineF midTangent() const; |
| |
| inline QLineF startTangent() const; |
| inline QLineF endTangent() const; |
| |
| inline void parameterSplitLeft(qreal t, QBezier *left); |
| inline std::pair<QBezier, QBezier> split() const; |
| |
| int shifted(QBezier *curveSegments, int maxSegmets, |
| qreal offset, float threshold) const; |
| |
| QBezier bezierOnInterval(qreal t0, qreal t1) const; |
| QBezier getSubRange(qreal t0, qreal t1) const; |
| |
| qreal x1, y1, x2, y2, x3, y3, x4, y4; |
| }; |
| |
| inline QPointF QBezier::midPoint() const |
| { |
| return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.); |
| } |
| |
| inline QLineF QBezier::midTangent() const |
| { |
| QPointF mid = midPoint(); |
| QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5)); |
| return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(), |
| mid.x() + dir.dx(), mid.y() + dir.dy()); |
| } |
| |
| inline QLineF QBezier::startTangent() const |
| { |
| QLineF tangent(pt1(), pt2()); |
| if (tangent.isNull()) |
| tangent = QLineF(pt1(), pt3()); |
| if (tangent.isNull()) |
| tangent = QLineF(pt1(), pt4()); |
| return tangent; |
| } |
| |
| inline QLineF QBezier::endTangent() const |
| { |
| QLineF tangent(pt4(), pt3()); |
| if (tangent.isNull()) |
| tangent = QLineF(pt4(), pt2()); |
| if (tangent.isNull()) |
| tangent = QLineF(pt4(), pt1()); |
| return tangent; |
| } |
| |
| inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d) |
| { |
| qreal m_t = 1. - t; |
| b = m_t * m_t; |
| c = t * t; |
| d = c * t; |
| a = b * m_t; |
| b *= 3. * t; |
| c *= 3. * m_t; |
| } |
| |
| inline QPointF QBezier::pointAt(qreal t) const |
| { |
| // numerically more stable: |
| qreal x, y; |
| |
| qreal m_t = 1. - t; |
| { |
| qreal a = x1*m_t + x2*t; |
| qreal b = x2*m_t + x3*t; |
| qreal c = x3*m_t + x4*t; |
| a = a*m_t + b*t; |
| b = b*m_t + c*t; |
| x = a*m_t + b*t; |
| } |
| { |
| qreal a = y1*m_t + y2*t; |
| qreal b = y2*m_t + y3*t; |
| qreal c = y3*m_t + y4*t; |
| a = a*m_t + b*t; |
| b = b*m_t + c*t; |
| y = a*m_t + b*t; |
| } |
| return QPointF(x, y); |
| } |
| |
| inline QPointF QBezier::normalVector(qreal t) const |
| { |
| qreal m_t = 1. - t; |
| qreal a = m_t * m_t; |
| qreal b = t * m_t; |
| qreal c = t * t; |
| |
| return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c, -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c); |
| } |
| |
| inline QPointF QBezier::derivedAt(qreal t) const |
| { |
| // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3) |
| |
| qreal m_t = 1. - t; |
| |
| qreal d = t * t; |
| qreal a = -m_t * m_t; |
| qreal b = 1 - 4 * t + 3 * d; |
| qreal c = 2 * t - 3 * d; |
| |
| return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4, |
| a * y1 + b * y2 + c * y3 + d * y4); |
| } |
| |
| inline QPointF QBezier::secondDerivedAt(qreal t) const |
| { |
| qreal a = 2. - 2. * t; |
| qreal b = -4 + 6 * t; |
| qreal c = 2 - 6 * t; |
| qreal d = 2 * t; |
| |
| return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4, |
| a * y1 + b * y2 + c * y3 + d * y4); |
| } |
| |
| std::pair<QBezier, QBezier> QBezier::split() const |
| { |
| const auto mid = [](QPointF lhs, QPointF rhs) { return (lhs + rhs) * .5; }; |
| |
| const QPointF mid_12 = mid(pt1(), pt2()); |
| const QPointF mid_23 = mid(pt2(), pt3()); |
| const QPointF mid_34 = mid(pt3(), pt4()); |
| const QPointF mid_12_23 = mid(mid_12, mid_23); |
| const QPointF mid_23_34 = mid(mid_23, mid_34); |
| const QPointF mid_12_23__23_34 = mid(mid_12_23, mid_23_34); |
| |
| return { |
| fromPoints(pt1(), mid_12, mid_12_23, mid_12_23__23_34), |
| fromPoints(mid_12_23__23_34, mid_23_34, mid_34, pt4()), |
| }; |
| } |
| |
| inline void QBezier::parameterSplitLeft(qreal t, QBezier *left) |
| { |
| left->x1 = x1; |
| left->y1 = y1; |
| |
| left->x2 = x1 + t * ( x2 - x1 ); |
| left->y2 = y1 + t * ( y2 - y1 ); |
| |
| left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot |
| left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot |
| |
| x3 = x3 + t * ( x4 - x3 ); |
| y3 = y3 + t * ( y4 - y3 ); |
| |
| x2 = left->x3 + t * ( x3 - left->x3); |
| y2 = left->y3 + t * ( y3 - left->y3); |
| |
| left->x3 = left->x2 + t * ( left->x3 - left->x2 ); |
| left->y3 = left->y2 + t * ( left->y3 - left->y2 ); |
| |
| left->x4 = x1 = left->x3 + t * (x2 - left->x3); |
| left->y4 = y1 = left->y3 + t * (y2 - left->y3); |
| } |
| |
| QT_END_NAMESPACE |
| |
| #endif // QBEZIER_P_H |