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#include "qsplineseries.h"
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QTCOMMERCIALCHART_BEGIN_NAMESPACE
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QSplineSeries::QSplineSeries(QObject *parent) :
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QLineSeries(parent)
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{
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connect(this,SIGNAL(pointAdded(int)), this, SLOT(updateControlPoints()));
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connect(this,SIGNAL(pointRemoved(int)), this, SLOT(updateControlPoints()));
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connect(this,SIGNAL(pointReplaced(int)), this, SLOT(updateControlPoints()));
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}
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void QSplineSeries::calculateControlPoints()
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{
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// Based on http://www.codeproject.com/Articles/31859/Draw-a-Smooth-Curve-through-a-Set-of-2D-Points-wit
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// CPOL Licence
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int n = m_x.size() - 1;
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if (n == 1)
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{ // Special case: Bezier curve should be a straight line.
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// firstControlPoints = new Point[1];
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// 3P1 = 2P0 + P3
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m_controlPoints.append(QPointF((2 * m_x[0] + m_x[1]) / 3, (2 * m_y[0] + m_y[1]) / 3));
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// P2 = 2P1 P0
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m_controlPoints.append(QPointF(2 * m_controlPoints[0].x() - m_x[0], 2 * m_controlPoints[0].y() - m_y[0]));
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return;
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}
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// Calculate first Bezier control points
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// Right hand side vector
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// Set of equations for P0 to Pn points.
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//
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// | 2 1 0 0 ... 0 0 0 ... 0 0 0 | | P1_1 | | P0 + 2 * P1 |
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// | 1 4 1 0 ... 0 0 0 ... 0 0 0 | | P1_2 | | 4 * P1 + 2 * P2 |
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// | 0 1 4 1 ... 0 0 0 ... 0 0 0 | | P1_3 | | 4 * P2 + 2 * P3 |
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// | . . . . . . . . . . . . | | ... | | ... |
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// | 0 0 0 0 ... 1 4 1 ... 0 0 0 | * | P1_i | = | 4 * P(i-1) + 2 * Pi |
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// | . . . . . . . . . . . . | | ... | | ... |
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// | 0 0 0 0 0 0 0 0 ... 1 4 1 | | P1_(n-1)| | 4 * P(n-2) + 2 * P(n-1) |
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// | 0 0 0 0 0 0 0 0 ... 0 2 7 | | P1_n | | 8 * P(n-1) + Pn |
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//
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QList<qreal> rhs;
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rhs.append(m_x[0] + 2 * m_x[1]);
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// Set right hand side X values
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for (int i = 1; i < n - 1; ++i)
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rhs.append(4 * m_x[i] + 2 * m_x[i + 1]);
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rhs.append((8 * m_x[n - 1] + m_x[n]) / 2.0);
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// Get first control points X-values
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QList<qreal> x = getFirstControlPoints(rhs);
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rhs[0] = m_y[0] + 2 * m_y[1];
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// Set right hand side Y values
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for (int i = 1; i < n - 1; ++i)
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rhs[i] = 4 * m_y[i] + 2 * m_y[i + 1];
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rhs[n - 1] = (8 * m_y[n - 1] + m_y[n]) / 2.0;
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// Get first control points Y-values
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QList<qreal> y = getFirstControlPoints(rhs);
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// Fill output arrays.
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for (int i = 0; i < n; ++i)
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{
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// First control point
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m_controlPoints.append(QPointF(x[i], y[i]));
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// Second control point
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if (i < n - 1)
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m_controlPoints.append(QPointF(2 * m_x[i + 1] - x[i + 1], 2 * m_y[i + 1] - y[i + 1]));
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else
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m_controlPoints.append(QPointF((m_x[n] + x[n - 1]) / 2, (m_y[n] + y[n - 1]) / 2));
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}
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}
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QList<qreal> QSplineSeries::getFirstControlPoints(QList<qreal> rhs)
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{
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QList<qreal> x; // Solution vector.
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QList<qreal> tmp; // Temp workspace.
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qreal b = 2.0;
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x.append(rhs[0] / b);
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tmp.append(0);
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for (int i = 1; i < rhs.size(); i++) // Decomposition and forward substitution.
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{
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tmp.append(1 / b);
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b = (i < rhs.size() - 1 ? 4.0 : 3.5) - tmp[i];
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x.append((rhs[i] - x[i - 1]) / b);
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}
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for (int i = 1; i < rhs.size(); i++)
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x[rhs.size() - i - 1] -= tmp[rhs.size() - i] * x[rhs.size() - i]; // Backsubstitution.
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return x;
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}
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void QSplineSeries::updateControlPoints()
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{
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if(m_x.size() > 1)
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{
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m_controlPoints.clear();
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calculateControlPoints();
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}
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}
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#include "moc_qsplineseries.cpp"
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QTCOMMERCIALCHART_END_NAMESPACE
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