It is possible to drag with pressed right mouse button and to zoom with mouse wheel. And initially everything works rather smooth. But when I zoom to the smallest circle the performance of drawing is significantly degraded. Why? And how can I fix it?

Qt Code: 
  1. #ifndef WIDGET_H
  2. #define WIDGET_H
  3.  
  4. #include <QWidget>
  5. #include <QList>
  6.  
  7. struct circle {
  9.     qreal r;
  10.     circle(QPointF center, qreal radius): c(center), r(radius) {}
  11. };
  12.  
  13. class Widget : public QWidget
  14. {
  15.     Q_OBJECT
  16.  
  17. public:
  18.     Widget(QWidget *parent = 0);
  19.  
  20. protected:
  21.     void paintEvent(QPaintEvent *event);
  22.  
  23.     void mousePressEvent(QMouseEvent *event);
  24.     void mouseReleaseEvent(QMouseEvent *event);
  25.     void mouseMoveEvent(QMouseEvent *event);
  26.  
  27.     void wheelEvent(QWheelEvent *event);
  28.  
  29. private:
  30.     QList<circle> circles;
  31.     QPointF shift;
  32.     qreal scale;
  33.     QPoint previous;
  34.     bool isDragging;
  35. };
  36.  
  37. #endif // WIDGET_H
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Qt Code: 
  1. #include "widget.h"
  2.  
  3. #include <math.h>
  4. #include <QPainter>
  5. #include <QMouseEvent>
  6. #include <QWheelEvent>
  7.  
  8. circle tangent2(const circle &c1, const circle &c2, qreal r, const QPointF &p)
  9. {
  10.     qreal r1 = c1.r + r;
  11.     qreal r2 = c2.r + r;
  12.     qreal d = c1.r + c2.r;
  13.     qreal dx = (d*d - r2*r2 + r1*r1)/(2*d);
  14.     qreal dy = sqrt(r1*r1 - dx*dx);
  15.     QPointF v = (c2.c - c1.c)/d;
  16.     QPointF n(-v.y(), v.x());
  17.     QPointF pv = p - c1.c;
  18.     if (pv.x()*n.x() + pv.y()*n.y() < 0)
  19.         n = -n;
  20.     QPointF c = c1.c + dx*v + dy*n;
  21.     return circle(c, r);
  22. }
  23.  
  24. circle tangent3(const circle &c1, const circle &c2, const circle &c3)
  25. {
  26.     qreal k1 = 1/c1.r;
  27.     qreal k2 = 1/c2.r;
  28.     qreal k3 = 1/c3.r;
  29.     qreal a = k1 + k2 + k3;
  30.     qreal b = 2*sqrt(k1*k2 + k2*k3 + k3*k1);
  31.     qreal k = qMax(qAbs(a - b), a + b);
  32.     return tangent2(c1, c2, 1/k, c3.c);
  33. }
  34.  
  35. Widget::Widget(QWidget *parent)
  36.     : QWidget(parent), shift(300, 400), scale(30), isDragging(false)
  37. {
  38.     setAutoFillBackground(false);
  39.     circle c1(QPointF(0, 0), 5);
  40.     circle c2(QPointF(8, 0), 3);
  41.     circle c3 = tangent2(c1, c2, 4, QPointF(0, -1));
  42.     circles << c1 << c2 << c3;
  43.     for (int i = 0; i < 6; ++i) {
  44.         circle c = tangent3(c1, c2, c3);
  45.         circles << c;
  46.         c1 = c2;
  47.         c2 = c3;
  48.         c3 = c;
  49.     }
  50. }
  51.  
  52. void Widget::paintEvent(QPaintEvent *event)
  53. {
  54.     QPainter painter(this);
  55.     painter.fillRect(0, 0, width(), height(), Qt::darkGray);
  56.     painter.setBrush(Qt::NoBrush);
  57.     painter.setPen(QPen(QBrush(Qt::white), 1.5));
  58.     painter.setRenderHint(QPainter::Antialiasing, true);
  59.     foreach(const circle &c, circles)
  60.         painter.drawEllipse(c.c * scale + shift, c.r * scale, c.r * scale);
  61. }
  62.  
  63. void Widget::mousePressEvent(QMouseEvent *event)
  64. {
  65.     if (!isDragging && event->button() == Qt::RightButton) {
  66.         isDragging = true;
  67.         previous = event->pos();
  68.     }
  69. }
  70.  
  71. void Widget::mouseReleaseEvent(QMouseEvent *event)
  72. {
  73.     if (isDragging && event->button() == Qt::RightButton) {
  74.         isDragging = false;
  75.     }
  76. }
  77.  
  78. void Widget::mouseMoveEvent(QMouseEvent *event)
  79. {
  80.     if (isDragging) {
  81.         shift += event->pos() - previous;
  82.         previous = event->pos();
  83.         repaint();
  84.     }
  85. }
  86.  
  87. void Widget::wheelEvent(QWheelEvent *event)
  88. {
  89.     int numDegrees = event->delta() / 8;
  90.     int numTicks = numDegrees / 15;
  91.     qreal factor = pow(1.2, -numTicks);
  92.     shift += (1 - factor) * (event->pos() - shift);
  93.     scale *= factor;
  94.     repaint();
  95. }
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Qt Code: 
  1. #include <QtGui/QApplication>
  2. #include "widget.h"
  3.  
  4. int main(int argc, char *argv[])
  5. {
  6.     QApplication a(argc, argv);
  7.     Widget w;
  8.     w.resize(800, 600);
  9.     w.show();
  10.     return a.exec();
  11. }
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