#include<QWidget>
#include<QVector>

classWidget:publicQWidget
{
Q_OBJECT

public:
Widget(QWidget*parent=nullptr);
~Widget();

protected:
virtualvoidmousePressEvent(QMouseEvent*event);
virtualvoidmouseReleaseEvent(QMouseEvent*event);
virtualvoidmouseDoubleClickEvent(QMouseEvent*event);
virtualvoidmouseMoveEvent(QMouseEvent*event);
virtualvoidpaintEvent(QPaintEvent*event);

private:
voiddrawSpline();
qrealN(intk,inti,qrealu);
qrealN1(inti,qrealu);
qrealN2(inti,qrealu);
qrealN3(inti,qrealu);

private:
QVector<QPointF>m_ctrlPoints;//控制點(diǎn)
QVector<QPointF>m_curvePoints;//曲線上的點(diǎn)
};

#endif//WIDGET_H

Widget::Widget(QWidget*parent)
:QWidget(parent)
{
}

Widget::~Widget()
{

}

voidWidget::mousePressEvent(QMouseEvent*event)
{
//單擊鼠標(biāo)左鍵獲取控制點(diǎn)
if(event->buttons()==Qt::LeftButton){
m_ctrlPoints.push_back(event->pos());
}
//單擊鼠標(biāo)右鍵清空控制點(diǎn)
elseif(event->buttons()==Qt::RightButton){
m_ctrlPoints.clear();
}
update();
}

voidWidget::mouseReleaseEvent(QMouseEvent*event)
{

}

voidWidget::mouseDoubleClickEvent(QMouseEvent*event)
{

}

voidWidget::mouseMoveEvent(QMouseEvent*event)
{

}

voidWidget::paintEvent(QPaintEvent*event)
{
drawSpline();
}

voidWidget::drawSpline()
{
QPainterpainter(this);
intcurrentK=3;//階數(shù)
m_curvePoints.clear();
for(qrealu=currentK;u<m_ctrlPoints.size();u+=0.01){
QPointFpt(0.0,0.0);
for(inti=0;i<m_ctrlPoints.size();++i){
QPointFpts=m_ctrlPoints[i];
pts*=N(currentK,i,u);
pt+=pts;
}
m_curvePoints.push_back(pt);
}

//drawcontrolpoints
QPenctrlPen1(QColor(0,0,255));
ctrlPen1.setWidth(5);
painter.setPen(ctrlPen1);
for(inti=0;i<m_ctrlPoints.size();++i){
painter.drawPoint(m_ctrlPoints[i]);
}
//drawcontrollines
QPenctrlPen2(QColor(255,0,0));
ctrlPen2.setWidth(1);
ctrlPen2.setStyle(Qt::DashDotDotLine);
painter.setPen(ctrlPen2);
for(inti=0;i<m_ctrlPoints.size()-1;++i){
painter.drawLine(m_ctrlPoints[i],m_ctrlPoints[i+1]);
}
//drawsplinecurve
QPencurvePen(QColor(0,0,0));
curvePen.setWidth(2);
painter.setPen(curvePen);
for(inti=0;i<m_curvePoints.size()-1;++i){
painter.drawLine(m_curvePoints[i],m_curvePoints[i+1]);
}
}

qrealWidget::N(intk,inti,qrealu)
{
switch(k){
case1:
returnN1(i,u);
case2:
returnN2(i,u);
case3:
returnN3(i,u);
default:
break;
}
}

qrealWidget::N1(inti,qrealu)
{
qrealt=u-i;
if(0<=t&&t<1){
returnt;
}
if(1<=t&&t<2){
return2-t;
}
return0;
}

qrealWidget::N2(inti,qrealu)
{
qrealt=u-i;
if(0<=t&&t<1){
return0.5*t*t;
}
if(1<=t&&t<2){
return3*t-t*t-1.5;
}
if(2<=t&&t<3){
return0.5*pow(3-t,2);
}
return0;
}

qrealWidget::N3(inti,qrealu)
{
qrealt=u-i;
qreala=1.0/6.0;
if(0<=t&&t<1){
returna*t*t*t;
}
if(1<=t&&t<2){
returna*(-3*pow(t-1,3)+3*pow(t-1,2)+3*(t-1)+1);
}
if(2<=t&&t<3){
returna*(3*pow(t-2,3)-6*pow(t-2,2)+4);
}
if(3<=t&&t<4){
returna*pow(4-t,3);
}
return0;
}