利用qt绘制一个有刻度的平面圆形图，然后在平面圆形图里有两条圆心出发的指针为一条黄线和一条红线，红线指针随鼠标移动而移动，黄线指针在鼠标点击时发生移动，用三角函数求平面上两条指针的平面夹角度数，并在ui界面显示每次变化的角度

好的，这是一个比较复杂的问题，需要分步骤来实现。

首先，我们需要绘制一个有刻度的平面圆形图。可以使用Qt的绘图功能，绘制一个圆形，并在圆周上绘制刻度线。代码如下：

void MyWidget::paintEvent(QPaintEvent *event)
{
    QPainter painter(this);
    painter.setRenderHint(QPainter::Antialiasing, true);
    painter.translate(width() / 2, height() / 2);  // 将圆心移到窗口中心

    int r = qMin(width(), height()) / 2 - 20;  // 圆形半径
    painter.drawEllipse(-r, -r, 2 * r, 2 * r);  // 绘制圆形

    int n = 36;  // 刻度线数量
    for (int i = 0; i < n; ++i) {
        painter.drawLine(0, -r, 0, -r + 10);  // 绘制刻度线
        painter.rotate(360 / n);  // 旋转画布
    }
}

接下来，我们需要绘制两条指针。一条红线指针，一条黄线指针。红线指针随鼠标移动而移动，黄线指针在鼠标点击时发生移动。代码如下：

void MyWidget::mousePressEvent(QMouseEvent *event)
{
    Q_UNUSED(event);
    QPointF pos = mapFromGlobal(QCursor::pos());  // 鼠标点击位置
    m_yellowAngle = angle(pos);  // 计算黄线指针的初始角度
    update();  // 更新界面
}

void MyWidget::mouseMoveEvent(QMouseEvent *event)
{
    QPointF pos = mapFromGlobal(QCursor::pos());  // 鼠标当前位置
    m_redAngle = angle(pos);  // 计算红线指针的角度
    update();  // 更新界面
}

void MyWidget::paintEvent(QPaintEvent *event)
{
    // ...

    // 绘制红线指针
    painter.save();
    painter.rotate(m_redAngle);
    painter.setPen(Qt::red);
    painter.drawLine(0, 0, 0, -r * 0.8);
    painter.restore();

    // 绘制黄线指针
    painter.save();
    painter.rotate(m_yellowAngle);
    painter.setPen(Qt::yellow);
    painter.drawLine(0, 0, 0, -r * 0.6);
    painter.restore();

    // ...
}

double MyWidget::angle(const QPointF &pos)
{
    QPointF center(width() / 2, height() / 2);
    QPointF vec = pos - center;
    double angle = qRadiansToDegrees(qAtan2(vec.y(), vec.x()));
    return angle;
}

最后，我们需要用三角函数求平面上两条指针的平面夹角度数，并在ui界面显示每次变化的角度。代码如下：

void MyWidget::mouseMoveEvent(QMouseEvent *event)
{
    // ...

    double angle = m_redAngle - m_yellowAngle;  // 计算夹角
    while (angle < 0) angle += 360;
    while (angle > 360) angle -= 360;
    m_angleLabel->setText(QString::number(angle));  // 显示角度

    // ...
}

完整代码如下：

#include <QtWidgets>

class MyWidget : public QWidget
{
public:
    MyWidget(QWidget *parent = nullptr)
        : QWidget(parent)
        , m_redAngle(0)
        , m_yellowAngle(0)
    {
        setFixedSize(400, 400);
        m_angleLabel = new QLabel(this);
        m_angleLabel->move(width() / 2, height() - 30);
        m_angleLabel->setAlignment(Qt::AlignHCenter);
        m_angleLabel->setFixedWidth(100);
    }

protected:
    void paintEvent(QPaintEvent *event) override
    {
        QPainter painter(this);
        painter.setRenderHint(QPainter::Antialiasing, true);
        painter.translate(width() / 2, height() / 2);

        int r = qMin(width(), height()) / 2 - 20;
        painter.drawEllipse(-r, -r, 2 * r, 2 * r);

        int n = 36;
        for (int i = 0; i < n; ++i) {
            painter.drawLine(0, -r, 0, -r + 10);
            painter.rotate(360 / n);
        }

        painter.save();
        painter.rotate(m_redAngle);
        painter.setPen(Qt::red);
        painter.drawLine(0, 0, 0, -r * 0.8);
        painter.restore();

        painter.save();
        painter.rotate(m_yellowAngle);
        painter.setPen(Qt::yellow);
        painter.drawLine(0, 0, 0, -r * 0.6);
        painter.restore();
    }

    void mousePressEvent(QMouseEvent *event) override
    {
        Q_UNUSED(event);
        QPointF pos = mapFromGlobal(QCursor::pos());
        m_yellowAngle = angle(pos);
        update();
    }

    void mouseMoveEvent(QMouseEvent *event) override
    {
        QPointF pos = mapFromGlobal(QCursor::pos());
        m_redAngle = angle(pos);
        update();

        double angle = m_redAngle - m_yellowAngle;
        while (angle < 0) angle += 360;
        while (angle > 360) angle -= 360;
        m_angleLabel->setText(QString::number(angle));
    }

    double angle(const QPointF &pos)
    {
        QPointF center(width() / 2, height() / 2);
        QPointF vec = pos - center;
        double angle = qRadiansToDegrees(qAtan2(vec.y(), vec.x()));
        return angle;
    }

private:
    double m_redAngle;
    double m_yellowAngle;
    QLabel *m_angleLabel;
};

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);

    MyWidget widget;
    widget.show();

    return app.exec();
}