//对别人的代码稍作修改，让自己更容易理解，绘制多边形的大致思路是一样的
DrawPolygon.h

#ifndef DRAWPOLYGON_H
#define DRAWPOLYGON_H

#include <QWidget>
#include <QMouseEvent>
#include <QPaintEvent>
#include <QPointF>
#include <QVector>
#include <QLineF>
#include <QPainter>
namespace Ui {
class DrawPolygon;
}

class DrawPolygon : public QWidget
{
    Q_OBJECT

public:
    explicit DrawPolygon(QWidget *parent = nullptr);
    ~DrawPolygon();

    void drawPolygon(QPainter *painter);                 //绘制多边形
protected:
    void paintEvent(QPaintEvent *);                      //绘制
    void mousePressEvent(QMouseEvent *);                 //按下
    void mouseMoveEvent(QMouseEvent *);                  //移动
    void mouseReleaseEvent(QMouseEvent *);               //松开
    void mouseDoubleClickEvent(QMouseEvent *);           //双击
private:
    Ui::DrawPolygon *ui;

    bool drawIsPolygon;                                  //是否在绘制多边形
    bool mouseIsMove;                                    //是否在移动
    bool mouseIsSingleClick;                             //是否是绘图之后的单击状态（为了区分单击和双击状态时的不同绘制）

    QVector<QPointF> pointList;                          //存储所有绘制的点
    QPointF movePoint;                                   //移动状态下的点（还没有绘制完成）
};

#endif // DRAWPOLYGON_H

DrawPolygon.cpp

#include "drawpolygon.h"
#include "ui_drawpolygon.h"

DrawPolygon::DrawPolygon(QWidget *parent) :
    QWidget(parent),
    ui(new Ui::DrawPolygon)
{
    ui->setupUi(this);
    //设置背景颜色
    this->setAutoFillBackground(true);
    this->setBackgroundRole(QPalette::Base);

    drawIsPolygon = false;
    mouseIsMove = false;
    mouseIsSingleClick = false;
    //设置鼠标追踪
    setMouseTracking(true);
}

DrawPolygon::~DrawPolygon()
{
    delete ui;
}

void DrawPolygon::drawPolygon(QPainter *painter)
{
    drawIsPolygon = true;
    if(drawIsPolygon)
    {
        QVector<QLineF> lineList;
        painter->setPen(QColor(250,200,0));
        //存储前面的线段   线段的个数：pointList.size() - 1
        for(int i = 0; i < pointList.size() - 1; i++ )
        {
            QLineF line(QPointF(pointList[i].x(), pointList[i].y()), QPointF(pointList[i + 1].x(), pointList[i + 1].y()));
            lineList.push_back(line);
        }
        //存储还未生成的线段
        if(mouseIsMove && pointList.size() > 0)
        {
            QLineF line(QPointF(pointList[pointList.size() - 1].x(), pointList[pointList.size() - 1].y()), movePoint);
            lineList.push_back(line);
        }
        //绘制所有线段
        painter->drawLines(lineList);
    }
}

void DrawPolygon::paintEvent(QPaintEvent *)
{
    QPainter painter(this);
    //绘制多边形
    drawPolygon(&painter);
}

void DrawPolygon::mousePressEvent(QMouseEvent *e)
{
    if(drawIsPolygon)
    {
        //如果不是绘图后的单击状态
        if(!mouseIsSingleClick)
        {
            //清空所有的点（当进行下一次绘制时不会有其他点的影响）
            pointList.clear();
            mouseIsSingleClick = true ;
        }
    }
}

void DrawPolygon::mouseMoveEvent(QMouseEvent *e)
{
    //正在绘制多边形 并且 是绘图后的单击状态
    if(drawIsPolygon && mouseIsSingleClick)
    {
        //移动的点（用来动态绘制 鼠标移动连接的线段）
        movePoint = e->pos();
        mouseIsMove = true;
        this->update();
    }

}

void DrawPolygon::mouseReleaseEvent(QMouseEvent *e)
{
    //正在绘制多边形 并且 是绘图后的单击状态
    if(drawIsPolygon && mouseIsSingleClick)
    {
        //将点保存到容器中（鼠标松开之后才能确定生成的点）
        pointList.push_back(e->pos());
        mouseIsMove = false;
        this->update();
    }
}

void DrawPolygon::mouseDoubleClickEvent(QMouseEvent *e)
{
    if(drawIsPolygon)
    {
        mouseIsSingleClick = false;
        //将第一个点传给容器，为了让最后一个点与第一个点在双击之后进行相连
        pointList.push_back(pointList[0]);
        this->update();
    }
}

运行结果：

参考博客：
https://blog.csdn.net/charlee44/article/details/104696765