效果：按钮弹出分屏选择

QT分屏按钮

// gridpopwidget.h
#ifndef GRIDPOPWIDGET_H
#define GRIDPOPWIDGET_H

#include <QWidget>
#include <QMouseEvent>

class GridPopWidget : public QWidget
{
    Q_OBJECT
public:
    explicit GridPopWidget(QWidget *parent = nullptr);
    ~GridPopWidget();

protected:
    virtual void mouseMoveEvent(QMouseEvent *event) override;
    virtual void mousePressEvent(QMouseEvent *event) override;
signals:
    void sig_layout(int, int);

private:
    QList<QList<QWidget *> >   wArr;
};

#endif // GRIDPOPWIDGET_H

// gridpopwidget.cpp
#include "gridpopwidget.h"
#include <QGridLayout>

#define  BACKGROUND "background-color:black; padding:0px;margin:0px;border:1px solid gray;"
#define  HIGHLIGHT  "background-color:white"
#define  CSSNORMAL  "background-color:darkgray;"
#define  GRIDROW    4
#define  GRIDCOL    5
#define  GRIDSIZE  25
#define  GRIDSPACE  0
GridPopWidget::GridPopWidget(QWidget *parent) :
    QWidget(parent)
{
    setMouseTracking(true);
    setStyleSheet(QString("QWidget{%1}").arg(BACKGROUND));
    QGridLayout *glayout = new QGridLayout(this);
    for(int i=0; i<GRIDROW; ++i)
    {
        QList<QWidget*> ws;
        for (int j=0; j<GRIDCOL; ++j)
        {
            QWidget* w = new QWidget(this);
            w->setMouseTracking(true);
            w->setStyleSheet(CSSNORMAL);
            glayout->addWidget(w,i,j,Qt::AlignCenter);
            w->setFixedSize(GRIDSIZE,GRIDSIZE);
            ws.append(w);
        }
        wArr.append(ws);
    }
    glayout->setSpacing(GRIDSPACE);setLayout(glayout);
    resize(GRIDSIZE*GRIDCOL,GRIDSIZE*GRIDROW);
    hide();
}

GridPopWidget::~GridPopWidget()
{
}

void GridPopWidget::mouseMoveEvent(QMouseEvent *e)
{
    QWidget::mouseMoveEvent(e);
    QPoint p = e->pos();
    foreach (QList<QWidget *> ws, wArr) {
        foreach (QWidget *w, ws) {
            if( w->pos().x() < p.x() && w->pos().y() < p.y() )
                w->setStyleSheet(HIGHLIGHT);
            else
                w->setStyleSheet(CSSNORMAL);
        }
    }
}

void GridPopWidget::mousePressEvent(QMouseEvent *e)
{
    QWidget::mousePressEvent(e);
    int row = 0, col = 0;
    QPoint p = e->pos();
    QPoint lim = this->rect().bottomRight();
    if (p.x() > lim.x() || p.y() > lim.y()) return;

    foreach (QList<QWidget *> ws, wArr) {
        if (p.y() > ws.first()->pos().y()) row++;
    }
    foreach (QWidget *w, wArr[0]) {
        if (p.x() > w->pos().x()) col++;
    }
    emit sig_layout(row,col);
    hide();
}

// mainwindow.ui
// 拖动一个 QToolButton

// mainwindow.h
#include <gridpopwidget.h>

class MainWindow : public QMainWindow
{
    Q_OBJECT
public:
protected:
    virtual void mousePressEvent(QMouseEvent *event) override;
    virtual void resizeEvent(QResizeEvent *event) override;
public slots:
    void setSplitLayout(int row,int col);
    void setGridPopWidget();
private:
    GridPopWidget    *gridwidget;
}；

// mainwindow.cpp
#include <QToolButton>
#include <QMenu>
#include <QComboBox>
MainWindow::MainWindow(QWidget *parent)
{
    gridwidget = new GridPopWidget(this); ui->statusBar->addPermanentWidget(ui->toolButton);
    connect(gridwidget,&GridPopWidget::sig_layout,this,&MainWindow::setSplitLayout);
    connect(ui->toolButton,&QToolButton::clicked,this,&MainWindow::setGridPopWidget);
}

void MainWindow::resizeEvent(QResizeEvent *e)
{
   if(gridwidget->isVisible())
		gridwidget->hide();
}

void MainWindow::mousePressEvent(QMouseEvent *e)
{
   if( e->pos().x() < gridwidget->pos().x() || 
       e->pos().y() < gridwidget->pos().y() )
   {
       gridwidget->hide();
   }
}

void MainWindow::setSplitLayout(int row, int col)
{  //TODO: 具体实现分屏
   qDebug() << "row:" << row << ", col:" << col;
}

void MainWindow::setGridPopWidget()
{
   gridwidget->move(width()-gridwidget->width(),
                    height()-gridwidget->height()-ui->statusBar->height()+5);
   gridwidget->show();
}