Qt---用QPainter画一个3D的正方体

闲的蛋疼

My3DBox .h

#include 
using namespace Eigen;

#define SQUARE_LENGTH 200//是一个边长200的正方体
#define CAMERA_DISTANCE 300//视点距离

class My3DBox : public QWidget
{
    Q_OBJECT
public:
    explicit My3DBox(QWidget *parent = 0);
protected:
    QPoint m_mousePos;
    Vector3d m_vector[8];//正方形8个点坐标

    void mouseMoveEvent(QMouseEvent *);
    void paintEvent(QPaintEvent *);

    void drawPlane(const QPoint *points,QPainter &painter);
    Matrix3d getMartix();
    QPoint ToPoint(Vector3d vector);
    void drawUp(QPoint *points,QPainter &painter);//正方体面的绘制
    void drawDown(QPoint *points,QPainter &painter);
    void drawLeft(QPoint *points,QPainter &painter);
    void drawRight(QPoint *points,QPainter &painter);
};

My3DBox .cpp

#include "widget.h"

#define PI 3.1415926

My3DBox::My3DBox(QWidget *parent) :
    QWidget(parent),m_mousePos(0,0)
{
    setMouseTracking(true);//在任何情况下启用mouseMoveEvent
    setGeometry(400,200,500,500);

    m_vector[0] << -100,100,100;//设置正方体顶点初始位置
    m_vector[1] << 100,100,100;
    m_vector[2] << -100,-100,100;
    m_vector[3] << 100,-100,100;
    m_vector[4] << -100,100,-100;
    m_vector[5] << 100,100,-100;
    m_vector[6] << -100,-100,-100;
    m_vector[7] << 100,-100,-100;
}

void My3DBox::mouseMoveEvent(QMouseEvent *e)//此处把坐标原点从左上角变换至屏幕中心
{
    if(e->pos().x() < 0)
        m_mousePos.setX(-width()/2);
    else if(e->pos().x() > width())
        m_mousePos.setX(width()/2);
    else
        m_mousePos.setX(e->pos().x() - width()/2);

    if(e->pos().y() < 0)
        m_mousePos.setY(height()/2);
    else if(e->pos().y() > height())
        m_mousePos.setY(-height()/2);
    else
        m_mousePos.setY(-e->pos().y() + height()/2);

    update();
}

void My3DBox::paintEvent(QPaintEvent *)
{
    QPainter painter(this);
    painter.setRenderHint(QPainter::Antialiasing);
    painter.setRenderHint(QPainter::SmoothPixmapTransform);
    painter.setPen(Qt::NoPen);

    painter.fillRect(rect(),QColor(3,22,52));

    Vector3d vector[8];
    Matrix3d matrix = getMartix();//获取变换矩阵

    QPoint points[8];//正面0123 左面4062 右面1537 上面4501 下面 2367(以观察者的方向为主)
    for(int i = 0;i < 8;++i)//计算变换后坐标
    {
        vector[i] = matrix*m_vector[i];
        points[i] = ToPoint(vector[i]);

        points[i].setX(points[i].x()+width()/2);//将坐标系原点变换至左上角
        points[i].setY(-points[i].y()+height()/2);
    }

    //一共要画5个面，最后画正面
    if(qAbs(m_mousePos.x()) > qAbs(m_mousePos.y()))
    {
        if(m_mousePos.x() > 0)
        {
            if(m_mousePos.y() > 0)
                drawDown(points,painter);
            else
                drawUp(points,painter);
            drawLeft(points,painter);
        }
        else
        {
            if(m_mousePos.y() > 0)
                drawDown(points,painter);
            else
                drawUp(points,painter);
            drawRight(points,painter);
        }
    }
    else
    {
        if(m_mousePos.y() > 0)
        {
            if(m_mousePos.x() > 0)
                drawLeft(points,painter);
            else
                drawRight(points,painter);
            drawDown(points,painter);
        }
        else
        {
            if(m_mousePos.x() > 0)
                drawLeft(points,painter);
            else
                drawRight(points,painter);
            drawUp(points,painter);
        }
    }
    //画正面
    QPoint point[4] =
    {
        points[0],
        points[1],
        points[3],
        points[2]
    };
    drawPlane(point,painter);
}

void My3DBox::drawPlane(const QPoint *points,QPainter &painter)
{
    QLinearGradient linearGradient(points[1],points[3]);//设置渐变色
    linearGradient.setColorAt(0.0,QColor(150,150,250));
    linearGradient.setColorAt(1.0,QColor(170,170,255));
    painter.setBrush(QBrush(linearGradient));
    painter.drawConvexPolygon(points,4);
}

Matrix3d My3DBox::getMartix()
{
    double unit_x = 0;//同方向单位向量的x和y
    double unit_y = 0;
    double z = 0;

    if(m_mousePos.x() != 0 || m_mousePos.y() != 0)
    {
        unit_x = m_mousePos.x()/qSqrt(m_mousePos.x()*m_mousePos.x() + m_mousePos.y()*m_mousePos.y());
        unit_y = m_mousePos.y()/qSqrt(m_mousePos.x()*m_mousePos.x() + m_mousePos.y()*m_mousePos.y());
        z = qSqrt(m_mousePos.x()*m_mousePos.x() + m_mousePos.y()*m_mousePos.y())/qSqrt(width()*width()/4 + height()*height()/4);
    }

    Matrix3d M_Z;
    if(unit_x == 0 && unit_y == 0)
        M_Z << 1,0,0,
               0,1,0,
               0,0,1;
    else
        M_Z << unit_y,-unit_x,0,
               unit_x,unit_y,0,
               0,0,1;

    Matrix3d M_X;
    if(z == 0)
        M_X << 1,0,0,
               0,1,0,
               0,0,1;
    else
        M_X << 1,0,0,
               0,cos(z*PI/2.6),sin(z*PI/2.6),
               0,-sin(z*PI/2.6),cos(z*PI/2.6);//为什么PI/2大于90度？因为没画背面所以必须小于90度(偷懒)

    return M_Z.inverse()*M_X*M_Z;
}

QPoint My3DBox::ToPoint(Vector3d vector)//将3d坐标投影至平面上
{
    QPoint point;

    point.setX(CAMERA_DISTANCE*vector[0]/(CAMERA_DISTANCE-vector[2]));
    point.setY(CAMERA_DISTANCE*vector[1]/(CAMERA_DISTANCE-vector[2]));

    return point;
}

void My3DBox::drawUp(QPoint *points,QPainter &painter)
{
    QPoint point[4] =
    {
        points[4],
        points[5],
        points[1],
        points[0]
    };
    drawPlane(point,painter);
}

void My3DBox::drawDown(QPoint *points,QPainter &painter)
{
    QPoint point[4] =
    {
        points[2],
        points[3],
        points[7],
        points[6]
    };
    drawPlane(point,painter);
}

void My3DBox::drawLeft(QPoint *points,QPainter &painter)
{
    QPoint point[4] =
    {
        points[4],
        points[0],
        points[2],
        points[6]
    };
    drawPlane(point,painter);
}

void My3DBox::drawRight(QPoint *points,QPainter &painter)
{
    QPoint point[4] =
    {
        points[1],
        points[5],
        points[7],
        points[3]
    };
    drawPlane(point,painter);
}