使用QPainter画一个3D正方体

#include <Eigen/Geometry>
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);
};

#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);
}