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);
}