MFC下实现图形学之Hermite、Bezier曲线的绘制

//*******************************************************
//捕捉鼠标左键按下消息，获得两个起始控制点的坐标
//*******************************************************
void CDrawCurvesView::OnLButtonDown(UINT nFlags, CPoint point) 
{
 // TODO: Add your message handler code here and/or call default
 oldPoint = point;
 newPoint = point;
 CurveCtrlPoints[count++] = point;
 SetCapture();
 isLButtonDown = true;
 CRect rect;
    GetClientRect(&rect);
 ClientToScreen(&rect);  //用用户区坐标重新计算屏幕坐标
    ClipCursor(&rect);      //限制光标在用户区内
                            //默认处理，调用基类消息处理函数
    CView::OnLButtonDown(nFlags, point);
}
//******************************************
//按下键盘清除客户区的内容，为下次绘制作准备
//******************************************
void CDrawCurvesView::OnKeyDown(UINT nChar, UINT nRepCnt, UINT nFlags) 
{
 // TODO: Add your message handler code here and/or call default
 count = 0;
 Invalidate();
 CView::OnKeyDown(nChar, nRepCnt, nFlags);
}
//******************
//矩阵乘法
//******************
void CDrawCurvesView::MultiMatrix(int a[4][4],double b[4][2])
{
 int i,j,k;
 for(i=0;i<4;i++)
      for(j=0;j<2;j++)
     result[i][j] = 0;

 for(i=0;i<2;i++)
   for(j=0;j<4;j++)
    for(k=0;k<4;k++)
             result[j][i] += a[j][k]*b[k][i]; 
}
//***************************************
// 捕捉鼠标移动消息，绘制橡皮筋线，
//作为Hermite曲线的控制点处的切线
//***************************************
void CDrawCurvesView::OnMouseMove(UINT nFlags, CPoint point) 
{
 // TODO: Add your message handler code here and/or call default
 if(isLButtonDown)
 {
    CView::OnMouseMove(nFlags, point);
    CClientDC dc(this);
    dc.SetROP2(R2_NOT);
    dc.MoveTo(newPoint);
    dc.LineTo(oldPoint);
    dc.MoveTo(newPoint);
    dc.LineTo(point);
    oldPoint = point;
 }
}
//*****************************************************
//捕捉鼠标左键松开消息，并在捕捉到第四个控制点
//后，根据从菜单选择项的不同，开始绘制不同曲线
//******************************************************
void CDrawCurvesView::OnLButtonUp(UINT nFlags, CPoint point) 
{
 // TODO: Add your message handler code here and/or call default
 isLButtonDown=false;//标志鼠标释放
    ReleaseCapture();//释放鼠标捕捉
    ClipCursor(NULL);//
 CurveCtrlPoints[count++] = point;
  if(count == 4)
  { 
  CClientDC dc(this);
  CPen pen;
  pen.CreatePen(PS_SOLID,3,RGB(255,0,0));
  dc.SelectObject(pen);
  switch(type)
  {
    case HERMITE:
             DrawHermiteCurve(dc,200);
    break;
    case BEZIER:
     DrawBezierCurve(dc,400);
     break;
  }
  pen.DeleteObject();
 }
 CView::OnLButtonUp(nFlags, point);
}
//*******************************************
//菜单响应函数，当菜单项选为Hermite时,
//绘制曲线的类型设置为HERMITE
//*******************************************
void CDrawCurvesView::OnHermite() 
{
 // TODO: Add your command handler code here
 type = HERMITE;
}
//******************************************
//菜单响应函数，当菜单项选为Bezier时,
//绘制曲线的类型设置为BEZIER
//******************************************
void CDrawCurvesView::OnBezier() 
{
 // TODO: Add your command handler code here
 type = BEZIER;
}
//**************************
//绘制hermite曲线的函数
//**************************
void CDrawCurvesView::DrawHermiteCurve(CDC &dc,int nPoints)
{
 int a[4][4] =
 {
  {2,-2,1,1},
  {-3,3,-2,-1},
  {0,0,1,0},
  {1,0,0,0}
 };
    double b[4][2] = {
  {CurveCtrlPoints[0].x,CurveCtrlPoints[0].y},
  {CurveCtrlPoints[2].x,CurveCtrlPoints[2].y},
  {CurveCtrlPoints[1].x-CurveCtrlPoints[0].x,CurveCtrlPoints[1].y-CurveCtrlPoints[1].y},
  {CurveCtrlPoints[3].x-CurveCtrlPoints[2].x,CurveCtrlPoints[3].y-CurveCtrlPoints[2].y}
 };
 CPoint *pt=new CPoint[nPoints];
 double delt = 1.0/nPoints;
 double u = 0.0;
    MultiMatrix(a,b);
 for(int i = 0; i < nPoints; i++)
 {
       pt[i].x =(int) (pow(u,3)*result[0][0] + pow(u,2)*result[1][0]
     + u*result[2][0] + result[3][0]);
    pt[i].y =(int) (pow(u,3)*result[0][1] + pow(u,2)*result[1][1]
     + u*result[2][1] + result[3][1]);
    u += delt;
 }
 dc.Polyline(pt,nPoints);
 delete pt;
}
//************************
//绘制Bezier曲线的函数
//************************
void CDrawCurvesView::DrawBezierCurve(CDC &dc,int nPoints)
{
  double t = 0.0,delt = 0.0;
  delt = 1.0/(double)nPoints;
  CPoint *points = new CPoint[nPoints+1]; 
  for(int i=0; i<= nPoints;i++)
  {
   points[i] = Decas(4,t);
   t += delt;
  }
  dc.Polyline(points,nPoints);
}
//********************************
//绘制Bezier曲线的辅助函数，
//主要完成t在某个值时，bezier
//曲线上的一个点的坐标的计算
//*********************************
CPoint CDrawCurvesView::Decas(int ptNum, double t)
{
 CPoint *coeffa = new CPoint[ptNum+1],coeffa0;
    for(int i=0;i<=ptNum;i++)
 {
  coeffa[i] = CurveCtrlPoints[i];
 }
 for(int r = 1;r <= ptNum;r++)
  for(int j = 0;j < ptNum-r;j++)
  {
   coeffa[j].x=(int)(coeffa[j].x+t*(coeffa[j+1].x-coeffa[j].x));
   coeffa[j].y=(int)(coeffa[j].y+t*(coeffa[j+1].y-coeffa[j].y));
  }
     coeffa0 = coeffa[0];
  delete coeffa;
  return coeffa0;
}