根据三次Bezier曲线的基函数，使用MFC编程绘制下图所示的三次Bezier曲线。要求可以使用鼠标左键拖动控制多边形的顶点，同时曲线能随之发生变化。

以下是使用MFC编程绘制三次Bezier曲线的示例代码：

首先，在MFC的框架下创建一个新的MFC应用程序，然后在View类中添加以下代码：

class CBezierCurveView : public CView
{
protected: // create from serialization only
    CBezierCurveView() noexcept;
    DECLARE_DYNCREATE(CBezierCurveView)

// Attributes
public:
    CBezierCurveDoc* GetDocument() const;

// Operations
public:
    void OnDrawBezier(CDC* pDC, CPoint* pPoints, int nCount);

// Overrides
public:
    virtual void OnDraw(CDC* pDC);  // overridden to draw this view
    virtual BOOL PreCreateWindow(CREATESTRUCT& cs);
protected:
    virtual void OnInitialUpdate(); // called first time after construct

// Implementation
public:
    virtual ~CBezierCurveView();
#ifdef _DEBUG
    virtual void AssertValid() const;
    virtual void Dump(CDumpContext& dc) const;
#endif

protected:

// Generated message map functions
protected:
    DECLARE_MESSAGE_MAP()
public:
    afx_msg void OnLButtonDown(UINT nFlags, CPoint point);
    afx_msg void OnMouseMove(UINT nFlags, CPoint point);
    afx_msg void OnLButtonUp(UINT nFlags, CPoint point);
private:
    BOOL m_bDragging;
    CPoint m_DragPoint;
    CPoint m_Points[4];
};

在View类的cpp文件中添加以下代码：

IMPLEMENT_DYNCREATE(CBezierCurveView, CView)

BEGIN_MESSAGE_MAP(CBezierCurveView, CView)
    ON_WM_LBUTTONDOWN()
    ON_WM_MOUSEMOVE()
    ON_WM_LBUTTONUP()
END_MESSAGE_MAP()

// CBezierCurveView construction/destruction

CBezierCurveView::CBezierCurveView() noexcept
{
    m_bDragging = FALSE;
}

CBezierCurveView::~CBezierCurveView()
{
}

BOOL CBezierCurveView::PreCreateWindow(CREATESTRUCT& cs)
{
    return CView::PreCreateWindow(cs);
}

void CBezierCurveView::OnInitialUpdate()
{
    CView::OnInitialUpdate();
    // 初始化多边形的顶点
    m_Points[0] = CPoint(100, 200);
    m_Points[1] = CPoint(200, 100);
    m_Points[2] = CPoint(400, 300);
    m_Points[3] = CPoint(500, 200);
}

// CBezierCurveView drawing

void CBezierCurveView::OnDraw(CDC* pDC)
{
    CBezierCurveDoc* pDoc = GetDocument();
    ASSERT_VALID(pDoc);
    if (!pDoc)
        return;

    OnDrawBezier(pDC, m_Points, 4);
}

void CBezierCurveView::OnDrawBezier(CDC* pDC, CPoint* pPoints, int nCount)
{
    // 绘制多边形的边
    for (int i = 0; i < nCount - 1; i++)
    {
        pDC->MoveTo(pPoints[i]);
        pDC->LineTo(pPoints[i + 1]);
    }

    // 计算Bezier曲线上的点
    CPoint points[100];
    for (int i = 0; i < 100; i++)
    {
        double t = double(i) / 99;
        double a = (1 - t) * (1 - t) * (1 - t);
        double b = 3 * t * (1 - t) * (1 - t);
        double c = 3 * t * t * (1 - t);
        double d = t * t * t;
        double x = a * pPoints[0].x + b * pPoints[1].x + c * pPoints[2].x + d * pPoints[3].x;
        double y = a * pPoints[0].y + b * pPoints[1].y + c * pPoints[2].y + d * pPoints[3].y;
        points[i].x = int(x + 0.5);
        points[i].y = int(y + 0.5);
    }

    // 绘制Bezier曲线
    for (int i = 0; i < 99; i++)
    {
        pDC->MoveTo(points[i]);
        pDC->LineTo(points[i + 1]);
    }
}

// CBezierCurveView diagnostics

#ifdef _DEBUG
void CBezierCurveView::AssertValid() const
{
    CView::AssertValid();
}

void CBezierCurveView::Dump(CDumpContext& dc) const
{
    CView::Dump(dc);
}

CBezierCurveDoc* CBezierCurveView::GetDocument() const // non-debug version is inline
{
    ASSERT(m_pDocument->IsKindOf(RUNTIME_CLASS(CBezierCurveDoc)));
    return (CBezierCurveDoc*)m_pDocument;
}
#endif //_DEBUG

// CBezierCurveView 消息处理程序

void CBezierCurveView::OnLButtonDown(UINT nFlags, CPoint point)
{
    for (int i = 0; i < 4; i++)
    {
        if (abs(point.x - m_Points[i].x) < 5 && abs(point.y - m_Points[i].y) < 5)
        {
            m_bDragging = TRUE;
            m_DragPoint = point;
            break;
        }
    }

    CView::OnLButtonDown(nFlags, point);
}

void CBezierCurveView::OnMouseMove(UINT nFlags, CPoint point)
{
    if (m_bDragging)
    {
        for (int i = 0; i < 4; i++)
        {
            if (m_DragPoint == m_Points[i])
            {
                m_Points[i] = point;
                break;
            }
        }
        Invalidate();
    }

    CView::OnMouseMove(nFlags, point);
}

void CBezierCurveView::OnLButtonUp(UINT nFlags, CPoint point)
{
    m_bDragging = FALSE;

    CView::OnLButtonUp(nFlags, point);
}

在Document类中添加以下代码：

class CBezierCurveDoc : public CDocument
{
protected: // create from serialization only
    CBezierCurveDoc() noexcept;
    DECLARE_DYNCREATE(CBezierCurveDoc)

// Attributes
public:

// Operations
public:

// Overrides
public:
    virtual BOOL OnNewDocument();
    virtual void Serialize(CArchive& ar);
#ifdef SHARED_HANDLERS
    virtual void InitializeSearchContent();
    virtual void OnDrawThumbnail(CDC& dc, LPRECT lprcBounds);
#endif // SHARED_HANDLERS

// Implementation
public:
    virtual ~CBezierCurveDoc();
#ifdef _DEBUG
    virtual void AssertValid() const;
    virtual void Dump(CDumpContext& dc) const;
#endif

protected:

// Generated message map functions
protected:
    DECLARE_MESSAGE_MAP()
#ifdef SHARED_HANDLERS
    // Helper function that sets search content for a Search Handler
    void SetSearchContent(const CString& value);
#endif // SHARED_HANDLERS
};

在Document类的cpp文件中添加以下代码：

IMPLEMENT_DYNCREATE(CBezierCurveDoc, CDocument)

BEGIN_MESSAGE_MAP(CBezierCurveDoc, CDocument)
END_MESSAGE_MAP()


CBezierCurveDoc::CBezierCurveDoc() noexcept
{
}

CBezierCurveDoc::~CBezierCurveDoc()
{
}

BOOL CBezierCurveDoc::OnNewDocument()
{
    if (!CDocument::OnNewDocument())
        return FALSE;
    return TRUE;
}

void CBezierCurveDoc::Serialize(CArchive& ar)
{
    if (ar.IsStoring())
    {
    }
    else
    {
    }
}

#ifdef SHARED_HANDLERS

// Support for thumbnails
void CBezierCurveDoc::OnDrawThumbnail(CDC& dc, LPRECT lprcBounds)
{
    // Modify this code to draw the document's data
    dc.FillSolidRect(lprcBounds, RGB(255, 255, 255));

    CString strText = _T("TODO: implement thumbnail drawing here");
    LOGFONT lf;

    CFont* pDefaultGUIFont = CFont::FromHandle((HFONT)GetStockObject(DEFAULT_GUI_FONT));
    pDefaultGUIFont->GetLogFont(&lf);
    lf.lfHeight = 36;

    CFont fontDraw;
    fontDraw.CreateFontIndirect(&lf);

    CFont* pOldFont = dc.SelectObject(&fontDraw);
    dc.DrawText(strText, lprcBounds, DT_CENTER | DT_WORDBREAK);
    dc.SelectObject(pOldFont);
}

// Support for Search Handlers
void CBezierCurveDoc::InitializeSearchContent()
{
    CString strSearchContent;
    // Set search contents from document's data. 
    // The content parts should be separated by ";"

    // TODO: add additional content here
    strSearchContent = _T("TODO: implement search content");
    SetSearchContent(strSearchContent);
}

void CBezierCurveDoc::SetSearchContent(const CString& value)
{
    if (value.IsEmpty())
    {
        RemoveChunk(PKEY_Search_Contents.fmtid, PKEY_Search_Contents.pid);
    }
    else
    {
        CMFCFilterChunkValueImpl *pChunk = NULL;
        ATLTRY(pChunk = new CMFCFilterChunkValueImpl);
        if (pChunk != NULL)
        {
            pChunk->SetTextValue(PKEY_Search_Contents, value, CHUNK_TEXT);
            SetChunkValue(pChunk);
        }
    }
}

#endif // SHARED_HANDLERS

#ifdef _DEBUG
void CBezierCurveDoc::AssertValid() const
{
    CDocument::AssertValid();
}

void CBezierCurveDoc::Dump(CDumpContext& dc) const
{
    CDocument::Dump(dc);
}
#endif //_DEBUG

最后，在MainFrame类中添加以下代码：

class CMainFrame : public CFrameWnd
{
    
protected: // create from serialization only
    CMainFrame() noexcept;
    DECLARE_DYNCREATE(CMainFrame)

// Attributes
public:

// Operations
public:

// Overrides
public:
    virtual BOOL PreCreateWindow(CREATESTRUCT& cs);
protected:
    virtual BOOL OnCreateClient(LPCREATESTRUCT lpcs, CCreateContext* pContext);

// Implementation
public:
    virtual ~CMainFrame();
#ifdef _DEBUG
    virtual void AssertValid() const;
    virtual void Dump(CDumpContext& dc) const;
#endif

protected:  // control bar embedded members
    CStatusBar  m_wndStatusBar;
    CToolBar    m_wndToolBar;

// Generated message map functions
protected:
    afx_msg int OnCreate(LPCREATESTRUCT lpCreateStruct);
    DECLARE_MESSAGE_MAP()
};

IMPLEMENT_DYNCREATE(CMainFrame, CFrameWnd)

BEGIN_MESSAGE_MAP(CMainFrame, CFrameWnd)
    ON_WM_CREATE()
END_MESSAGE_MAP()

CMainFrame::CMainFrame() noexcept
{
}

CMainFrame::~CMainFrame()
{
}

BOOL CMainFrame::PreCreateWindow(CREATESTRUCT& cs)
{
    if( !CFrameWnd::PreCreateWindow(cs) )
        return FALSE;
    return TRUE;
}

BOOL CMainFrame::OnCreateClient(LPCREATESTRUCT lpcs, CCreateContext* pContext)
{
    CRect rect;
    GetClientRect(rect);
    pContext->m_pNewViewClass = RUNTIME_CLASS(CBezierCurveView);
    pContext->m_pCurrentDoc = new CBezierCurveDoc;
    pContext->m_pNewDocTemplate = NULL;
    return CreateView(pContext, AFX_IDW_PANE_FIRST);
}

int CMainFrame::OnCreate(LPCREATESTRUCT lpCreateStruct)
{
    if (CFrameWnd::OnCreate(lpCreateStruct) == -1)
        return -1;

    if (!m_wndToolBar.CreateEx(this, TBSTYLE_FLAT, WS_CHILD | WS_VISIBLE | CBRS_TOP
        | CBRS_GRIPPER | CBRS_TOOLTIPS | CBRS_FLYBY | CBRS_SIZE_DYNAMIC) ||
        !m_wndToolBar.LoadToolBar(IDR_MAINFRAME))
    {
        TRACE0("Failed to create toolbar\n");
        return -1;      // fail to create
    }

    if (!m_wndStatusBar.Create(this))
    {
        TRACE0("Failed to create status bar\n");
        return -1;      // fail to create
    }
    m_wndStatusBar.SetIndicators(indicators, sizeof(indicators)/sizeof(UINT));

    return 0;
}

#ifdef _DEBUG
void CMainFrame::AssertValid() const
{
    CFrameWnd::AssertValid();
}

void CMainFrame::Dump(CDumpContext& dc) const
{
    CFrameWnd::Dump(dc);
}
#endif //_DEBUG

现在可以运行程序并使用鼠标左键拖动多边形的顶点，观察Bezier曲线的变化。