vc实现bezier曲面,要求用不同颜色显 示曲面和曲面的控制网格,并且可以取消曲面控制网格的显示,允 许交互式地改变控制网格的定点位置,以观看曲面形状的改变;能 够通过对话框、菜单等方式设置曲面的配置参数（书写代码）

下面是一个基于MFC框架的示例代码，用于实现bezier曲面的交互式显示和修改：

//BezierSurface.h

#pragma once

#include <vector>
#include <afxwin.h>
#include <afxdlgs.h>

using namespace std;

class BezierSurface : public CView
{
protected:
    DECLARE_DYNCREATE(BezierSurface)

    int m_nRows;            //行数
    int m_nCols;            //列数
    int m_nSelRow;          //选中的行
    int m_nSelCol;          //选中的列
    int m_nCtlPtSize;       //控制点大小
    bool m_bDrawGrid;       //是否绘制控制网格
    bool m_bDragging;       //是否正在拖动控制点
    bool m_bDraggingCtrlPt; //是否正在拖动控制点
    CPoint m_ptDragStart;   //拖动起始点
    CPoint m_ptDragLast;    //拖动过程中上一次的点
    vector<vector<CPoint>> m_ctrlPts;  //控制点集合
    vector<vector<CPoint>> m_bezierPts;//bezier曲线集合

public:
    BezierSurface();
    virtual ~BezierSurface();

    void Init(int nRows, int nCols);
    void SetCtlPtSize(int nSize) { m_nCtlPtSize = nSize; }
    void SetDrawGrid(bool bDraw) { m_bDrawGrid = bDraw; }
    bool IsDrawGrid() const { return m_bDrawGrid; }

    // Overrides
public:
    virtual void OnDraw(CDC* pDC);      //绘制函数
    virtual void OnInitialUpdate();     //初始化函数
    virtual BOOL PreCreateWindow(CREATESTRUCT& cs);

protected:
    virtual void OnUpdate(CView* /*pSender*/, LPARAM /*lHint*/, CObject* /*pHint*/);
    virtual void OnActivateView(BOOL bActivate, CView* pActivateView, CView* pDeactiveView);
    virtual void OnLButtonDown(UINT nFlags, CPoint point);
    virtual void OnLButtonUp(UINT nFlags, CPoint point);
    virtual void OnMouseMove(UINT nFlags, CPoint point);
    virtual BOOL OnEraseBkgnd(CDC* pDC);

    DECLARE_MESSAGE_MAP()
};

//BezierSurface.cpp

#include "stdafx.h"
#include "BezierSurface.h"

#ifdef _DEBUG
#define new DEBUG_NEW
#endif

IMPLEMENT_DYNCREATE(BezierSurface, CView)

BezierSurface::BezierSurface()
{
    m_nRows = 0;
    m_nCols = 0;
    m_nSelRow = -1;
    m_nSelCol = -1;
    m_nCtlPtSize = 5;
    m_bDrawGrid = true;
    m_bDragging = false;
    m_bDraggingCtrlPt = false;
}

BezierSurface::~BezierSurface()
{
}

void BezierSurface::Init(int nRows, int nCols)
{
    m_nRows = nRows;
    m_nCols = nCols;
    m_ctrlPts.resize(nRows);
    m_bezierPts.resize(nRows);
    for (int i = 0; i < nRows; i++) {
        m_ctrlPts[i].resize(nCols);
        m_bezierPts[i].resize(nCols);
        for (int j = 0; j < nCols; j++) {
            m_ctrlPts[i][j] = CPoint(i * 50, j * 50); //初始化控制点
        }
    }
}

void BezierSurface::OnDraw(CDC* pDC)
{
    //绘制bezier曲面
    for (int i = 0; i < m_nRows - 3; i++) {
        for (int j = 0; j < m_nCols - 3; j++) {
            //计算bezier曲线
            for (double t = 0.0; t <= 1.0; t += 0.01) {
                double u = 1.0 - t;
                double x = 0.0, y = 0.0, z = 0.0;
                for (int k = 0; k <= 3; k++) {
                    for (int l = 0; l <= 3; l++) {
                        double b = 1.0;
                        for (int m = 0; m < k; m++) {
                            b *= (u + m / 3.0);
                        }
                        for (int n = 0; n < 3 - k; n++) {
                            b *= (t + n / 3.0);
                        }
                        x += b * m_ctrlPts[i + k][j + l].x;
                        y += b * m_ctrlPts[i + k][j + l].y;
                    }
                }
                pDC->SetPixel(int(x), int(y), RGB(255, 0, 0));
            }
        }
    }

    if (m_bDrawGrid) {
        //绘制控制网格
        CPen pen(PS_SOLID, 1, RGB(192, 192, 192));
        CPen* pOldPen = pDC->SelectObject(&pen);
        for (int i = 0; i < m_nRows; i++) {
            for (int j = 0; j < m_nCols; j++) {
                if (i < m_nRows - 1) {
                    pDC->MoveTo(m_ctrlPts[i][j]);
                    pDC->LineTo(m_ctrlPts[i + 1][j]);
                }
                if (j < m_nCols - 1) {
                    pDC->MoveTo(m_ctrlPts[i][j]);
                    pDC->LineTo(m_ctrlPts[i][j + 1]);
                }
            }
        }
        pDC->SelectObject(pOldPen);
    }

    //绘制控制点
    for (int i = 0; i < m_nRows; i++) {
        for (int j = 0; j < m_nCols; j++) {
            if (i == m_nSelRow && j == m_nSelCol) {
                pDC->SelectStockObject(BLACK_BRUSH);
                pDC->SelectStockObject(BLACK_PEN);
            }
            else {
                pDC->SelectStockObject(WHITE_BRUSH);
                pDC->SelectStockObject(BLACK_PEN);
            }
            pDC->Ellipse(m_ctrlPts[i][j].x - m_nCtlPtSize, m_ctrlPts[i][j].y - m_nCtlPtSize,
                m_ctrlPts[i][j].x + m_nCtlPtSize, m_ctrlPts[i][j].y + m_nCtlPtSize);
        }
    }
}

void BezierSurface::OnInitialUpdate()
{
    CView::OnInitialUpdate();
    SetScrollSizes(MM_TEXT, CSize(0, 0));
}

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

void BezierSurface::OnUpdate(CView* /*pSender*/, LPARAM /*lHint*/, CObject* /*pHint*/)
{
    Invalidate();
}

void BezierSurface::OnActivateView(BOOL bActivate, CView* pActivateView, CView* pDeactiveView)
{
    CView::OnActivateView(bActivate, pActivateView, pDeactiveView);
    if (bActivate) {
        GetParentFrame()->SetWindowText(_T("Bezier Surface"));
    }
}

void BezierSurface::OnLButtonDown(UINT nFlags, CPoint point)
{
    CRect rc;
    for (int i = 0; i < m_nRows; i++) {
        for (int j = 0; j < m_nCols; j++) {
            rc.SetRect(m_ctrlPts[i][j].x - m_nCtlPtSize, m_ctrlPts[i][j].y - m_nCtlPtSize,
                m_ctrlPts[i][j].x + m_nCtlPtSize, m_ctrlPts[i][j].y + m_nCtlPtSize);
            if (rc.PtInRect(point)) {
                m_bDragging = true;
                m_bDraggingCtrlPt = true;
                m_nSelRow = i;
                m_nSelCol = j;
                m_ptDragStart = point;
                m_ptDragLast = point;
                SetCapture();
                return;
            }
        }
    }
}

void BezierSurface::OnLButtonUp(UINT nFlags, CPoint point)
{
    if (m_bDragging) {
        ReleaseCapture();
        m_bDragging = false;
        if (m_bDraggingCtrlPt) {
            m_bDraggingCtrlPt = false;
        }
        else {
            m_nSelRow = -1;
            m_nSelCol = -1;
        }
        Invalidate();
    }
}

void BezierSurface::OnMouseMove(UINT nFlags, CPoint point)
{
    if (m_bDragging) {
        if (m_bDraggingCtrlPt) {
            m_ctrlPts[m_nSelRow][m_nSelCol] += point - m_ptDragLast;
            m_ptDragLast = point;
        }
        else {
            int dx = point.x - m_ptDragStart.x;
            int dy = point.y - m_ptDragStart.y;
            for (int i = 0; i < m_nRows; i++) {
                for (int j = 0; j < m_nCols; j++) {
                    m_ctrlPts[i][j].x += dx;
                    m_ctrlPts[i][j].y += dy;
                }
            }
            m_ptDragStart = point;
        }
        Invalidate();
    }
}

BOOL BezierSurface::OnEraseBkgnd(CDC* pDC)
{
    return TRUE;
}

BEGIN_MESSAGE_MAP(BezierSurface, CView)
    ON_WM_LBUTTONDOWN()
    ON_WM_LBUTTONUP()
    ON_WM_MOUSEMOVE()
    ON_WM_ERASEBKGND()
END_MESSAGE_MAP()

使用方法：

1. 在主窗口的OnInitDialog函数中添加以下代码，初始化BezierSurface视图：

m_bezierView = new BezierSurface();
m_bezierView->Create(NULL, NULL, WS_CHILD | WS_VISIBLE, CRect(0, 0, 0, 0), this, ID_VIEW_BEZIER, NULL);
m_bezierView->Init(5, 5); //设置行数和列数

2. 在主窗口创建菜单，并添加响应函数，以便用户可以选择是否显示控制网格：

void CMainFrame::OnInitMenuPopup(CMenu* pPopupMenu, UINT nIndex, BOOL bSysMenu)
{
    if (!bSysMenu) {
        if (pPopupMenu->GetMenuItemID(0) == ID_VIEW_DRAWGRID) {
            pPopupMenu->CheckMenuItem(ID_VIEW_DRAWGRID, m_bezierView->IsDrawGrid() ? MF_CHECKED : MF_UNCHECKED);
        }
    }

    CMDIFrameWndEx::OnInitMenuPopup(pPopupMenu, nIndex, bSysMenu);
}

void CMainFrame::OnViewDrawgrid()
{
    m_bezierView->SetDrawGrid(!m_bezierView->IsDrawGrid());
    m_bezierView->Invalidate();
}

3. 在BezierSurface视图中添加对话框，以便用户可以设置曲面的配置参数：

void BezierSurface::OnConfig()
{
    CDialog dlg(IDD_CONFIG_DIALOG, this);
    dlg.DoModal();
}

4. 在对话框的OnInitDialog函数中添加控件，并添加响应函数，以便用户可以设置曲面的配置参数：

BOOL CConfigDialog::OnInitDialog()
{
    CDialog::OnInitDialog();

    m_nRowsCtrl.SetRange(2, 100);
    m_nRowsCtrl.SetPos(m_pBezierView->GetRowCount());
    m_nColsCtrl.SetRange(2, 100);
    m_nColsCtrl.SetPos(m_pBezierView->GetColCount());

    return TRUE;
}

void CConfigDialog::OnOK()
{
    int nRows = m_nRowsCtrl.GetPos();
    int nCols = m_nColsCtrl.GetPos();
    m_pBezierView->Init(nRows, nCols);
    CDialog::OnOK();
}