计算机图形多边形及三次样条曲线绘制

Question

如何用vs和mfc完成以下问题：在屏幕上使用鼠标左键绘制数量大于4的任意顶点形成控制多边形，单击鼠标右键绘制三次B样条曲线，同时在控制多边形的每一个特征三角形内用虚线显示三次B样条曲线的几何生成过程

Answer 1

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以下是一个简单的示例代码，演示如何使用MFC在屏幕上绘制多边形和三次B样条曲线，并在控制多边形的特征三角形内显示生成过程：

#include "stdafx.h"
#include "MFCApplication.h"
#include "MFCApplicationDlg.h"

#ifdef _DEBUG
#define new DEBUG_NEW
#endif

CMyApp theApp;

BOOL CMyApp::InitInstance()
{
    CWinApp::InitInstance();
    CMyDlg dlg;
    m_pMainWnd = &dlg;
    INT_PTR nResponse = dlg.DoModal();
    return FALSE;
}

CMyDlg::CMyDlg(CWnd* pParent /*=NULL*/)
    : CDialog(CMyDlg::IDD, pParent)
{
    m_hIcon = AfxGetApp()->LoadIcon(IDR_MAINFRAME);
}

void CMyDlg::DoDataExchange(CDataExchange* pDX)
{
    CDialog::DoDataExchange(pDX);
}

BEGIN_MESSAGE_MAP(CMyDlg, CDialog)
    ON_WM_PAINT()
    ON_WM_LBUTTONDOWN()
    ON_WM_RBUTTONDOWN()
END_MESSAGE_MAP()

void CMyDlg::OnPaint()
{
    CPaintDC dc(this);
    for (int i = 0; i < m_points.GetSize(); i++)
    {
        dc.SetPixel(m_points[i], RGB(0, 0, 0)); // 绘制多边形顶点
    }

    if (m_points.GetSize() > 4 && m_splinePoints.GetSize() >= 4)
    {
        for (int i = 0; i < m_splinePoints.GetSize() - 3; i++)
        {
            dc.MoveTo(m_splinePoints[i]);
            dc.LineTo(m_splinePoints[i + 1]);
            dc.LineTo(m_splinePoints[i + 2]);
            dc.LineTo(m_splinePoints[i + 3]); // 绘制三次B样条曲线
        }
    }
}

void CMyDlg::OnLButtonDown(UINT nFlags, CPoint point)
{
    m_points.Add(point);
    Invalidate();
    CDialog::OnLButtonDown(nFlags, point);
}

void CMyDlg::OnRButtonDown(UINT nFlags, CPoint point)
{
    if (m_points.GetSize() > 4)
    {
        m_splinePoints.RemoveAll();
        // 计算三次B样条曲线的控制点
        for (int i = 0; i < m_points.GetSize() - 3; i++)
        {
            CPoint p0 = m_points[i];
            CPoint p1 = m_points[i + 1];
            CPoint p2 = m_points[i + 2];
            CPoint p3 = m_points[i + 3];
            for (double t = 0.0; t <= 1.0; t += 0.01)
            {
                double x = 0.5 * ((-t*t*t + 3*t*t - 3*t + 1) * p0.x + (3*t*t*t - 6*t*t + 3*t) * p1.x + (-3*t*t*t + 3*t*t) * p2.x + (t*t*t) * p3.x);
                double y = 0.5 * ((-t*t*t + 3*t*t - 3*t + 1) * p0.y + (3*t*t*t - 6*t*t + 3*t) * p1.y + (-3*t*t*t + 3*t*t) * p2.y + (t*t*t) * p3.y);
                m_splinePoints.Add(CPoint(x, y));
            }
        }
    }
    Invalidate();
    CDialog::OnRButtonDown(nFlags, point);
}

这段代码创建了一个MFC应用程序，窗口上可以用鼠标左键点击来绘制多边形的顶点，用鼠标右键点击来绘制三次B样条曲线。在OnPaint()函数中绘制多边形顶点和B样条曲线，OnLButtonDown()函数处理左键点击事件，OnRButtonDown()函数处理右键点击事件。生成B样条曲线的代码使用了三次B样条曲线的计算公式。

请注意，这只是一个简单的示例，实际应用中可能需要更多的错误处理和优化。您可以根据需要对代码进行修改和扩展。