使用GDI绘制抛物线，双曲线。放大缩小和移动。

以下是使用GDI绘制抛物线和双曲线的示例代码，包括放大、缩小和移动功能：

#include <windows.h>
#include <cmath>

LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);

int WINAPI WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance,
    PSTR szCmdLine, int iCmdShow)
{
    static TCHAR szAppName[] = TEXT("Parabola and Hyperbola");
    HWND hwnd;
    MSG msg;
    WNDCLASS wndclass;

    wndclass.style = CS_HREDRAW | CS_VREDRAW;
    wndclass.lpfnWndProc = WndProc;
    wndclass.cbClsExtra = 0;
    wndclass.cbWndExtra = 0;
    wndclass.hInstance = hInstance;
    wndclass.hIcon = LoadIcon(NULL, IDI_APPLICATION);
    wndclass.hCursor = LoadCursor(NULL, IDC_ARROW);
    wndclass.hbrBackground = (HBRUSH)GetStockObject(WHITE_BRUSH);
    wndclass.lpszMenuName = NULL;
    wndclass.lpszClassName = szAppName;

    if (!RegisterClass(&wndclass))
    {
        MessageBox(NULL, TEXT("This program requires Windows NT!"),
            szAppName, MB_ICONERROR);
        return 0;
    }

    hwnd = CreateWindow(szAppName, TEXT("Parabola and Hyperbola"),
        WS_OVERLAPPEDWINDOW | WS_CLIPCHILDREN | WS_CLIPSIBLINGS,
        CW_USEDEFAULT, CW_USEDEFAULT, CW_USEDEFAULT, CW_USEDEFAULT,
        NULL, NULL, hInstance, NULL);

    ShowWindow(hwnd, iCmdShow);
    UpdateWindow(hwnd);

    while (GetMessage(&msg, NULL, 0, 0))
    {
        TranslateMessage(&msg);
        DispatchMessage(&msg);
    }

    return msg.wParam;
}

LRESULT CALLBACK WndProc(HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    static int cxClient, cyClient;
    static int xCenter, yCenter;
    static double scaleX = 1.0, scaleY = 1.0;
    static double xMove = 0.0, yMove = 0.0;
    static POINT ptPrev;
    static bool bDragging = false;

    switch (message)
    {
    case WM_SIZE:
        cxClient = LOWORD(lParam);
        cyClient = HIWORD(lParam);
        xCenter = cxClient / 2;
        yCenter = cyClient / 2;
        return 0;

    case WM_KEYDOWN:
        switch (wParam)
        {
        case VK_ADD:
            scaleX *= 1.1;
            scaleY *= 1.1;
            InvalidateRect(hwnd, NULL, TRUE);
            return 0;

        case VK_SUBTRACT:
            scaleX /= 1.1;
            scaleY /= 1.1;
            InvalidateRect(hwnd, NULL, TRUE);
            return 0;

        case VK_LEFT:
            xMove -= 10.0 / scaleX;
            InvalidateRect(hwnd, NULL, TRUE);
            return 0;

        case VK_RIGHT:
            xMove += 10.0 / scaleX;
            InvalidateRect(hwnd, NULL, TRUE);
            return 0;

        case VK_UP:
            yMove -= 10.0 / scaleY;
            InvalidateRect(hwnd, NULL, TRUE);
            return 0;

        case VK_DOWN:
            yMove += 10.0 / scaleY;
            InvalidateRect(hwnd, NULL, TRUE);
            return 0;
        }
        return 0;

    case WM_LBUTTONDOWN:
        SetCapture(hwnd);
        ptPrev.x = LOWORD(lParam);
        ptPrev.y = HIWORD(lParam);
        bDragging = true;
        return 0;

    case WM_MOUSEMOVE:
        if (bDragging)
        {
            xMove += (LOWORD(lParam) - ptPrev.x) / scaleX;
            yMove += (HIWORD(lParam) - ptPrev.y) / scaleY;
            InvalidateRect(hwnd, NULL, TRUE);
            ptPrev.x = LOWORD(lParam);
            ptPrev.y = HIWORD(lParam);
        }
        return 0;

    case WM_LBUTTONUP:
        ReleaseCapture();
        bDragging = false;
        return 0;

    case WM_PAINT:
    {
        PAINTSTRUCT ps;
        HDC hdc = BeginPaint(hwnd, &ps);

        // set up coordinate transformation
        SetMapMode(hdc, MM_ANISOTROPIC);
        SetViewportOrgEx(hdc, xCenter, yCenter, NULL);
        SetWindowExtEx(hdc, cxClient, -cyClient, NULL);
        SetViewportExtEx(hdc, (int)(cxClient / scaleX), (int)(cyClient / scaleY), NULL);
        SetWindowOrgEx(hdc, (int)(-xMove * scaleX), (int)(yMove * scaleY), NULL);

        // draw parabola
        MoveToEx(hdc, -1000, (int)(1000 * 1000), NULL);
        for (int x = -1000; x <= 1000; x++)
        {
            int y = (int)(-x * x / 1000.0);
            LineTo(hdc, x, y);
        }

        // draw hyperbola
        MoveToEx(hdc, -1000, 0, NULL);
        for (int x = -1000; x <= -1; x++)
        {
            int y = (int)(1000 * sqrt(1.0 + x * x / 1000.0));
            LineTo(hdc, x, y);
        }
        for (int x = 1; x <= 1000; x++)
        {
            int y = (int)(-1000 * sqrt(1.0 + x * x / 1000.0));
            LineTo(hdc, x, y);
        }

        EndPaint(hwnd, &ps);
        return 0;
    }

    case WM_DESTROY:
        PostQuitMessage(0);
        return 0;
    }

    return DefWindowProc(hwnd, message, wParam, lParam);
}

在上述代码中，我们使用 `SetMapMode` 和 `SetViewportOrgEx` 等 GDI 函数设置了坐标系的变换，使得我们可以方便地实现放大、缩小和移动功能。抛物线和双曲线的绘制都是通过 `LineTo` 函数实现的，具体细节可以参考代码注释。