第26周-window程序设计(基础篇)-第5章(图形基础)-贝塞尔曲线BEZIER.C

本文介绍了一种使用四个点（两个端点和两个控制点）来定义的二维贝塞尔曲线，并展示了如何通过调整控制点来改变曲线形状。文章还讨论了贝塞尔曲线的数学表达式及其在Windows API中的实现。

1、贝塞尔曲线BEZIER.C：

/*
贝塞尔曲线：一条二维的贝塞尔曲线由四个点定义－两个端点和两个控制点。
曲线的端点在两个端点上，控制点就好像「磁石」一样把曲线从两个端点间的直线处拉走。
这一点可以由底下的BEZIER互动交谈程序做出最好的展示。
BEZIER.C——Bezier Splines(样条函数) Demo.
*/

#include<windows.h>
LRESULT CALLBACK WndProc (HWND, UINT, WPARAM, LPARAM) ;  
int WINAPI WinMain (HINSTANCE hInstance, HINSTANCE hPrevInstance,  
PSTR szCmdLine, int iCmdShow)  
 {  
   static TCHAR szAppName[] = TEXT ("Bezier") ;  
   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) ;  
   wndclasswndclass.lpszMenuName= NULL ;  
   wndclass.lpszClassName= szAppName ;  
  
   if (!RegisterClass (&wndclass))  
    {  
      MessageBox (NULL, TEXT ("Program requires Windows NT!"),  
      szAppName, MB_ICONERROR) ;  
      return 0 ;  
     }  
  
   hwnd = CreateWindow (szAppName, TEXT ("Bezier Splines"),  
          WS_OVERLAPPEDWINDOW,  
          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 ;  
  }  
  
  void DrawBezier (HDC hdc, POINT apt[])
    { 
      PolyBezier (hdc, apt, 4) ;
      MoveToEx (hdc, apt[0].x, apt[0].y, NULL) ;
      LineTo (hdc, apt[1].x, apt[1].y) ;

      MoveToEx (hdc, apt[2].x, apt[2].y, NULL) ;
      LineTo (hdc, apt[3].x, apt[3].y) ;
     }

LRESULT CALLBACK WndProc (HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam)  
{  
  static POINT apt[4];  
  HDC hdc ;  
  int cxClient,cyClient;
  PAINTSTRUCT ps ;  
  
  switch (message)  
   {  
     case WM_SIZE:  
  
       cxClient = LOWORD (lParam) ;  
       cyClient = HIWORD (lParam) ;  

       apt[0].x = cxClient / 4 ;
       apt[0].y = cyClient / 2 ;
       apt[1].x = cxClient / 2 ;
       apt[1].y = cyClient / 4 ;
       apt[2].x = cxClient / 2 ;
       apt[2].y = 3 * cyClient / 4 ;
       apt[3].x = 3 * cxClient / 4 ;
       apt[3].y = cyClient / 2 ;

       return 0 ;
     case WM_LBUTTONDOWN:
     case WM_RBUTTONDOWN:
     case WM_MOUSEMOVE:

      if (wParam & MK_LBUTTON || wParam & MK_RBUTTON)
       {
         hdc = GetDC (hwnd) ;
         SelectObject (hdc, GetStockObject (WHITE_PEN)) ;
         DrawBezier (hdc, apt) ;
         if (wParam & MK_LBUTTON)
          {
            apt[1].x = LOWORD (lParam) ;
            apt[1].y = HIWORD (lParam) ;
           }
         if (wParam & MK_RBUTTON)
          {
            apt[2].x = LOWORD (lParam) ;
            apt[2].y = HIWORD (lParam) ;
           }
         SelectObject (hdc, GetStockObject (BLACK_PEN)) ;
         DrawBezier (hdc, apt) ;
         ReleaseDC (hwnd, hdc) ;
        }
       return 0 ;

     case WM_PAINT:  
       
      InvalidateRect (hwnd, NULL, TRUE) ;
      hdc = BeginPaint (hwnd, &ps) ;
      DrawBezier (hdc, apt) ;
      EndPaint (hwnd, &ps) ;
      return 0 ;

    case WM_DESTROY:  
       PostQuitMessage (0) ;  
       return 0 ;  
    }  
   return DefWindowProc (hwnd, message, wParam, lParam) ;  
 } 

/*
1、在这个程序中，两个顶点设定在显示区域的上下居中、左右位于1/4和3/4处的位置；两个控制点可以改变，按住鼠标左键或右键并拖动鼠标可以分别改动两个控制点之一。
2、，贝塞尔曲线总是受限于一个四边形（叫做「凸包」），这个四边形由端点和控制点连接而成。
3、曲线总是与第一个控制点到起点的直线相切，并保持同一方向；同时，也与第二个控制点到终点的直线
相切，并保持同一方向。这是用于推导贝塞尔公式时所做的另外两个假设。
*/

/*32位系统前后操作贝塞尔曲线对比*/
前：
x(t) = (1 - t)3 x0 + 3t (1 - t)2 x1 + 3t2 (1 - t) x2 + t3 x3
y(t) = (1 - t)3 y0 + 3t (1 - t)2 y1 + 3t2 (1 - t) y2 + t3 y3
后：
PolyBezier (hdc, apt, iCount) ;
PolyBezierTo (hdc, apt, iCount) ;
/*apt都是POINT结构的数组。对PolyBezier，前四个点（按照顺序）给出贝塞尔曲线的起点、第一个控制点、第二个控制点和终点。此后的每一条贝塞尔曲线只需给出三个点，因为后一条贝塞尔曲线的起点就是前一条贝塞尔曲线的终点，所以，iCount参数等于1加上您所绘制的这些首尾相接曲线条数的三倍。*/

/*注意：在画一系列相连的贝塞尔曲线时，只有当第一条贝塞尔曲线的第二个控制点、第一条贝塞尔曲线的终点（也就是第二条曲线的起点）和第二条贝塞尔曲线的第一个控制点线性相关时，也就是说这三个点在同一条直线上时，曲线在连接点处才是光滑的。*/

可编译代码：

#if defined(UNICODE) && !defined(_UNICODE)
    #define _UNICODE
#elif defined(_UNICODE) && !defined(UNICODE)
    #define UNICODE
#endif

#include <tchar.h>
#include <windows.h>

/*  Declare Windows procedure  */
LRESULT CALLBACK WindowProcedure (HWND, UINT, WPARAM, LPARAM);

/*  Make the class name into a global variable  */
TCHAR szClassName[ ] = _T("Bezier");

int WINAPI WinMain (HINSTANCE hThisInstance,
                     HINSTANCE hPrevInstance,
                     LPSTR lpszArgument,
                     int nCmdShow)
{
    HWND hwnd;               /* This is the handle for our window */
    MSG messages;            /* Here messages to the application are saved */
    WNDCLASSEX wincl;        /* Data structure for the windowclass */

    /* The Window structure */
    wincl.hInstance = hThisInstance;
    wincl.lpszClassName = szClassName;
    wincl.lpfnWndProc = WindowProcedure;      /* This function is called by windows */
    wincl.style = CS_DBLCLKS;                 /* Catch double-clicks */
    wincl.cbSize = sizeof (WNDCLASSEX);

    /* Use default icon and mouse-pointer */
    wincl.hIcon = LoadIcon (NULL, IDI_APPLICATION);
    wincl.hIconSm = LoadIcon (NULL, IDI_APPLICATION);
    wincl.hCursor = LoadCursor (NULL, IDC_ARROW);
    wincl.lpszMenuName = NULL;                 /* No menu */
    wincl.cbClsExtra = 0;                      /* No extra bytes after the window class */
    wincl.cbWndExtra = 0;                      /* structure or the window instance */
    /* Use Windows's default colour as the background of the window */
    wincl.hbrBackground = (HBRUSH) COLOR_BACKGROUND;

    /* Register the window class, and if it fails quit the program */
    if (!RegisterClassEx (&wincl))
        return 0;

    /* The class is registered, let's create the program*/
    hwnd = CreateWindowEx (
           0,                   /* Extended possibilites for variation */
           szClassName,         /* Classname */
           _T("Bezier"),       /* Title Text */
           WS_OVERLAPPEDWINDOW, /* default window */
           CW_USEDEFAULT,       /* Windows decides the position */
           CW_USEDEFAULT,       /* where the window ends up on the screen */
           544,                 /* The programs width */
           375,                 /* and height in pixels */
           HWND_DESKTOP,        /* The window is a child-window to desktop */
           NULL,                /* No menu */
           hThisInstance,       /* Program Instance handler */
           NULL                 /* No Window Creation data */
           );

    /* Make the window visible on the screen */
    ShowWindow (hwnd, nCmdShow);

    /* Run the message loop. It will run until GetMessage() returns 0 */
    while (GetMessage (&messages, NULL, 0, 0))
    {
        /* Translate virtual-key messages into character messages */
        TranslateMessage(&messages);
        /* Send message to WindowProcedure */
        DispatchMessage(&messages);
    }

    /* The program return-value is 0 - The value that PostQuitMessage() gave */
    return messages.wParam;
}
 void DrawBezier (HDC hdc, POINT apt[])
    {
      PolyBezier (hdc, apt, 4) ;
      MoveToEx (hdc, apt[0].x, apt[0].y, NULL) ;
      LineTo (hdc, apt[1].x, apt[1].y) ;

      MoveToEx (hdc, apt[2].x, apt[2].y, NULL) ;
      LineTo (hdc, apt[3].x, apt[3].y) ;
     }

/*  This function is called by the Windows function DispatchMessage()  */

LRESULT CALLBACK WindowProcedure (HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam)
{
  static POINT apt[4];
  HDC hdc ;
  int cxClient,cyClient;
  PAINTSTRUCT ps ;

    switch (message)                  /* handle the messages */
    {
         case WM_SIZE:

       cxClient = LOWORD (lParam) ;
       cyClient = HIWORD (lParam) ;

       apt[0].x = cxClient / 4 ;
       apt[0].y = cyClient / 2 ;
       apt[1].x = cxClient / 2 ;
       apt[1].y = cyClient / 4 ;
       apt[2].x = cxClient / 2 ;
       apt[2].y = 3 * cyClient / 4 ;
       apt[3].x = 3 * cxClient / 4 ;
       apt[3].y = cyClient / 2 ;

       return 0 ;
     case WM_LBUTTONDOWN:
     case WM_RBUTTONDOWN:
     case WM_MOUSEMOVE:

      if (wParam & MK_LBUTTON || wParam & MK_RBUTTON)
       {
         hdc = GetDC (hwnd) ;
         SelectObject (hdc, GetStockObject (WHITE_PEN)) ;
         DrawBezier (hdc, apt) ;
         if (wParam & MK_LBUTTON)
          {
            apt[1].x = LOWORD (lParam) ;
            apt[1].y = HIWORD (lParam) ;
           }
         if (wParam & MK_RBUTTON)
          {
            apt[2].x = LOWORD (lParam) ;
            apt[2].y = HIWORD (lParam) ;
           }
         SelectObject (hdc, GetStockObject (BLACK_PEN)) ;
         DrawBezier (hdc, apt) ;
         ReleaseDC (hwnd, hdc) ;
        }
       return 0 ;

     case WM_PAINT:

      InvalidateRect (hwnd, NULL, TRUE) ;
      hdc = BeginPaint (hwnd, &ps) ;
      DrawBezier (hdc, apt) ;
      EndPaint (hwnd, &ps) ;
      return 0 ;
        case WM_DESTROY:
            PostQuitMessage (0);       /* send a WM_QUIT to the message queue */
            break;
        default:                      /* for messages that we don't deal with */
            return DefWindowProc (hwnd, message, wParam, lParam);
    }

    return 0;
}