/****************************************************************************
*                   R O E S S L E R   A T T R A C T O R                     * 
* ------------------------------------------------------------------------- *
* TUTORIAL:                                                                 *
*                                                                           *
*  Until recently, the only known attractors were the fixed point, the      *
*  limit cycle and the torus. In 1963, Edwards Lorenz, meteorologist at the *
*  M.I.T.,discovered a practical example of a simple dynamic system presen- *
*  ting a complex behaviour. To adapt them to computers available at that   *
*  time, he began with simplifying the equations of metéorology to obtain   *
*  finally a model composed of three differential equations with three      *
*  unknown variables x, y, z and three parameters a, b, c:                  *
*                                                                           *
*                 dx / dt = - a x + a y                                     *
*		  dy / dt = b x - y - x z                                           *
*		  dz / dt = -c z + x y                                              *
*                                                                           *
*  During very long simulations on a computer, Lorentz decided, to check a  *
*  result, to restart the same calculation halfway in order to spare time.  *
*  For that, he reinjected into the computer the intermediate date obtaine  *
*  earlier. He was very surprised to see that the new results were comple-  *
*  tely different from the first ones. After he suspected some computer     *
*  failure, Lorenz understood at last that the big difference between both  *
*  solutions came from very small differences in data. These small pertur-  *
*  bations exponentially amplified themselves, being doubled every four     *
*  days in simulated time, so after two months the results became entirely  *
*  different !                                                              *
*                                                                           *
*  Lorenz then realized that it would be very difficult to make meteorolo-  *
*  gical foresights in the long term, the slightest change in initial con-  *
*  ditions leading to a radically different evolution of atmosphere.        *
*                                                                           *
*  This is still the case today with atmospheric models much more sophis-   *
*  ticated.                                                                 *
*                                                                           *
*  None of the three attractors known at the time could predict the beha-   *
*  viour of such a dynamic system. Lorenz had just discovered a strange or  *
*  "chaotic" attractor to which his name was given, see program lorentz.pas *
*                                                                           *
*  The Roessler attractor is similar to the Lorenz attractor, by taking the *
*  following differential system of equations:                              *
*                                                                           *
*		  dx / dt = -( y + z )                                              *
*		  dy / dt = x + ( y / 5 )                                           *
*		  dz / dt = 1/5 + z ( x - 5,7 )                                     *
*                                                                           *
* ------------------------------------------------------------------------- *
*  REFERENCE:                                                               *
*     "Graphisme dans le plan et dans l'espace avec Turbo Pascal 4.0        *
*      By R. Dony - MASSON, Paris 1990" [BIBLI 12].                         *
*                                                                           *
*                                C++ version in API style by J-P Moreau     *
*                              (to be used with roessler.mak and gr2d.cpp)  *
*                                          (www.jpmoreau.fr)                *
****************************************************************************/
#include <windows.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

HDC  hdc;
RECT rect;

//Functions used here of module Gr2D.cpp
void Fenetre(double,double,double,double); 
void Cloture(int,int,int,int); 
void Bordure();
void MoveXY(double,double);
void LineXY(double,double);

//"home made" graphic commands for hdc environment used by above functions
void DrawPixel(int ix,int iy) {
  //sorry, no other available command found
  Rectangle(hdc,rect.left+ix,rect.top+iy,
	            rect.left+ix+2,rect.top+iy+1);
}

void Swap(int *i1,int *i2) {
  int it;
  it=*i1; *i1=*i2; *i2=it;
}

void DrawLine(int ix1,int iy1,int ix2,int iy2) {
  int i,il,ix,iy;
  float dx,dy;
  if (ix2<ix1) {
	Swap(&ix1,&ix2); Swap(&iy1,&iy2);
  }
  il=(int) sqrt((ix2-ix1)*(ix2-ix1)+(iy2-iy1)*(iy2-iy1));
  dx=(float) (ix2-ix1)/il; 
  dy=(float) (iy2-iy1)/il;
  ix=ix1; iy=iy1;
  for (i=1;i<il+1; i++) {
	DrawPixel(ix,iy);
	ix=(int) (ix1+i*dx); 
	iy=(int) (iy1+i*dy);
  }
}

void OutText(int ix,int iy,char *s) {
  RECT rct;
  rct.left=ix; rct.right=ix+10*strlen(s);
  rct.top=iy-5; rct.bottom=iy+15;
  DrawText(hdc, s, -1, &rct,
                DT_SINGLELINE | DT_CENTER | DT_VCENTER);
}


double A,B,C,x,y,z;

void f() {
  double delta = 0.005;
  double dx,dy,dz;
  dx=-(y+z);
  dy=x+y*A;
  dz=B+z*(x-C);
  x=x+delta*dx;
  y=y+delta*dy;
  z=z+delta*dz;
}

void Roessler()  {
  long i=0;
  do {
    i++;
    f();
  } while (i<=1000);
  MoveXY(x,y+z+z);
  for (i=1; i<250000; i++) {
    f();
    LineXY(x,y+z+z);
  }
}


// Roessler Attractor
void Roessler_Attractor() {

  extern MaxX, MaxY;

  //client drawing zone in pixels
  MaxX=(rect.right-rect.left);
  MaxY=(rect.bottom-rect.top);

  A=0.2; B=0.2; C=5.7;
  x=-10; y=-1; z=-1;
  Fenetre(-10,13,-17,55);
  Cloture(15,MaxX-15,15,MaxY-15);
  Bordure();
  Roessler();
}



//Handle window Paint and Destroy messages
long FAR PASCAL /*_export*/ WndProc(HWND hwnd,
    UINT message, UINT wParam, LONG lParam) 
{
    
    HPEN hpen, hpenOld;   
    PAINTSTRUCT ps;

    switch (message) {
        case WM_PAINT:
	    hdc = BeginPaint(hwnd, &ps);
	    GetClientRect(hwnd, &rect);
            hpen = CreatePen(PS_SOLID, 1, RGB(0, 0, 255));
            hpenOld = SelectObject(hdc,hpen);

            Roessler_Attractor();
               
            SelectObject(hdc,hpenOld);
            DeleteObject(hpen);
            EndPaint(hwnd, &ps);
            return 0;
        case WM_DESTROY:
            PostQuitMessage(0);
            return 0;
    }
    return DefWindowProc(hwnd, message, wParam, lParam);
}

// main program
int PASCAL WinMain(HANDLE hInstance, HANDLE hPrevInstance,
    LPSTR lpszCmdParam, int nCmdShow)
{
    static char szAppName[] = "Roessler";
    HWND        hwnd;
    MSG         msg;
    WNDCLASS    wndclass;

    if (!hPrevInstance) {
        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 = GetStockObject(WHITE_BRUSH);
        wndclass.lpszMenuName  = NULL;
        wndclass.lpszClassName = szAppName;

        RegisterClass(&wndclass);
    }

    hwnd = CreateWindow(szAppName,  // window class name
        " ROESSLER ATTRACTOR",      // window caption
        WS_OVERLAPPEDWINDOW,        // window style                       
        CW_USEDEFAULT,              // initial x position
        CW_USEDEFAULT,              // initial y position
        CW_USEDEFAULT,              // initial x size
        CW_USEDEFAULT,              // initial y size
        NULL,                       // parent window handle
        NULL,                       // window menu handle
        hInstance,                  // program instance handle
        NULL);                      // creation parameters

   ShowWindow(hwnd, nCmdShow);
   UpdateWindow(hwnd);

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

//end of file roessler.cpp