Computing Z given X and Y

[HellOfMice]

I need some help because, I am very good useing math.
The user draws a rectangle with the mouse.
SO I have (X1,Y1) and (X2,Y2)

(X1,Y1) are the top left coordinates and
(X2,Y2) are the bottom right coordinates.

I have computed the slope and got the angle.

The rectangle drawn is at (X1,Y1,0)-(X2,Y2,0) but if want to display or to rotate along an axis I need the Z coordinate.

Code Select Expand


static int Create3DObject(HWND __hWnd,int __iX_First,int __iY_First,int __iX_Last,int __iY_Last)
{
   int         _iX1, _iY1, _iX2, _iY2 ;
   int         _iWidth, _iHeight ;
   int         _iPrevIndex ;

   double      _dDistance, _dSlope, _dAngle ;
   double      _dDelta_X, _dDelta_Y ;

   LPOBJECT3D   _lpFirstObject, _lpTmpObject, _lpObject ;

   if((__iX_First == __iX_Last) && (__iY_First == __iY_Last))
   {
      Error("Cannot create an object if the distance between points is equal to 0") ;
      return (FALSE) ;
   }

   _iX1 = __iX_First ;
   _iY1 = __iY_First ;

   _iX2 = __iX_Last ;
   _iY2 = __iY_Last ;

   _iWidth = abs(_iX2 - _iX1) ;
   _iHeight = abs(_iY2 - _iY1) ;

   if(_iHeight == 0)
      return (Error("Cannot create an object if its height is equal to 0")) ;

   _dDistance = sqrt(pow((double) _iWidth,2) + pow((double) _iHeight,2)) ;

   if(_dDistance == 0.00)
      return (Error("Cannot create an object if the distance between points is equal to 0")) ;

   _dDelta_Y = ((double) _iY2) - ((double) _iY1) ;
   _dDelta_X = ((double) _iX2) - ((double) _iX1) ;

   _dSlope = _dDelta_Y / _dDelta_X ;

   _dAngle = VANISH_RAD_TO_DEG * atan2(_dDelta_Y,_dDelta_X) ;

   _lpFirstObject = (LPOBJECT3D) GetWindowLongPtr(__hWnd,GWLP_USERDATA) ;
   if(_lpFirstObject == NULL)
   {
      _lpObject = (LPOBJECT3D) malloc(sizeof(OBJECT3D)) ;
      if(_lpObject == NULL)
      {
         Error("Not enough memory for allocating a new object") ;
         return (FALSE) ;
      }

      _lpObject->Index                           = 1 ;

      _lpObject->Liste.lpPrev                        = NULL ;
      _lpObject->Liste.lpNext                        = NULL ;

      SetWindowLongPtr(__hWnd,GWLP_USERDATA,(LONG_PTR) _lpObject) ;
   }
   else
   {
      _iPrevIndex = 0 ;
      _lpTmpObject = _lpFirstObject ;

      while(_lpTmpObject->Liste.lpNext != NULL)
      {
         if(_iPrevIndex < _lpTmpObject->Index)
            _iPrevIndex = _lpTmpObject->Index ;

         _lpTmpObject = (LPOBJECT3D) _lpTmpObject->Liste.lpNext ;
      }

      _lpObject = (LPOBJECT3D) malloc(sizeof(OBJECT3D)) ;
      if(_lpObject == NULL)
      {
         Error("Not enough memory for allocating a new object") ;
         return (FALSE) ;
      }

      _lpTmpObject->Liste.lpNext                  = _lpObject ;
      _lpObject->Liste.lpPrev                     = _lpTmpObject ;
      _lpObject->Liste.lpNext                     = NULL ;

      _lpObject->Index                        = _iPrevIndex + 1 ;
   }

   _lpObject->ColorBrush                        = -1 ;            // NULL BRUSH
   _lpObject->ColorPen                           = 0x000000FF ;

//   z = sqrt(x² + y² - 2 * x * y * cos(γ)) ?

   _lpObject->Coordonnees3D.Distance         = _dDistance ;
   _lpObject->Coordonnees3D.Slope            = _dSlope ;
   _lpObject->Coordonnees3D.Angle            = _dAngle ;
   _lpObject->Coordonnees3D.DeltaX            = _dDelta_X ;
   _lpObject->Coordonnees3D.DeltaY            = _dDelta_Y ;

   _lpObject->Coordonnees3D.Left.x            = _iX1 ;
   _lpObject->Coordonnees3D.Left.y            = _iY1 ;
   _lpObject->Coordonnees3D.Left.z            = sqrt(pow((double) _iX1,2) + pow((double) _iY1,2) - (2 * (double) _iX1 * (double) _iY1 * cos(_dAngle))) ;

   _lpObject->Coordonnees3D.Right.x         = _iX2 ;
   _lpObject->Coordonnees3D.Right.y         = _iY2 ;
   _lpObject->Coordonnees3D.Right.z         = sqrt(pow((double) _iX2,2) + pow((double) _iY2,2) - (2 * (double) _iX2 * (double) _iY2 * cos(_dAngle))) ;

   _lpObject->Coordonnees3D.Rectangle.x      = _iX1 ;
   _lpObject->Coordonnees3D.Rectangle.y      = _iY1 ;
   _lpObject->Coordonnees3D.Rectangle.z      = sqrt(pow((double) _iX1,2) + pow((double) _iY1,2) - (2 * (double) _iX1 * (double) _iY1 * cos(_dAngle))) ;
   _lpObject->Coordonnees3D.Rectangle.width   = _iWidth ;
   _lpObject->Coordonnees3D.Rectangle.height   = _iHeight ;
   _lpObject->Coordonnees3D.Rectangle.Depth   = abs(_iX1 - _lpObject->Coordonnees3D.Rectangle.z) ;

   lpCurrentObject                        = _lpObject ;

   return (TRUE) ;
}


z = sqrt(x² + y² - 2 * x * y * cos(γ))

This is how I compute the Z.
It is a formula I found somewhere on the internet but I don't know it this is good.

Some help would be welcome.
Thank You / Merci

[frankie]

These MS docs about 2D transformations are woth to be read for your needs.
The articles contain a broad discussion of the topics from a mathematical point of view (MS uses matrix algebra). and also the list of GDI library functions that implement the transformations in case you don't want to reinvent the wheel.

[HellOfMice]

Thank You Fankie.
I take look.