Zooming graphics based on current mouse position

Too lazy to make the equations right (and most likely would made similar mistake as you… I do not know if it is just me but exactly this easy stuff I cant handle and drives me mad). Instead I am dealing with this kind of tasks as follows (it is much safer from mistakes):

1. create transform functions between screen and world coordinates

   So your mouse position is in screen coordinates and rendered stuff is in world coordinates. As this is only 2D then it is easy. make function that converts between these two. Your world to screen transform (if I am not overlooking something) is this:

   g.ScaleTransform(_scale, _scale);
   g.TranslateTransform(_translateX, _translateY);
   

   so:

   screen_x=(world_x*_scale)+_translateX;
   screen_y=(world_y*_scale)+_translateY;
   

   So the reverse:

   world_x=(screen_x-_translateX)/_scale;
   world_y=(screen_y-_translateY)/_scale;
   

2. change of zoom/scale

   The idea is that after zoom/scale change the mouse position should stay the same in world coordinates as before. so remember world coordinates of mouse before change. Then compute from it the screen position after change and the difference put into translation.

Here simple C++ example:

double x0=0.0,y0=0.0,zoom=1.0,mx,my;
//---------------------------------------------------------------------------
void scr2obj(double &ox,double &oy,double sx,double sy)
    {
    ox=(sx-x0)/zoom;
    oy=(sy-y0)/zoom;
    }
//---------------------------------------------------------------------------
void obj2scr(double &sx,double &sy,double ox,double oy)
    {
    sx=x0+(ox*zoom);
    sy=y0+(oy*zoom);
    }
//---------------------------------------------------------------------------
void __fastcall TForm1::FormMouseWheelDown(TObject *Sender, TShiftState Shift,TPoint &MousePos, bool &Handled)
    {
    double mx0,my0;
    scr2obj(mx0,my0,mx,my);
    zoom/=1.25; // zoom out
    obj2scr(mx0,my0,mx0,my0);
    x0+=mx-mx0;
    y0+=my-my0;
    _redraw=true;
    }
//---------------------------------------------------------------------------
void __fastcall TForm1::FormMouseWheelUp(TObject *Sender, TShiftState Shift, TPoint &MousePos, bool &Handled)
    {
    double mx0,my0;
    scr2obj(mx0,my0,mx,my);
    zoom*=1.25; // zoom in
    obj2scr(mx0,my0,mx0,my0);
    x0+=mx-mx0;
    y0+=my-my0;
    _redraw=true;
    }
//---------------------------------------------------------------------------
void __fastcall TForm1::FormMouseMove(TObject *Sender, TShiftState Shift, int X,int Y)
    {
    mx=X; my=Y;
    }
//---------------------------------------------------------------------------

the mx,my is actual mouse position in screen coordinates, the x0,y0 is the translation and zoom is the scale.

And here captured GIF animation of this:

[edit1] It looks like your gfx objects use transponed matrices

That means the order of transformations is reversed so the equations change a bit… Here your case example in C++:

void scr2obj(double &ox,double &oy,double sx,double sy) 
 { 
 // ox=(sx-x0)/zoom; 
 // oy=(sy-y0)/zoom; 
 ox=(sx/zoom)-x0; 
 oy=(sy/zoom)-y0; 
 } 
//--------------------------------------------------------------------------- 
void obj2scr(double &sx,double &sy,double ox,double oy) 
 { 
 // sx=x0+(ox*zoom); 
 // sy=y0+(oy*zoom); 
 sx=(x0+ox)*zoom; 
 sy=(y0+oy)*zoom; 
 } 
//--------------------------------------------------------------------------- 
void __fastcall TForm1::FormMouseWheelDown(TObject *Sender, TShiftState Shift,TPoint &MousePos, bool &Handled) 
 { 
 double mx0,my0; 
 scr2obj(mx0,my0,mx,my); 
 zoom/=1.25; // zoom out 
 obj2scr(mx0,my0,mx0,my0); 
 // x0+=mx-mx0; 
 // y0+=my-my0; 
 x0+=(mx-mx0)/zoom; 
 y0+=(my-my0)/zoom; 
 _redraw=true; 
 } 
//--------------------------------------------------------------------------- 
void __fastcall TForm1::FormMouseWheelUp(TObject *Sender, TShiftState Shift, TPoint &MousePos, bool &Handled) 
 { 
 double mx0,my0; 
 scr2obj(mx0,my0,mx,my); 
 zoom*=1.25; // zoom in 
 obj2scr(mx0,my0,mx0,my0); 
 // x0+=mx-mx0; 
 // y0+=my-my0; 
 x0+=(mx-mx0)/zoom; 
 y0+=(my-my0)/zoom; 
 _redraw=true; 
 } 
//---------------------------------------------------------------------------