Zoom In/Out without Changing the Cursor Location

Let’s say we draw a map into the window by using the transformation mentioned in Map to/from Window Coordinate Transformation. Now we want to zoom in/zoom out in the map. When we use the window center for zoom, it is easy to calculate the Upper-Left and Lower-Right map coordinates of the new window. Assume that we zoom in or zoom out by 2. In this situation calculation of the new Upper-Left and Lower-Right map coordinates in Zoom In function could be calculated as in the Figure-1, and in Zoom Out function as in Figure-2. Then we redraw our map by entering our new corner coordinates as used in Map to/from Window Coordinate Transformation.

But what will happen if we use mouse wheel and don’t want to change the map coordinates of the mouse cursor? I mean zooming without changing the cursor map coordinates.

We will use the same coordinate systems which are mentioned in Map to/from Window Coordinate Transformation, to find the required functionality. When we look at Figure-3 carefully, we could notice that the window coordinates of the mouse cursor (C_p, R_p) will not change when we zoom in/out. This means that map coordinates of the mouse cursor (X_p, Y_p) will not change either. Only map coordinates of the window corners can be changed when we zoom.

We have four unknowns: UL_x^”, UL_y^”, LR_x^” and LR_y^”. So, we need to find four equations to find the values of the unknowns. We assume we zoom in or zoom out by k.

If we leave X₀^” and Y₀^” alone in the first two equations and apply 3^rd and 4^th equations:

Then we can calculate S_x^” and S_y^”:

Finally, we can calculate LR_x^” and LR_y^”:

[*] public PointCoor[] CalculateZoomedWindow(PointCoor PreviousUpperLeft, PointCoor CursorWinLocation, int WinWidth, int WinHeight, double ZoomRatio, bool ZoomOut)
{
    double m = ZoomRatio;

    if (ZoomOut)
        m = 1/ZoomRatio;

    PointCoor CursorMapLocation = WindowToMap(CursorWinLocation);
    double ULX = CursorMapLocation.X - (CursorMapLocation.X - PreviousUpperLeft.X) / m;
    double ULY = (PreviousUpperLeft.Y - CursorMapLocation.Y) / m + CursorMapLocation.Y;
    double sx = (CursorMapLocation.X - ULX) / CursorWinLocation.X;
    double sy = (ULY - CursorMapLocation.Y) / CursorWinLocation.Y;
    double LRX = ULX + WinWidth * sx;
    double LRY = ULY - WinHeight * sy;

    PointCoor[] res = new PointCoor[2];
    res[0] = new PointCoor(ULX, ULY);
    res[1] = new PointCoor(LRX, LRY);

    return res;
}

[*] THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.