From window to opengl coordinate system intuitive explanation

I am trying to understand the map from window coordinate axis (origin top-left) to OpenGL coordinate axis (origin left-bottom) when using the mouse function. In relevant book this map is described by the two following lines:

points[count].x = (float) x / (w/2) - 1.0;
points[count].y = (float) (h-y) / (h/2) - 1.0;

I suspect that these two lines depict a scale. Could you please give an intuitive-mathematical explanation of this map?

Solved

What book are you referring to? The origin in NDC-space is the center of the viewport (0,0 is the center; -1,-1 is the bottom-left; 1,1 is the top-right). Any other coordinate space is defined by your projection matrix.

I believe what the book is trying to teach you is that NDC_-1,-1 is the bottom-left corner of your viewport and NDC_1,1 is the top-right corner.

A more complete mapping would include the X and Y location of your viewport:

• NDC_X = (2.0 * (Screen_X - Viewport_X) / Viewport_W) - 1.0;

• NDC_Y = (2.0 * (Screen_Y - Viewport_Y) / Viewport_H) - 1.0;

This mapping is illustrated below _{(the square on the right is the viewport):}

  

You of course have one additional step necessary since the Y-axis runs the opposite direction in your mouse coordinate system. That is why you see the Y-axis flipped in your mapping h-y