From window to opengl coordinate system intuitive explanation

Question

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?

Answer 1

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 hy