I was wondering how I would go about mapping 2D screen coordinates to a 3D world (specifically the xz plane) knowing:
-position of the camera
-equation of the screen plane
-equation of the xz plane
All I want to do is have the land on the xz plane light up when I hover the mouse over it.
Any help is greatly appreciated!
Thanks!
If your world is rotated and shifted such that the camera is at x=y=z=0 (world coordinates), the world z coordinate increases away from the viewer (into the screen), and the projection plane is parallel to the screen and is at z=d (world coordinate; d > 0), then you determine screen coordinates from world coordinates this way:
xs = d * xw / zwys = d * yw / zw
And that's pretty intuitive: the farther the object from the viewer/projection plane, the bigger its zw and the smaller xs and ys, closer to the vanishing point of xw=yw=0 and zw=+infinity, which projects onto the center of the projection plane xs=ys=0.
By rearranging each of the above you get xw and zw back:
xw = xs * zw / dzw = d * yw / ys
Now, if your object (the land) is a plane at a certain yw, then, well, that yw is known, so you can substitute it and get zw:
zw = d * yw / ys
Having found zw, you can now get xw by, again, substitution:
xw = xs * zw / d = xs * (d * yw / ys) / d = xs * yw / ys
So, there, given the setup described in the beginning and screen coordinates xs and ys of the mouse pointer (0,0 being the screen/window center), the distance between the camera and the projection plane d, and the land plane's yw you get the location of the land spot the mouse points at:
xw = xs * yw / yszw = d * yw / ys
Of course, these xw and zw are in the rotated and shifted world coordinates and if you want the original absolute coordinates in the "map" of the land, you un-rotate and un-shift them.
That's the gist of it.
