The zoom factor is directly proportional to the magnification of the scene being viewed. The relationship between zoom and FOV is slightly more complex, and is given by the following:
fov = 2 * arctan(1 / zoom)
zoom = 1 / tan(fov / 2)
where fov is the horizontal or width-wise Field Of View (ie. in the camera's horizontal plane and the image's x-direction). It must be in radians if the trigonometric functions use radians instead of degrees. (Degree-radian conversions here.)
Note that a zoom value of exactly 1 gives a 90 degree horizontal FOV, but a zoom of 2 does not give a horizontal FOV of 45 degrees.
The conversions between the zoom value and the field of view in planes other than the camera's horizontal (width-wise) can be found using the formulae given below.
Vertical FOV
The vertical FOV is the field of view in the y-direction of the rendered image.
fov = 2 * arctan(ratio / zoom)
zoom = 1 / [tan(fov / 2) * ratio]
where ratio is equal to (ImageWidth / ImageHeight)
Diagonal FOV
The diagonal FOV is the field of view across the diagonal of the rendered image.
fov = 2 * arctan(ratio / zoom)
zoom = 1 / [tan(fov / 2) * ratio]
where ratio is equal to (ImageWidth / ImageDiagonal), ie.
ratio = ImageWidth / squareroot(ImageWidth*ImageWidth ImageHeight*ImageHeight)
Terragen and LightWave use a similar conversion between Zoom and FOV. However, Terragen calculates the horizontal FOV from the zoom, whereas LightWave uses zoom to calculate the vertical FOV. Therefore, the following simple conversions can be used:
LWZoom = zoom * (ImageWidth / ImageHeight)
zoom = LWZoom * (ImageHeight / ImageWidth)
