When you do set extensions, and especially when you use tracked cameras, it is often necessary to do 2-d transformations outside of your original frame. The most common thing to do is zoom out on your original footage, revealing your set extension. For this, you basically need two images, with one image being bigger and with both of them perfectly aligned, pixel to pixel. Of course you can manually scale the bigger image to match, but instead you can use a little of Flame math to do it precisely.
Just adjusting the size of your setup does not work as you would expect to - it does not increase the field of view of your camera, but instead changes the output resolution. When you want to output a background that will align with our original picture and yet contain overscan you need to know how much overscan to apply in terms of the camera FOV.
Update: In Flame 2011 and up you can just use the “Camera FBX” node and tweak the settings of the film back. Below the recipe for Flame up to 2011.
First of all, name the tracked camera (or just the camera whose FOV is the base for the extension) “TrackCamera”. Make an axis that will be called “ApertureScale”. Parent the axis under your “TrackCamera”. Next, make a new fresh camera and parent it under the main one. Go to the “fov” channel in the channel editor for this camera and enter the following expression on it:degrees(atan(tan(radians(TrackCamera.fov / 2)) * (ApertureScale.scaling.x / 100))) * 2
Now change the X scale of the “ApretureScale” axis. You will see that the FOV of the camera changes and gives you the framing which is proportional to the original resolution, multiplied by the factor that you enter in the ApertureScale.position.x in percent. For example, if you want to have double the width of overscan, scale the ApertureScale axis to 200 percent and double the resolution of the setup.
You can also use the same rule for very precise overscan projectors (say you painted a frame which goes out of the crop of the original frame and you have to reproject it), but for it to work properly you should keep the center point of the original frame the same as the extendeded one.
Additional perk: removing zoom and reapplying it to a camera track
This is extremely useful when removing zoom from camera tracks (and adding it back afterwards). First you need some objects which are coupled to the camera (a mattebox flap will be a perfect example). Track the flap to get your two points as a scale track (save the tracker setup).
When done, stabilize with inverse scale (pin your image at the centerpoint since this is what you are going to track on!), and do your 3D track. It should come out fine since no zoom is involved at that point.
Now apply the tracker to the ApertureScale axis with Scale Inv - and get a reapplied zoom on your custom camera!