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Types of composites
There are, of course, an infinite number of ways of using Nuke. However, I have tried to list below a few of the generic directions that a compositor might take when looking for project ideas.
A color grade is simply editing the color values of a scene. This is perhaps the simplest option but its creative impact should not be underestimated. See here for an idea of how far this craft can be taken.
Despite its reputation as the compositor's tool of choice, green screen should not be the first port of call, there are plenty of other options. It is, however, a good option for placing people in impossible enviroments (e.g. the surface if the moon).
Live action with CG
The ability to capture and re-purpose movement from live action footage is one of the big-magic items of compositing. A camera tracker will often be the glue that binds them and an organised workflow will be important (one that takes you from one application to another and back again). Further magic can be had with an environment light that will capture the lighting from the live action and pass it to the CG.
Live action with live action
Seems bizarre to want to incorporate live action with live action. Why not just shoot the whole thing at once? Well: here's why, and here. This method comes into its own when shooting such 'multiple me' footage. Getting the timing right is crucial to such projects. It is wise to make a timing track, exact to a tenth of a second and that this track be marked by sound cues. This will be useful to help the actors get their movements synchronized with each other.
Of course, the problems start when camera movement is involved (and not just faked camera movement). Big studios can afford a camera that can reproduce exactly any movements that are programed into it. However, here is an excellent example of someone managing to pull it off with a simple tripod-mounted rig.
Still images are... kinda still. They can be moved around with Transform nodes but the effect can be flat and unexciting. A set of still images can be placed in a depth formation inside of a 3D environment and filmed with a moving camera. Zooms, pans etc can easily be faked in this way. An example is here. A simple carded panorama can be found in the Assets page. The screengrab below shows its construction with a basic cylinder. The limits of cards is that they are flat. A cure is, instead of feeding the image in as a flat texture, to project it onto the surface using camera projection.
This is a close cousin of carding. The main difference is that a projection can be accommodated by reasonably complex geometry. In the example in the Assets page a projection is placed on a simple pairing of cards. A screen shot below shows the projection camera at work. The script also uses simple cards.
In the beautifully drafted drawing below the green area was shot live-action whilst the red area was CG (or matte painting or live action footage or whatever). As long as the camera is not moving compositing them together should present no problem. A matte pull from a bright sky using a luma key is a good way to seperate the sky from the not-sky. A planr tracker can be used on simple camera motion to match movement.
Should there be overlap then some roto masking will be required. More work maybe... but it will add realism.
The red area of the first of the two images below marks the range of the limits of the original footage used in the replacement scene that follows. The original psd file for this scene is in the Assets page and an intro to the Photoshop to Nuke workflow is here. Scene extention is a subset of matt painting. This, of course, is a great option for people who can paint.
General tips on building a scene
Compositing is a very creative act. Over the years a set of well-tested tricks and tips have evolved that are likely, if used wisely, to sweeten your chances of success. See also Color Workflow#Color stylization for ideas on composition and Script Evaluation#Picture values for tips in scene evaluation.
Matching the different elements of a composite is the biggest issue in compositing. This match has to take into account all picture values: hue, saturation, lightness, grain, resolution, focus, movement, texture etc etc. It is wise that the compositor is entirely methodical in addressing these value and mentally ticks them off as the composite progresses.
One of the main things that unites objects with scenes is cast shadow. When making shadows care should be taken that they match shadows already within the target scene. The two points to look out for are shadow color and the hardness or softness of the shadow edge.
Lighting voodoo such as glows, godrays, lens flare, reflection etc. can 'paper over' the join between the different elements of the composite. The 'Tracker' composite in the Assets page shows a simple reflection faked from the source footage. However, remember that if a lens flare is included that you are implicitly telling the audience that the scene was shot with a camera seen with human eyes. A subtle but significant difference.
In the case of a background replacement or scene extension the painted (or CG'd) element should match the live action. Sometimes this might require a bit of set dressing. For example: if the scene is set in a ruin (as in the example above) then some rubble and debris in the live action will make it easier to unite the two.
Faking camera movement
Small pans and camera shakes can be added in post. There are nodes that can do this (CameraShake) or it can be faked with a simple Transform.
If an element is added to a scene then it can add realism to place it behind an element that looks as if it is part of that scene. This is called overlap and the ordering of scene elements in such a wrapped manner is a pictorial device that painters have used for thousands of years. An example is a situation where a man has been composited into a scene and is 'overlapped' behind a tree in the BG footage.
Any sort of movement within a painted or CG element will add realism. Smoke, birds flying, clouds moving, trees swaying etc. Remember to get the speed and scale of these things right.
To a compositor, sound is normally just the junk that comes with the footage which is usually discarded as irrelevant. However, if you are making your own project then a good sound track can be very helpful. The early VFX artists used sound extensively to hide the shortcoming of their work. Check out 'An American Werewolf in London' (VFX by Rick Baker) for an example of how effective this can be.