When making images of people, there's a constant tension between being close enough to provide intimacy and detail, and far enough to provide a full view of the person. More often than not, images of a person sacrifice the physical whole for the physical parts. Where we cut off the parts isn't an easy question, and isn't subject to a rule.
Instead, like any framing decision, the choice of what parts of a person stay in a frame is a question of gestalt.
One of the most erudite thinkers on visual perception and art is Rudolph Arnheim, and it is to him we turn to define the issues of how we frame images of people. First, some quotes from his classic Art and Visual Perception:
“There is no point to visual shapes apart from what they tell us.” p.4
“[T]he mind always functions as a whole. All perceiving is also thinking, all reasoning is also intuition, all observation is also invention.” p. 5
“No object is perceived as unique or isolated. Seeing something involves assigning it a place in the whole: a location in space, a score on the scale of size or brightness or distance.” p. 11
“[F]actors such as size, color, or direction contribute to visual balance in ways not necessarily paralleled physically.” p. 20
Applying these observations about visual perception to the framing of a portrait, the photographer's challenge is to perceive the whole of the image, and not to treat the subject as a butcher would: picking severable joints. How the whole comes together is a function of light, shadow, form, and the visual weight and meaning of each of those elements to the viewer. Whether or not the image has a gestalt balance won't be determined by where limbs are cut off.
The questions of balance and completeness in an image are artistic, and therefore there aren't an hard and fast rules. Understanding how the mind works in perceiving visual elements, though, enables the photographer to make purposeful decisions when framing, and to understand why certain images “work” while others don't. Sometimes we can cut off parts and retain the meaning of the whole. The challenge is picking the right parts, and in appreciating that any subject exists within the context of the whole frame. Again, Arnheim:
Good fragments are neither surprisingly complete nor distressingly incomplete; they have a particular charm of revealing unexpected merits of parts while the the same time pointing to a lost entity beyond themselves. A similar coherence of the total structure exists in organic shape. The geneticist Waddington says that although whole skeletons have a “quality of completeness,” which resists additions or omissions, the single bones have only “a certain degree of completeness.” Their shape carries implications about the other parts to which they are attached, and when isolated they are “like a tune which breaks off in the middle.” p.78.
Gestalt is the key to picking up the broken tune: although any particular part is primarily identified by its category (e.g., a hand belongs to a body; a tire belongs to a vehicle), the parts included in a composition achieve a higher level of belonging to the whole of the image. Where we are able to liberate a part from its original category and make it part of a new one, we can achieve a higher level of artistic presentation.
What you see is what you get
A couple of examples may help:
This studio image of Sydney has many simple gestalt forms. Because of the starkness of the black and white, it's easy for a spectator to perceive the repeated highlight shapes (in red), which visually form a vertical line. The highlights are paralleled by the black shapes, which give dimensionality to the highlights. There are also several strong diagonal lines running both vertically (blue) and horizontally (green). Because the image is strongly achromatic, and because the repetition of highlights and shapes is numerous, the cut off legs and hidden right arm don't stand out very much, if at all. The whole dominates the parts.
This image of a boy in Iran is more difficult. His left hand is cut off. If we only look at the boy, the missing part creates tension. Because the boy is about center in the frame, and closer to us, we tend to look at him as a whole, and the missing hand is disconcerting. (If the missing hand is intentional to create tension, no worries.)
But if we view the boy in the context of the entire frame, his left arm becomes a gestalt element. Rather than being an "arm," it's a vertical line which plays off other vertical lines in the frame (red), just as his right arm plays off the other diagonal lines in the frame (blue). The image moves from being about the boy, to being about a repetition of a very few gestalt forms. If the image were of the isolated boy, I wouldn't like the tension created by the missing hand. As a whole, however, I don't mind it at all because it functions to drive the spectator to view it as a gestalt element, and look for other such elements. These obviously are artistic choices, but the goal is for those choices to be informed by an understanding of how the mind perceives form.
As we have previously discussed, gestalt only occurs in a frame. That makes it difficult to perceive without constant practice. So next time you lift your camera, shift your attention away from the primary subject and take a look at the whole. You'll be surprised by how much you see!