An interpolation controls the proportions of a glyph by maintaining the relative position (in either the X or Y direction) of one or more “child” points that fall between two other “parent” points. The key word is “between”—the child point(s) cannot be further in the X or Y direction than either parent or on the same X or Y coordinate.
Interpolating is useful when a central feature of a glyph is not controlled, but other features have been because of known heights (Y direction) or side bearings (X direction). Y interpolations are common for these glyphs: 3, 4, 5, 6, 8, 9, A, B, E, F, G, H. K, P, R, X, Y, a, e, g, k, x, y, &, and *. X interpolations are common for 8, A, B, E, G, K, M, R, W, X, Y, k, m, v, w, x, y, &, *.
The simplest interpolation controls a single control point for a vertex relative to other points. For example, interpolating the vertex in the middle of the right side of a “B” can control it in the Y direction relative to the top and bottom of the center stem.
However, choices for interpolating can be more complicated. Consider the same center stem of the “B.” You’ll have to decide whether to interpolate the top or bottom of that stem relative to the top and bottom of the glyph. Either choice will result in problems at certain sizes that you can fix with exception hints (for details, see “Refining Pixel Patterns”). However, the better your choice, the fewer exception hints you’ll need to create, which reduces your work and the disk space required by the font.