an inverse pole figure

A pole figure asks: for this crystal plane, which way in the sample does it point? An inverse pole figure asks the opposite, and that is exactly why it is inverse: for this fixed sample direction, which crystal direction lines up with it? You choose one sample axis — the wire axis, or the sheet normal — and map which crystal directions the grains present along it, plotted in the crystal's own reference frame.

Because the plot lives in crystal coordinates, it is drawn inside the standard stereographic triangle — the small wedge that, by symmetry, contains every distinct crystal direction once (for cubic crystals the triangle with corners [001], [011], [111]). Each grain contributes the crystal direction that happens to lie along the chosen sample axis; where many grains agree, the triangle brightens near that crystal direction. A random sample fills the triangle uniformly. This form is especially natural for fibre textures, where a single sample axis (the wire or fibre axis) tells almost the whole story.

Inverse pole figures are compact and intuitive for one-axis (fibre) textures and are the basis of the familiar colour-coded EBSD orientation maps, where each grain is tinted by the crystal direction along the sample normal using the triangle as a colour key. Honest note: like a pole figure, an inverse pole figure is a partial view — it fixes one sample direction only and does not, by itself, capture the full three-parameter orientation of each grain; the complete description is still the orientation distribution function.