There are three main ways in which we display texture: pole figures, inverse pole figures, and orientation distribution functions. Pole figures are probably the easiest for people to visualise, and remain the most common way of displaying both texture and individual orientations from EBSD and XRD data. The pole figure is based on a spherical reference frame, and an imaginary line is drawn perpendicular from the crystal plane onto the sphere. A projection from this point on the sphere down to the flat projection plane completes the plot of this one point onto the pole figure.

When many points are placed onto the one pole figure, a clear preference for certain locations can be seen.

If we have measured sufficient data, a mathematical method known as spherical harmonics can be used to create a statistical fit of the individual datum points into a statistically correct curve. The pole figure can be considered to be a map of crystal orientations with reference to the sample geometry. It shows how one crystal plane prefers to be aligned within the specimen geometry.

An inverse pole figure, as the name implies, plots data as a mirror of the pole figure. The inverse pole figure is a map of the specimen direction or geometry with respect to the crystal directions. The IPF shows which of the different crystal orientations are preferred by the specimen geometry. Usually we plot one direction like the rolling direction, or the direction of solidification. The IPF has a triangular shape with one curved edge, and each edge of the IPF represents one of the main crystal planes.

Another method of describing the direction a crystal is pointing is to use a co-ordinate system known as Euler angles. This is also used in other fields such as astronomy. The three angles, Euler 1, 2 and 3, can be plotted in the same way as we would plot any other set of three Cartesian co-ordinates. Just like the pole figure, the regions where there are many points in a cluster indicate those regions that are preferred in the specimen. The data can be contoured by spherical harmonics just like the other two methods of showing texture. Some researchers prefer this description, but it is apparent that obtaining any reference between the ODF and the specimen geometry requires extensive experience.