Spectroscopists by necessity utilize group theory and normal coordinate treatment (NCT) to describe the normal modes of vibration of molecules. As discussed previously, the normal coordinates can be transformed to a Cartesian reference frame yielding a table of Cartesian displacement coordinates. Using known bond distances and bond angles, the equilibrium Cartesian coordinates can be calculated. However, equilibrium and displacement coordinates are very difficult to comprehend unless the graphical equivalent (or plot) is drawn.
P. LaBonville and Jack M. Williams, "Drawing Vibrational Modes by Computer," Appl. Spectrosc. 25, 672-674 (1971)