Three-dimensional texture visualization approaches: theoretical analysis and examples

Crystallographic textures are commonly represented in terms of Euler angle triplets and contour plots of planar sections through Euler space. In this paper, the basic theory is provided for the creation of alternative orientation representations using three-dimensional visualizations. The use of homochoric, cubochoric, Rodrigues and stereographic orientation representations is discussed, and illustrations are provided of fundamental zones for all rotational point-group symmetries. A connection is made to the more traditional Euler space representations. An extensive set of three-dimensional visualizations in both standard and anaglyph movies is available.