Designing Customized EBSD Software: Inverse Pole Figure Mapping of Crystal Orientations Using Finite Element Shape Functions

Inverse pole figure mapping is a common orientation visualization method used in electron backscatter diffraction (EBSD) software to display crystal orientations. Although this technique has been routinely used in commercial EBSD software, the coloring algorithm employed to map the orientation and construct the color key (standard stereographic triangle) has not been reported in the literature. This paper presents a simple algorithm to color the standard stereographic triangles of the 11 Laue groups by mapping the Maxwell color triangle to the curved standard stereographic triangles using nonlinear shape functions commonly employed in finite element methods. Detailed procedures are given to illustrate how the mapping is performed and how it is used to construct inverse pole figure maps from Euler angles. Color coding of the seven different standard stereographic triangles is demonstrated using a computer program written in C++. It is shown that the simple color-coding algorithm presented in this paper can be conveniently utilized to display orientation data in inverse pole figure maps, which is a critical part of designing customized EBSD software. It also provides a method to adjust the color center within the curved triangles to more uniformly distribute the color, which is not available in commercial EBSD software. The algorithm can also be used to design orientation representation software for other applications, e.g., crystal plasticity simulations, where representation of orientation data is also a routine task.