Area-preserving projections from hexagonal and triangular domains to the sphere and applications to electron back-scatter diffraction pattern simulations

摘要

We construct two new area-preserving projections, which map regular hexagons and regular triangles onto circles. Combination of these projections with the inverse Lambert equal-area projection from the disc to the two hemispheres of a sphere provide bi-directional conversions between uniform planar grids with three-fold and six-fold rotational symmetry and corresponding uniform grids on the sphere. An application example is given for the representation of the channeling-modified back-scattered electron yield for hexagonal titanium.