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

Author： Roşca D De Graef M

Publisher： IOP Publishing

ISSN： 0965-0393

Source： Modelling and Simulation in Materials Science and Engineering, Vol.21, Iss.5, 2013-07, pp. : 55021-55036

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

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.