Computationally efficient barycentric interpolation of large grain boundary octonion point sets

Abstract

We present a method for performing efficient barycentric interpolation for large grain boundary octonion point sets which reside on the surface of a hypersphere. This method includes removal of degenerate dimensions via singular value decomposition (SVD) transformations and linear projections, determination of intersecting facets via nearest neighbor (NN) searches, and interpolation. This method is useful for hyperspherical point sets for applications such as grain boundaries structure-property models, robotics, and specialized neural networks. We provide a case study of the method applied to the 7-sphere. We provide 1-sphere and 2-sphere visualizations to illustrate important aspects of these dimension reduction and interpolation methods. A MATLAB implementation is available at github.com/sgbaird-5dof/interp. • Barycentric interpolation is combined with hypersphere facet intersections, dimensionality reduction, and linear projections to reduce computational complexity without loss of information • A max nearest neighbor threshold is used in conjunction with facet intersection determination to reduce computational runtime.

Keywords

• Approximate and Efficient N-sphere Barycentric Interpolation