Unfortunately the description of Eternity pieces is a breach of C.Monckton's copyright. He does not wish the description of the pieces to be published in any form. The set of 770 pieces I used. The division of E pieces into triangles is unambiguous. For every piece we can therefore decide whether it is aligned with uderlying grid.
Pieces can go 'against the grain' in three different ways.
I use three different colors for these pieces. The boudaries of colored regions must be 'perpendicular'.