Finite cells, transforms and ellipsoids

Structure::finite_cell(tolerance) returns the atoms of one cell plus the periodic images that touch its faces, edges and corners, as a P1 structure. The duplicate check is coordinate-wise, so an atom at 0 and its image at 1 are both kept even though their periodic distance is zero.

xtalforge_core::transforms provides Cartesian helpers:

• translate, rotate, mirror, invert;
• align_vector and align_planes;
• fit_plane, returning Plane { normal, point };
• displacement_ellipsoid(uij, probability), returning Ellipsoid { axes, lengths, probability }.

uij is [U11, U22, U33, U12, U13, U23] in Angstrom squared. Probabilities 0.5, 0.9, 0.95 and 0.99 use the chi-square table for three degrees of freedom; values in between are interpolated.

use xtalforge::core::transforms;

let finite = structure.finite_cell(1e-6)?;
let rotated = transforms::rotate(&points, [0.0, 0.0, 1.0], 90.0, [0.0; 3])?;
let ellipsoid = transforms::displacement_ellipsoid([0.01, 0.02, 0.03, 0.0, 0.0, 0.0], 0.5)?;

These are free functions over points: they do not know about sites or undo. The command layer of Phase 3 wraps them. Anisotropic ellipsoids are also used by the CIF writer and the viewers.