def parse_symmetry(session, group, center=None, axis=None, molecule=None):
# Handle products of symmetry groups.
groups = group.split('*')
from chimerax.geometry import Places
ops = Places()
for g in groups:
ops = ops * group_symmetries(session, g, molecule)
# Apply center and axis transformation.
if center is not None or axis is not None:
from chimerax.geometry import Place, vector_rotation, translation
tf = Place()
if center is not None and tuple(center) != (0, 0, 0):
tf = translation([-c for c in center])
if axis is not None and tuple(axis) != (0, 0, 1):
tf = vector_rotation(axis, (0, 0, 1)) * tf
if not tf.is_identity():
ops = ops.transform_coordinates(tf)
return ops
def unit_cell_and_sym_axes(session, unit_cell):
cell = unit_cell.cell
from chimerax.core.models import Model
from chimerax.geometry import Places, Place
from collections import defaultdict
import numpy
from math import sqrt
from fractions import Fraction
from chimerax.clipper.clipper_python import (Coord_frac, Coord_orth,
RTop_frac, Vec3_double as
Vec3, Symop, Mat33_double as
Mat33)
axis_defs = defaultdict(lambda: list())
m = Model('Unit cell and symmetry', session)
# box_origin_frac = unit_cell.origin.coord_frac(unit_cell.grid)-Coord_frac([1,1,1])
# box_origin_xyz = box_origin_frac.coord_orth(cell).as_numpy()
box_size = unit_cell.grid.dim * 3
syms = unit_cell.symops
#syms = Places(place_array = unit_cell.all_symops_in_box(box_origin_xyz, box_size).all_matrices_orth(unit_cell.cell, '3x4'))
#syms = Places(place_array = unit_cell.symops.all_matrices_orth(unit_cell.cell, '3x4'))
identity = Mat33.identity()
# Need to check all operators covering a 3x3 unit cell block to ensure we
# get them all. Generate all possible length-3 combinations of -1, 0 and 1
u = v = w = numpy.linspace(-1, 1, 3)
frac_offsets = numpy.array(numpy.meshgrid(u, v, w)).T.reshape(-1, 3)
frac_offsets = [Vec3(f) for f in frac_offsets]
rot44 = numpy.identity(4)
for sym_index, s in enumerate(syms):
if s.rot.equals(identity, 1e-6):
# No rotation, therefore no symmetry axis
continue
rot = s.rot
trn = s.trn
ss = Symop(s)
so = ss.rtop_orth(cell)
pr = Place(axes=so.rot.as_numpy().T)
if pr.is_identity(tolerance=1e-5):
continue
central_axis, angle = pr.rotation_axis_and_angle()
central_axis /= numpy.linalg.norm(central_axis)
angle = abs(round(angle))
if angle == 0:
# Pure translation
continue
if angle not in (60, 90, 120, 180):
err_str = (
'This transform has a rotation angle of {} degrees, '
'which is not compatible with crystallographic symmetry. '
'In real crystals, only rotations yielding 2, 3, 4 or 6-fold '
'symmetry are possible.').format(angle)
raise RuntimeError(err_str)
fold_symmetry = 360 // angle
ca_frac = Coord_orth(100 * central_axis).coord_frac(cell).unit()
#screw_component = Coord_orth(so.screw_translation).coord_frac(cell)
# screw_component_orth = numpy.dot(so.trn.as_numpy(), central_axis) * central_axis
# screw_component = Coord_orth(screw_component_orth).coord_frac(cell).lattice_copy_zero()
#screw_component = Coord_frac((Vec3.dot(ss.trn, ca_frac) * ca_frac)).lattice_copy_zero()
#print('Symop: {}, symmetry: {}, fractional_translation: {}, central_axis_orth: {}, central_axis_frac: {}, screw_component_frac: {}'.format(
# sym_index, fold_symmetry, ss.trn.as_numpy(), central_axis, ca_frac, screw_component))
# screw_mag = numpy.linalg.norm(screw_component.as_numpy())
# print('Screw magnitude before normalisation: {}'.format(screw_mag))
# # if screw_mag > 1/12:
# # print('Non-zero screw translation vector: {} along axis: {} for fractional transform number {}: {}'.format(screw_component, central_axis, sym_index, s))
# screw_mag = numpy.linalg.norm([float(Fraction(s).limit_denominator(12)) for s in screw_component.as_numpy()])*sqrt(3) # LCM of possible fractional screw translations 1/(2,3,4 or 6)
# print('Screw magnitude after normalisation: {}'.format(screw_mag))
for offset in frac_offsets:
this_trn = trn + offset
tf = RTop_frac(rot, this_trn).rtop_orth(unit_cell.cell)
trn_orth = tf.trn.as_numpy()
screw_orth = numpy.dot(trn_orth, central_axis) * central_axis
perp_orth = trn_orth - screw_orth
# Remove any whole-unit-cell translation component
screw_frac = Coord_orth(screw_orth).coord_frac(
cell).lattice_copy_zero().as_numpy()
normalised_screw_frac = [
Fraction(s).limit_denominator(12) for s in screw_frac
]
normalised_screw_frac_float = numpy.array(
[float(s) for s in normalised_screw_frac])
screw_mag = numpy.linalg.norm(normalised_screw_frac_float)
rot44[:3, :3] = tf.rot.as_numpy()
rot44[:3, 3] = perp_orth
origin, slope = rotation_axis(rot44)
origin = Coord_orth(origin).coord_frac(cell).as_numpy()
slope = Coord_orth(slope * 100).coord_frac(cell).as_numpy()
axis_defs[(fold_symmetry, screw_mag)].append([origin, slope])
plane_points, plane_normals = unit_cell_planes(unit_cell,
fractional_coords=True,
pad=0.001)
plane_points = numpy.array([pp[0] for pp in plane_points])
for (fold_symmetry, screw_component), axes in axis_defs.items():
uvw0, uvw1 = plane_intersections_in_unit_cell(axes, plane_points,
plane_normals)
if uvw0 is None:
continue
from chimerax.clipper.clipper_python import Coord_frac
axyz0 = numpy.array([
Coord_frac(uvw).coord_orth(unit_cell.cell).as_numpy()
for uvw in uvw0
])
axyz1 = numpy.array([
Coord_frac(uvw).coord_orth(unit_cell.cell).as_numpy()
for uvw in uvw1
])
d = sym_axis_drawing(fold_symmetry, screw_component, axyz0, axyz1)
if d is not None:
m.add_drawing(d)
bd = unit_cell_box_drawing(unit_cell_corners(unit_cell))
m.add_drawing(bd)
return m
