def transformation_and_inverse(origin, step, axes):
ox, oy, oz = origin
d0, d1, d2 = step
ax, ay, az = axes
from chimerax.geometry import Place
tf = Place(((d0 * ax[0], d1 * ay[0], d2 * az[0],
ox), (d0 * ax[1], d1 * ay[1], d2 * az[1], oy),
(d0 * ax[2], d1 * ay[2], d2 * az[2], oz)))
tf_inv = tf.inverse()
return tf, tf_inv
def ses_surface_geometry(xyz,
radii,
probe_radius=1.4,
grid_spacing=0.5,
sas=False):
'''
Calculate a solvent excluded molecular surface using a distance grid
contouring method. Vertex, normal and triangle arrays are returned.
If sas is true then the solvent accessible surface is returned instead.
'''
# Compute bounding box for atoms
xyz_min, xyz_max = xyz.min(axis=0), xyz.max(axis=0)
pad = 2 * probe_radius + radii.max() + grid_spacing
origin = [x - pad for x in xyz_min]
# Create 3d grid for computing distance map
from math import ceil
s = grid_spacing
shape = [
int(ceil((xyz_max[a] - xyz_min[a] + 2 * pad) / s)) for a in (2, 1, 0)
]
# print('ses surface grid size', shape, 'spheres', len(xyz))
from numpy import empty, float32, sqrt
try:
matrix = empty(shape, float32)
except (MemoryError, ValueError):
raise MemoryError(
'Surface calculation out of memory trying to allocate a grid %d x %d x %d '
% (shape[2], shape[1], shape[0]) +
'to cover xyz bounds %.3g,%.3g,%.3g ' % tuple(xyz_min) +
'to %.3g,%.3g,%.3g ' % tuple(xyz_max) +
'with grid size %.3g' % grid_spacing)
max_index_range = 2
matrix[:, :, :] = max_index_range
# Transform centers and radii to grid index coordinates
from chimerax.geometry import Place
xyz_to_ijk_tf = Place(
((1.0 / s, 0, 0, -origin[0] / s), (0, 1.0 / s, 0, -origin[1] / s),
(0, 0, 1.0 / s, -origin[2] / s)))
from numpy import float32
ijk = xyz.astype(float32)
xyz_to_ijk_tf.transform_points(ijk, in_place=True)
ri = radii.astype(float32)
ri += probe_radius
ri /= s
# Compute distance map from surface of spheres, positive outside.
from chimerax.map import sphere_surface_distance
sphere_surface_distance(ijk, ri, max_index_range, matrix)
# Get the SAS surface as a contour surface of the distance map
from chimerax.map import contour_surface
level = 0
sas_va, sas_ta, sas_na = contour_surface(matrix,
level,
cap_faces=False,
calculate_normals=True)
if sas:
xyz_to_ijk_tf.inverse().transform_points(sas_va, in_place=True)
return sas_va, sas_na, sas_ta
# Compute SES surface distance map using SAS surface vertex
# points as probe sphere centers.
matrix[:, :, :] = max_index_range
rp = empty((len(sas_va), ), float32)
rp[:] = float(probe_radius) / s
sphere_surface_distance(sas_va, rp, max_index_range, matrix)
ses_va, ses_ta, ses_na = contour_surface(matrix,
level,
cap_faces=False,
calculate_normals=True)
# Transform surface from grid index coordinates to atom coordinates
xyz_to_ijk_tf.inverse().transform_points(ses_va, in_place=True)
# Delete connected components more than 1.5 probe radius from atom spheres.
kvi = []
kti = []
from ._surface import connected_pieces
vtilist = connected_pieces(ses_ta)
for vi, ti in vtilist:
v0 = ses_va[vi[0], :]
d = xyz - v0
d2 = (d * d).sum(axis=1)
adist = (sqrt(d2) - radii).min()
if adist < 1.5 * probe_radius:
kvi.append(vi)
kti.append(ti)
from .split import reduce_geometry
from numpy import concatenate
keepv = concatenate(kvi) if kvi else []
keept = concatenate(kti) if kti else []
va, na, ta = reduce_geometry(ses_va, ses_na, ses_ta, keepv, keept)
return va, na, ta
for b in standard_bases.values():
pts = [b["atoms"][n] for n in b["ring atom names"][0:2]]
y_axis = pts[0] - pts[1]
# insure that y_axis is perpendicular to z_axis
# (should be zero already)
y_axis[2] = 0.0
normalize_vector(y_axis)
x_axis = numpy.cross(y_axis, z_axis)
xf = Place(matrix=((x_axis[0], y_axis[0], z_axis[0],
0.0), (x_axis[1], y_axis[1], z_axis[1], 0.0),
(x_axis[2], y_axis[2], z_axis[2], 0.0))
# TODO: orthogonalize=True
)
# axis, angle = xf.getRotation()
# print("axis = %s, angle = %s" % (axis, angle))
b["correction factor"] = xf.inverse()
del b, pts, x_axis, y_axis, z_axis, xf
system_dimensions = {
# predefined dimensions in local coordinate frame
# note: (0, 0) corresponds to position of C1'
'small': {
ANCHOR: BASE,
PURINE: ((0.0, -4.0), (2.1, 0.0)),
PYRIMIDINE: ((0.0, -2.1), (2.1, 0.0)),
PSEUDO_PYRIMIDINE: ((0.0, -2.1), (2.1, 0.0)),
},
'long': {
ANCHOR: BASE,
PURINE: ((0.0, -5.0), (2.1, 0.0)),
PYRIMIDINE: ((0.0, -3.5), (2.1, 0.0)),
