def interpolate_corkscrew(xf, c0, c1, minimum_rotation = 0.1):
'''
Rotate and move along a circular arc perpendicular to the rotation axis and
translate parallel the rotation axis. This makes the initial geometric center c0
traverse a helical path to the final center c1. The circular arc spans an angle
equal to the rotation angle so it is nearly a straight segment for small angles,
and for the largest possible rotation angle of 180 degrees it is a half circle
centered half-way between c0 and c1 in the plane perpendicular to the rotation axis.
Rotations less than the minimum (degrees) are treated as no rotation.
'''
from chimerax.geometry import normalize_vector
dc = c1 - c0
axis, angle = xf.rotation_axis_and_angle() # a is in degrees.
if abs(angle) < minimum_rotation:
# Use linear instead of corkscrew interpolation to
# avoid numerical precision problems at small rotation angles.
# ChimeraX bug #2928.
center = c0
shift = dc
else:
from chimerax.geometry import inner_product, cross_product, norm
tra = inner_product(dc, axis) # Magnitude of translation along rotation axis.
shift = tra*axis
vt = dc - tra * axis # Translation perpendicular to rotation axis.
v0 = cross_product(axis, vt)
if norm(v0) == 0 or angle == 0:
center = c0
else:
import math
l = 0.5*norm(vt) / math.tan(math.radians(angle / 2))
center = c0 + 0.5*vt + l*normalize_vector(v0)
return axis, angle, center, shift
def curve_segment_end(curve, t, length, tolerance=1e-3, max_steps=100):
'''
Compute a point on the curve beyond curve parameter value t which is
a distance length from the point at position t. Can return None if
convergence fails. This iteratively takes linear steps based on the
curve velocity vector to find the desired end point.
'''
if length == 0:
return t
xyz0 = curve.position(t)
v = curve.velocity(t)
frac = 0.5
from chimerax.geometry import norm, inner_product
t1 = t + frac * length / norm(v)
for step in range(max_steps):
xyz1 = curve.position(t1)
d = norm(xyz1 - xyz0)
if abs(d - length) < tolerance * length:
return t1
v1 = curve.velocity(t1)
# Want |xyz1 + v1*dt - xyz0| = length
delta = xyz1 - xyz0
a, b, c = (inner_product(v1, v1), 2 * inner_product(v1, delta),
inner_product(delta, delta) - length * length)
dt1, dt2 = quadratic_roots(a, b, c)
if dt1 is None:
# No point in tangent line is within target length.
# Go to closest approach
dt1 = dt2 = -b / 2 * a
dt_min = dt1 if abs(dt1) < abs(dt2) else dt2
t1 += frac * dt_min
return None
def rotation_step(points,
point_weights,
center,
data_array,
xyz_to_ijk_transform,
ijk_step_size,
metric,
syminv=[],
values=None,
gradients=None):
axis = torque_axis(points,
point_weights,
center,
data_array,
xyz_to_ijk_transform,
metric,
syminv=syminv,
values=values,
gradients=gradients)
from chimerax.geometry import norm, place
na = norm(axis)
if len(points) == 1 or na == 0:
axis = (0, 0, 1)
angle = 0
else:
axis /= na
angle = angle_step(axis, points, center, xyz_to_ijk_transform,
ijk_step_size)
move_tf = place.rotation(axis, angle, center)
return move_tf
def translation_step(points,
point_weights,
center,
data_array,
xyz_to_ijk_transform,
ijk_step_size,
metric,
syminv=[],
values=None,
gradients=None):
g = gradient_direction(points,
point_weights,
data_array,
xyz_to_ijk_transform,
metric,
syminv=syminv,
values=values,
gradients=gradients)
from numpy import array, float, dot as matrix_multiply
gijk = matrix_multiply(xyz_to_ijk_transform.matrix[:, :3], g)
from chimerax.geometry import norm, place
n = norm(gijk)
if n > 0:
delta = g * (ijk_step_size / n)
else:
delta = array((0, 0, 0), float)
delta_tf = place.translation(delta)
return delta_tf
def angle_pos(atom_pos, bond_pos, bond_length, degrees, coplanar=None):
if coplanar is not None and len(coplanar) > 0:
# may have one or two coplanar positions specified,
# if two, compute both resultant positions and average
# (the up vector has to be negated for the second one)
xforms = []
if len(coplanar) > 2:
raise ValueError("More than 2 coplanar positions specified!")
for cpos in coplanar:
up = cpos - atom_pos
if xforms:
up = tinyarray.negative(up)
# lookAt puts ref point opposite that of zAlign, so
# also rotate 180 degrees around y axis
xform = rotation(
(0.0, 1.0, 0.0), 180.0) * look_at(atom_pos, bond_pos, up)
xforms.append(xform)
else:
xforms = [z_align(atom_pos, bond_pos)]
points = []
for xform in xforms:
radians = pi * degrees / 180.0
angle = tinyarray.array(
[0.0, bond_length * sin(radians), bond_length * cos(radians)])
points.append(xform.inverse() * angle)
if len(points) > 1:
midpoint = points[0] + (points[1] - points[0]) / 2.0
v = midpoint - atom_pos
v = v * bond_length / norm(v)
return atom_pos + v
return tinyarray.array(points[0])
def mouse_drag(self, event):
v = self._map
if v is None or self._xy_last is None:
self.mouse_down(event)
return
xl, yl = self._xy_last
x, y = event.position()
dx, dy = (x - xl, yl - y)
if dx == 0 and dy == 0:
return
camera = self.session.main_view.camera
if event.shift_down():
# Translate slab
ro = v.rendering_options
spacing = ro.tilted_slab_spacing
slab_normal = v.scene_position.transform_vector(
ro.tilted_slab_axis)
move_dir = camera.position.transform_vector((dx, dy, 0))
from chimerax.geometry import inner_product, norm
sign = 1 if inner_product(move_dir, slab_normal) > 0 else -1
dist = sign * norm(move_dir) * spacing
self._move_slab(dist)
else:
# Rotate slab
from math import sqrt
dn = sqrt(dx * dx + dy * dy)
rangle = dn
raxis = camera.position.transform_vector((-dy / dn, dx / dn, 0))
self._rotate_slab(raxis, rangle)
self._xy_last = (x, y)
def _line_orientation(from_point, to_point, axis, height):
if from_point is None and to_point is None and axis is None:
return None
c,h,r = None, height, None
from chimerax.core.commands import Axis, Center
if isinstance(axis, Axis):
axis = axis.scene_coordinates()
if isinstance(from_point, Center):
from_point = from_point.scene_coordinates()
if isinstance(to_point, Center):
to_point = to_point.scene_coordinates()
from chimerax.geometry import vector_rotation, norm
if axis is not None:
r = vector_rotation((0,0,1), axis)
else:
from numpy import array, float32
axis = array((0,0,1), float32)
if from_point is not None and to_point is not None:
c = 0.5 * (from_point + to_point)
v = to_point - from_point
r = vector_rotation((0,0,1), v)
h = norm(v)
elif from_point is not None and to_point is None:
c = from_point + 0.5*height*axis
elif from_point is None and to_point is not None:
c = to_point - 0.5*height*axis
return h, c, r
def buried_sphere_area(i, centers, radii, draw=False):
if draw:
surf0 = sphere_model([i], centers, radii)
from chimerax.geometry import norm
jlist = [
j for j in range(len(centers))
if j != i and norm(centers[j] - centers[i]) < radii[j] + radii[i]
]
# jlist = list(range(i)) + list(range(i+1,len(centers)))
print(len(jlist), 'spheres intersect sphere', i)
surfn = sphere_model(jlist, centers, radii)
for p in surfn.child_drawings():
p.color = (.7, .7, .9, .7)
draw.add_models((surf0, surfn))
r = radii[i]
# Check if sphere is completely contained in another sphere
if sphere_in_another_sphere(i, centers, radii):
area = 4 * pi * r * r
return area
# Compute sphere intersections
circles = sphere_intersection_circles(i, centers, radii)
# Compute analytical buried area on sphere.
area = area_in_circles_on_unit_sphere(circles, draw, centers[i], r) * r * r
return area
def random_direction():
z = (1,1,1)
from chimerax.geometry import norm, normalize_vector
from random import random
while norm(z) > 1:
z = (1-2*random(), 1-2*random(), 1-2*random())
return normalize_vector(z)
def line_position(xyz, line):
xyz1, xyz2 = line
dxyz = xyz - xyz1
xyz12 = xyz2 - xyz1
from chimerax.geometry import norm, inner_product
d2 = norm(xyz12)
f = inner_product(dxyz, xyz12) / d2
return f
def _center_point_matching_depth(self, point):
cam_pos = self.camera.position.origin()
vd = self.camera.view_direction()
hyp = point - cam_pos
from chimerax.geometry import inner_product, norm
distance = inner_product(hyp, vd)
cr = cam_pos + distance * vd
old_cofr = self._center_of_rotation
if norm(cr - old_cofr) < 1e-6 * distance:
# Avoid jitter if camera has not moved
cr = old_cofr
return cr
def cut_distances(va, nc=4):
from chimerax.geometry import norm
cuts = []
cut = [0] * nc
n = len(va) // (4 * nc)
for s in range(n - 1):
for c in range(nc):
e = va[c * n:] if s % 2 == 0 else va[((c + nc // 2) % nc) * n:]
cut[c] += norm(e[s + 1] - e[s])
cuts.append(tuple(cut))
return cuts
def tetra_pos(bondee,
bonded,
bond_len,
toward=None,
away=None,
toward2=None,
away2=None):
new_bonded = []
cur_bonded = bonded[:]
if len(cur_bonded) == 0:
pos = single_pos(bondee, bond_len, toward, away)
toward = toward2
away = away2
new_bonded.append(pos)
cur_bonded.append(pos)
if len(cur_bonded) == 1:
# add at 109.5 degree angle
coplanar = toward or away
if coplanar:
coplanar = [coplanar]
else:
coplanar = None
pos = angle_pos(bondee,
cur_bonded[0],
bond_len,
109.5,
coplanar=coplanar)
if toward or away:
# find the other 109.5 position in the toward/away
# plane and the closer/farther position as appropriate
old = normalize(bondee - cur_bonded[0])
new = pos - bondee
midpoint = tinyarray.array(bondee + old * norm(new) * cos705)
other_pos = pos + (midpoint - pos) * 2
d1 = sqlength(pos - (toward or away))
d2 = sqlength(other_pos - (toward or away))
if toward is not None:
if d2 < d1:
pos = other_pos
elif away is not None and d2 > d1:
pos = other_pos
new_bonded.append(pos)
cur_bonded.append(pos)
if len(cur_bonded) == 2:
# add along anti-bisector of current bonds and raised up
# 54.75 degrees from plane of those bonds (half of 109.5)
v1 = normalize(cur_bonded[0] - bondee)
v2 = normalize(cur_bonded[1] - bondee)
anti_bi = normalize(tinyarray.negative(v1 + v2))
# in order to stabilize the third and fourth tetrahedral
# positions, cross the longer vector by the shorter
if sqlength(v1) > sqlength(v2):
cross_v = normalize(cross_product(v1, v2))
else:
cross_v = normalize(cross_product(v2, v1))
anti_bi = anti_bi * cos5475 * bond_len
cross_v = cross_v * sin5475 * bond_len
pos = bondee + anti_bi + cross_v
if toward or away:
other_pos = bondee + anti_bi - cross_v
d1 = sqlength(pos - (toward or away))
d2 = sqlength(other_pos - (toward or away))
if toward is not None:
if d2 < d1:
pos = other_pos
elif away is not None and d2 > d1:
pos = other_pos
new_bonded.append(pos)
cur_bonded.append(pos)
if len(cur_bonded) == 3:
unitized = []
for cb in cur_bonded:
v = normalize(cb - bondee)
unitized.append(bondee + v)
pl = Plane(unitized)
normal = pl.normal
# if normal on other side of plane from bondee, we need to
# invert the normal; the (signed) distance from bondee
# to the plane indicates if it is on the same side
# (positive == same side)
d = pl.distance(bondee)
if d < 0.0:
normal = tinyarray.negative(normal)
new_bonded.append(bondee + normal * bond_len)
return new_bonded
def layout(self, params, circuit_segments):
p = params
from chimerax.geometry import translation, rotation, Place, vector_rotation, norm
from math import pi, cos, sin
# Compute helix axis direction.
# The helix rotation axis is does not make a 90 degree angle with
# the P-P basepair line. It makes an angle of approximately 110 degrees.
pa = p.pair_tilt * pi / 180
from numpy import array
axis = array((cos(pa), sin(pa), 0))
# Compute screw motion that advances basepair along helix.
# Initial basepair P-P is spans (0,0,0) to (pair_width,0,0).
rtf = rotation(axis,
p.stem_twist,
center=(0.5 * p.pair_width, 0, -p.pair_off_axis))
ttf = translation(p.pair_spacing * axis)
stf = ttf * rtf
# Specify initial orientations of basepair nucleotides
# so P-atoms are on helix and paired P atom is in the
# oriented xy plane.
p0, p1 = (0, 0, 0), (p.pair_width, 0, 0)
tf1 = self.stem_residue_orientation(p0, stf * p0, p1)
p2 = stf.inverse() * p1
tf2 = self.stem_residue_orientation(p1, p2, p0)
# Keep track of basepair P-P orientation used to
# orient the loop at the end of the stem.
ctf = Place()
# Layout nucleotides for both strands of double helix.
coords = {}
for i in range(self.length):
coords[self.base5p + i] = tf1
coords[self.base3p - i] = tf2
tf1 = stf * tf1
tf2 = stf * tf2
ctf = stf * ctf
# The next segment after the stem should put its first
# P-atom at a position on the helix so that the last
# nucleotide of the stem has the right orientation to
# make a base pair. To achieve this the initial basepair
# P-P does not lie on the x-axis. Instead we tilt the
# entire helix so the paired P is advanced up the helix
# by one position.
width = norm(p2)
ttf = vector_rotation(p2, p1)
for b, tf in coords.items():
coords[b] = ttf * coords[b]
# Added circuit at end of stem.
ccoords = self.circuit.layout(p, gap=width)
# Position the end circuit using the P-P orientation at
# the end of the stem and taking account of the tilt of
# the entire helix.
ctf = ttf * ctf * ttf.inverse()
for b, tf in ccoords.items():
coords[b] = ctf * tf
# Use segment width for the tilted helix.
seg = [Segment(coords, width, 0)]
return seg
def tile(session,
models=None,
columns=None,
spacing_factor=1.3,
view_all=True):
"""Tile models onto a square(ish) grid."""
# Keep only models that we think might work
# Surfaces are excluded on the assumption that they will move
# with their associated models
from chimerax.atomic import Structure
from chimerax.map.volume import Volume
tilable_classes = [Structure, Volume]
def tilable(m):
for klass in tilable_classes:
if isinstance(m, klass):
return True
return False
if models is None:
models = [m for m in session.models.list() if tilable(m)]
models = [m for m in models if tilable(m) and m.bounds() is not None]
if len(models) == 0:
from chimerax.core.errors import UserError
raise UserError("No models found for tiling.")
# Size each tile to the maximum size (+buffer) among all models
spacing = max([m.bounds().radius() for m in models]) * spacing_factor
# First model is the anchor
anchor = models[0].bounds().center()
anchor_spec = '#' + models[0].id_string
from .view import UndoView
undo = UndoView("tile", session, models)
with session.undo.block():
# Simultaneously ove model toward anchor in scene coordinate system
# and toward final target position in screen coordinate system
import math, numpy
from chimerax.geometry import norm
if columns is None:
columns = int(round(math.sqrt(len(models))))
commands = []
for i, m in enumerate(models[1:], start=1):
center = m.bounds().center()
# First move in scene coordinates to superimpose model onto anchor
view_delta = anchor - center
view_dist = norm(view_delta)
if view_dist > 0:
commands.append("move %.2f,%.2f,%.2f %.2f coord %s models %s" %
(view_delta[0], view_delta[1], view_delta[2],
view_dist, anchor_spec, m.atomspec))
# Then move in screen coordinates to final grid position
row, col = divmod(i, columns)
screen_delta = numpy.array([col * spacing, -row * spacing, 0],
dtype=numpy.float32)
screen_dist = norm(screen_delta)
if screen_dist > 0:
commands.append("move %.2f,%.2f,%.2f %.2f models %s" %
(screen_delta[0], screen_delta[1],
screen_delta[2], screen_dist, m.atomspec))
# Make everything visible on screen
if view_all:
commands.append("view")
from chimerax.core.commands import run
run(session, "; ".join(commands), log=False)
undo.finish(session, models)
session.undo.register(undo)
session.logger.info("%d model%s tiled" %
(len(models), "s" if len(models) != 1 else ""))