def plane(coords, findBounds=False):
"""Compute a plane given an Nx3 Numpy array.
Returns a Plane whose origin is the centroid of the coords.
If 'findBounds' is True, returns an additional Point (the
furthest point projected into plane) and an additional
floating-point number (distance from origin to that point).
Tip: you generally generate the input Numpy array with
numpyArrayFromAtoms()
"""
import numpy
from numpy.linalg import eig, svd, eigh
centroid = coords.mean(0)
centered = coords - centroid
ignore, vals, vecs = svd(centered)
normal = vecs[numpy.argmin(vals)]
from chimera import Point, Plane, Vector
origin = Point(*centroid)
plane = Plane(origin, Vector(*normal))
if findBounds:
maxSqDist = None
for coord in coords:
projected = plane.nearest(Point(*coord))
sqDist = origin.sqdistance(projected)
if maxSqDist == None or sqDist > maxSqDist:
maxSqDist = sqDist
furthest = projected
from math import sqrt
return plane, projected, sqrt(maxSqDist)
return plane
def pointDistances(self, target):
if isinstance(target, chimera.Point):
points = [target]
else:
points = target
from chimera import cross, Plane
dists = []
minExt = min(self.extents)
maxExt = max(self.extents)
xfCenter = self.xformCenter()
xfDirection = self.xformDirection()
minPt = xfCenter + xfDirection * minExt
maxPt = xfCenter + xfDirection * maxExt
for pt in points:
v = pt - xfCenter
c1 = cross(v, xfDirection)
if c1.length == 0.0:
# colinear
inPlane = pt
else:
plane = Plane(xfCenter, cross(c1, xfDirection))
inPlane = plane.nearest(pt)
ptExt = (inPlane - xfCenter) * xfDirection
if ptExt < minExt:
measurePt = minPt
elif ptExt > maxExt:
measurePt = maxPt
else:
measurePt = inPlane
dists.append(pt.distance(measurePt))
return dists
def plane(coords, findBounds=False): """Compute a plane given an Nx3 Numpy array. Returns a Plane whose origin is the centroid of the coords. If 'findBounds' is True, returns an additional Point (the furthest point projected into plane) and an additional floating-point number (distance from origin to that point). Tip: you generally generate the input Numpy array with numpyArrayFromAtoms() """ import numpy from numpy.linalg import eig, svd, eigh centroid = coords.mean(0) centered = coords - centroid ignore, vals, vecs = svd(centered) normal = vecs[numpy.argmin(vals)] from chimera import Point, Plane, Vector origin = Point(*centroid) plane = Plane(origin, Vector(*normal)) if findBounds: maxSqDist = None for coord in coords: projected = plane.nearest(Point(*coord)) sqDist = origin.sqdistance(projected) if maxSqDist == None or sqDist > maxSqDist: maxSqDist = sqDist furthest = projected from math import sqrt return plane, projected, sqrt(maxSqDist) return plane
def _axisDistance(self, axis, infinite=False):
from chimera import angle, cross, Plane
# shortest distance between lines is perpendicular to both...
sDir = self.xformDirection()
aDir = axis.xformDirection()
if angle(sDir, aDir) in [0.0, 180.0]:
# parallel
return self._axisEndsDist(axis)
shortDir = cross(sDir, aDir)
# can use analytically shortest dist only if each axis
# penetrates the plane formed by the other axis and the
# perpendicular
if not infinite:
for a1, a2 in [(axis, self), (self, axis)]:
normal = cross(a1.xformDirection(), shortDir)
plane = Plane(a1.xformCenter(), normal)
d1 = plane.distance(a2.xformCenter() +
a2.xformDirection() * a2.extents[0])
d2 = plane.distance(a2.xformCenter() +
a2.xformDirection() * a2.extents[1])
if cmp(d1, 0.0) == cmp(d2, 0.0):
# both ends on same side of plane
return self._axisEndsDist(axis)
# D is perpendicular distance to origin
d1 = Plane(self.xformCenter(), shortDir).equation()[3]
d2 = Plane(axis.xformCenter(), shortDir).equation()[3]
return abs(d1 - d2)
def clip_model(m, axis, origin, offset, slab, thickness, flip):
if origin is None:
origin = m.clipPlane.origin.data()
if axis is None:
axis = (-m.clipPlane.normal).data()
if flip:
axis = tuple([-x for x in axis])
if offset != 0:
origin = apply_offset(origin, axis, offset)
from chimera import Plane, Point, Vector
p = Plane()
p.origin = Point(*origin)
p.normal = -Vector(*axis)
m.clipPlane = p
if not slab is None:
m.useClipThickness = slab
if not thickness is None:
m.clipThickness = thickness
m.useClipPlane = True
def tetraPos(bondee,
bonded,
bondLen,
toward=None,
away=None,
toward2=None,
away2=None):
newBonded = []
curBonded = bonded[:]
if len(curBonded) == 0:
pos = singlePos(bondee, bondLen, toward, away)
toward = toward2
away = away2
newBonded.append(pos)
curBonded.append(pos)
if len(curBonded) == 1:
# add at 109.5 degree angle
coplanar = toward or away
if coplanar:
coplanar = [coplanar]
else:
coplanar = None
pos = anglePos(bondee, curBonded[0], bondLen, 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 = bondee - curBonded[0]
old.normalize()
new = pos - bondee
midpoint = bondee + old * new.length * cos705
otherPos = pos + (midpoint - pos) * 2
d1 = (pos - (toward or away)).sqlength()
d2 = (otherPos - (toward or away)).sqlength()
if toward:
if d2 < d1:
pos = otherPos
elif away and d2 > d1:
pos = otherPos
newBonded.append(pos)
curBonded.append(pos)
if len(curBonded) == 2:
# add along anti-bisector of current bonds and raised up
# 54.75 degrees from plane of those bonds (half of 109.5)
v1 = curBonded[0] - bondee
v2 = curBonded[1] - bondee
v1.normalize()
v2.normalize()
antiBi = v1 + v2
antiBi.negate()
antiBi.normalize()
# in order to stabilize the third and fourth tetrahedral
# positions, cross the longer vector by the shorter
if v1.sqlength() > v2.sqlength():
crossV = cross(v1, v2)
else:
crossV = cross(v2, v1)
crossV.normalize()
antiBi = antiBi * cos5475 * bondLen
crossV = crossV * sin5475 * bondLen
pos = bondee + antiBi + crossV
if toward or away:
otherPos = bondee + antiBi - crossV
d1 = (pos - (toward or away)).sqlength()
d2 = (otherPos - (toward or away)).sqlength()
if toward:
if d2 < d1:
pos = otherPos
elif away and d2 > d1:
pos = otherPos
newBonded.append(pos)
curBonded.append(pos)
if len(curBonded) == 3:
unitized = []
for cb in curBonded:
v = cb - bondee
v.normalize()
unitized.append(bondee + v)
pl = Plane(unitized)
norm = 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:
norm.negate()
newBonded.append(bondee + norm * bondLen)
return newBonded
import chimera
from chimera import Plane, Xform, cross, Vector, Point
m = chimera.openModels.list()[0]
b = chimera.selection.currentBonds()[0]
bondVec = b.atoms[0].coord() - b.atoms[1].coord()
bondVec.normalize()
axis = Vector(1.0, 0.0, 0.0)
crossProd = cross(axis, bondVec)
if crossProd.sqlength() > 0:
from math import acos, degrees
xform = Xform.rotation(crossProd, degrees(acos(axis * bondVec)))
xform.invert()
else:
xform = Xform.identity()
m.openState.xform = xform
# okay, that puts the bond parallel to the X axis, now swing the plane of
# the rest of the molecule into the xy plane...
molPlane = Plane([a.xformCoord() for a in m.atoms[:3]])
angle = chimera.angle(molPlane.normal, Vector(0, 0, -1))
xform2 = Xform.rotation(b.atoms[0].xformCoord() - b.atoms[1].xformCoord(),
angle)
xform2.multiply(xform)
m.openState.xform = xform2
def tetraPos(bondee, bonded, bondLen, toward=None, away=None, toward2=None, away2=None): newBonded = [] curBonded = bonded[:] if len(curBonded) == 0: pos = singlePos(bondee, bondLen, toward, away) toward = toward2 away = away2 newBonded.append(pos) curBonded.append(pos) if len(curBonded) == 1: # add at 109.5 degree angle coplanar = toward or away if coplanar: coplanar = [coplanar] else: coplanar = None pos = anglePos(bondee, curBonded[0], bondLen, 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 = bondee - curBonded[0] old.normalize() new = pos - bondee midpoint = bondee + old * new.length * cos705 otherPos = pos + (midpoint - pos) * 2 d1 = (pos - (toward or away)).sqlength() d2 = (otherPos - (toward or away)).sqlength() if toward: if d2 < d1: pos = otherPos elif away and d2 > d1: pos = otherPos newBonded.append(pos) curBonded.append(pos) if len(curBonded) == 2: # add along anti-bisector of current bonds and raised up # 54.75 degrees from plane of those bonds (half of 109.5) v1 = curBonded[0] - bondee v2 = curBonded[1] - bondee v1.normalize() v2.normalize() antiBi = v1 + v2 antiBi.negate() antiBi.normalize() # in order to stabilize the third and fourth tetrahedral # positions, cross the longer vector by the shorter if v1.sqlength() > v2.sqlength(): crossV = cross(v1, v2) else: crossV = cross(v2, v1) crossV.normalize() antiBi = antiBi * cos5475 * bondLen crossV = crossV * sin5475 * bondLen pos = bondee + antiBi + crossV if toward or away: otherPos = bondee + antiBi - crossV d1 = (pos - (toward or away)).sqlength() d2 = (otherPos - (toward or away)).sqlength() if toward: if d2 < d1: pos = otherPos elif away and d2 > d1: pos = otherPos newBonded.append(pos) curBonded.append(pos) if len(curBonded) == 3: unitized = [] for cb in curBonded: v = cb - bondee v.normalize() unitized.append(bondee + v) pl = Plane(unitized) norm = 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: norm.negate() newBonded.append(bondee + norm * bondLen) return newBonded