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| | {{Infobox psico |
| | |module = psico.xtal |
| | }} |
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| [[File:SupercellExample.png|200px|thumb|right|Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19]] | | [[File:SupercellExample.png|200px|thumb|right|Example with 2 unit cells in c-direction, created with: supercell 1,1,2,2x19]] |
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| <source lang="python"> | | <source lang="python"> |
| run supercell.py | | # import psico.xtal, or run the standalone script: |
| | run https://raw.githubusercontent.com/speleo3/pymol-psico/master/psico/xtal.py |
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| fetch 2x19, async=0 | | fetch 2x19, async=0 |
| supercell 2,1,1, 2x19, green | | supercell 2,1,1, 2x19, green |
| supercell 1,1,2, 2x19, orange, name=super2 | | supercell 1,1,2, 2x19, orange, name=super2 |
| </source>
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|
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| == The Code ==
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|
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| <source lang="python">
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| '''
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| (c) 2010 Thomas Holder
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|
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| PyMOL python script (load with `run supercell.py`)
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| Usage: See "help supercell" and "help symexpcell"
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| '''
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| from pymol import cmd, cgo, xray
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| from math import cos, sin, radians, sqrt
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| import numpy
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|
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| def cellbasis(angles, edges):
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| '''
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| For the unit cell with given angles and edge lengths calculate the basis
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| transformation (vectors) as a 4x4 numpy.array
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| '''
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| rad = [radians(i) for i in angles]
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| basis = numpy.identity(4)
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| basis[0][1] = cos(rad[2])
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| basis[1][1] = sin(rad[2])
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| basis[0][2] = cos(rad[1])
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| basis[1][2] = (cos(rad[0]) - basis[0][1]*basis[0][2])/basis[1][1]
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| basis[2][2] = sqrt(1 - basis[0][2]**2 - basis[1][2]**2)
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| edges.append(1.0)
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| return basis * edges # numpy.array multiplication!
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|
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| def supercell(a=1, b=1, c=1, object=None, color='blue', name='supercell', withmates=1):
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| '''
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| DESCRIPTION
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|
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| Draw a supercell, as requested by Nicolas Bock on the pymol-users
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| mailing list (Subject: [PyMOL] feature request: supercell construction
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| Date: 04/12/2010 10:12:17 PM (Mon, 12 Apr 2010 14:12:17 -0600))
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|
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| USAGE
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|
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| supercell a, b, c [, object [, color [, name [, withmates]]]]
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|
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| ARGUMENTS
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|
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| a, b, c = integer: repeat cell in x,y,z direction a,b,c times
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| {default: 1,1,1}
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|
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| object = string: name of object to take cell definition from
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|
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| color = string: color of cell {default: blue}
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|
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| name = string: name of the cgo object to create {default: supercell}
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|
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| withmates = bool: also create symmetry mates in displayed cells
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| {default: 1}
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|
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| SEE ALSO
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|
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| show cell
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|
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| '''
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| if object is None:
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| object = cmd.get_object_list()[0]
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| withmates = int(withmates)
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|
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| sym = cmd.get_symmetry(object)
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| cell_edges = sym[0:3]
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| cell_angles = sym[3:6]
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|
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| basis = cellbasis(cell_angles, cell_edges)
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| assert isinstance(basis, numpy.ndarray)
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|
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| ts = list()
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| for i in range(int(a)):
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| for j in range(int(b)):
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| for k in range(int(c)):
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| ts.append([i,j,k])
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|
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| obj = [
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| cgo.BEGIN,
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| cgo.LINES,
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| cgo.COLOR,
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| ]
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| obj.extend(cmd.get_color_tuple(color))
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|
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| for t in ts:
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| shift = basis[0:3,0:3] * t
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| shift = shift[:,0] + shift[:,1] + shift[:,2]
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|
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| for i in range(3):
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| vi = basis[0:3,i]
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| vj = [
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| numpy.array([0.,0.,0.]),
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| basis[0:3,(i+1)%3],
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| basis[0:3,(i+2)%3],
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| basis[0:3,(i+1)%3] + basis[0:3,(i+2)%3]
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| ]
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| for j in range(4):
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| obj.append(cgo.VERTEX)
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| obj.extend((shift + vj[j]).tolist())
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| obj.append(cgo.VERTEX)
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| obj.extend((shift + vj[j] + vi).tolist())
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|
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| if withmates:
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| symexpcell('m%d%d%d_' % tuple(t), object, *t)
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|
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| obj.append(cgo.END)
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|
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| cmd.delete(name)
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| cmd.load_cgo(obj, name)
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|
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| def symexpcell(prefix='mate', object=None, a=0, b=0, c=0):
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| '''
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| DESCRIPTION
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|
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| Creates all symmetry-related objects for the specified object that
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| occur with their bounding box center within the unit cell.
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|
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| USAGE
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| symexpcell prefix, object, [a, b, c]
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|
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| ARGUMENTS
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| prefix = string: prefix of new objects
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| object = string: object for which to create symmetry mates
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| a, b, c = integer: create neighboring cell {default: 0,0,0}
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|
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| SEE ALSO
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|
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| symexp, http://www.pymolwiki.org/index.php/SuperSym
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| '''
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| if object is None:
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| object = cmd.get_object_list()[0]
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|
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| sym = cmd.get_symmetry(object)
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| cell_edges = sym[0:3]
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| cell_angles = sym[3:6]
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| spacegroup = sym[6]
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|
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| basis = cellbasis(cell_angles, cell_edges)
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| basis = numpy.matrix(basis)
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|
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| extent = cmd.get_extent(object)
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| center = sum(numpy.array(extent)) * 0.5
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| center = numpy.matrix(center.tolist() + [1.0]).T
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| center_cell = basis.I * center
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|
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| extra_shift = [[float(i)] for i in (a,b,c)]
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|
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| i = 0
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| matrices = xray.sg_sym_to_mat_list(spacegroup)
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| for mat in matrices:
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| i += 1
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|
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| mat = numpy.matrix(mat)
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| shift = numpy.floor(mat * center_cell)
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| mat[0:3,3] -= shift[0:3,0]
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| mat[0:3,3] += extra_shift
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|
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| mat = basis * mat * basis.I
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| mat_list = list(mat.flat)
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|
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| name = '%s%d' % (prefix, i)
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| cmd.create(name, object)
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| cmd.transform_object(name, mat_list)
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| cmd.color(i+1, name)
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|
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| cmd.extend('symexpcell', symexpcell)
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| cmd.extend('supercell', supercell)
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|
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| # tab-completion of arguments
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| cmd.auto_arg[3]['supercell'] = [ cmd.object_sc, 'object', '']
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| </source> | | </source> |
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