def test_P23_TC3(cell=200, **kwargs):
# delete all; run ~/pymol/symgen.py; test_P23_TD2B( depth=2, cell=200,
# symdef_scale=0.000001, generic_names=1 )
G = [SymElem("C3", cen=cell * Vec(0.0, 0.0, 0.0)),
SymElem("T", cen=cell * Vec(0.5, 0.5, 0.5)), ]
test_xtal(G, cell, tag="P23_TC3", **kwargs)
cube(cell * Vec(0, 0, 0), cell * Vec(1, 1, 1))
def test_P23_TD2A(cell=200,**kwargs): # delete all; run ~/pymol/symgen.py; test_P23_TD2B( depth=2, cell=200, symdef_scale=0.000001, generic_names=1 ) G = [ SymElem( "D2", cen=cell*Vec(0.0,0.0,0.0) ), SymElem( "T" , cen=cell*Vec(0.0,0.0,0.5) ), ] component_pos=[ Vec(-8,-7,6), Vec(-7,0,-11), ] test_xtal(G,cell,component_pos=component_pos,tag="P23_TD2A",**kwargs) cube( cell*Vec(0,0,-0.5), cell*Vec(1,1,0.5) )
def test_I213(depth=16, cell=100, maxrad=9e9):
# C3 and C2 at angle = 54.7356 offset = 0.176777
# C3 axis=[-0.57735,0.57735,0.57735] origin=[-0.166667,0.166667,-0.333333]
# C2 axis=[1,0,0] origin=[0,0.5,0.25]
# AXS = [ Vec(-1,1,1),
# Vec( 1,0,0) ]
# CEN = [ cell * Vec(-1,1,-2)/6.0 ,
# cell * Vec(0,0.5,0.25) ]
AXS = [Vec(1, 1, 1),
Vec(1, 0, 0)]
CEN = [cell * Vec(0, 0, 0),
cell * Vec(0, 0, 0.25)]
G = [
SymElem("C3", axis=AXS[0], cen=CEN[0]),
SymElem("C2", axis=AXS[1], cen=CEN[1])
]
symtrie = generate_sym_trie(G, depth=depth)
# buildcgo = BuildCGO( nodes=[ CEN1+Vec(2,3,4), CEN2+Vec(2,4,3), ] )
nodes = [
CEN[0] + projperp(AXS[0], randnorm()) * 8.0,
CEN[1] + projperp(AXS[1], randnorm()) * 8.0
]
buildcgo = BuildCGO(nodes=nodes, maxrad=maxrad,
origin=cell * Vec(0.5, 0.5, 0.5), showlinks=True)
symtrie.visit(buildcgo)
buildcgo.show()
cube(Vec(0, 0, 0), cell * Vec(1, 1, 1))
for g in G:
print "show", g
g.show(radius=2.0, sphereradius=4.0)
return AXS, CEN
def test_I4132(cell=100, **kwargs):
# delete all; test_I4132(depth=7,shownodes=0,cell=200,maxrad=180); run /Users/sheffler/pymol/misc/G222.py; gyroid(200,r=180)
# delete all; run /Users/sheffler/pymol/symgen.py; test_I4132( cell=150,
# depth=7, shownodes=0, maxrad=150 ); gyroid(150,r=150,c=Vec(75,75,75))
r = random.random
G = [
SymElem("D3", cen=cell * Vec(0.625, 0.625, 0.625),
axis=Vec(1, 1, 1), axis2=Vec(1, -1, 0), col=(0, 1, 0)),
SymElem("D2", cen=cell * Vec(0.625, 0.500, 0.750),
axis=Vec(1, 0, 0), axis2=Vec(0, -1, 1), col=(0, 1, 1)),
SymElem("D3", cen=cell * Vec(0.375, 0.375, 0.375),
axis=Vec(1, 1, 1), axis2=Vec(1, -1, 0), col=(1, 0, 0)),
SymElem("D2", cen=cell * Vec(0.375, 0.500, 0.250),
axis=Vec(1, 0, 0), axis2=Vec(0, -1, 1), col=(1, 1, 0)),
# SymElem( "C3", axis=Vec(1,1,1) ),
# SymElem( "C2", axis=Vec(1,1,0), cen=cell*Vec(-1, 1, 1)/8.0 ),
# SymElem( "C2", axis=Vec(1,1,0), cen=cell*Vec( 1,-1,-1)/8.0 ),
# SymElem( "C2", axis=Vec(1,1,0), cen=cell*Vec( 1,-1,-1)/8.0, col=(1,1,0) ),
# SymElem( "D3", cen=cell*Vec(0.125,0.125,0.125), axis=Vec(1,1,1), axis2=Vec(1,-1,0), col=(0,1,0) ),
# SymElem( "D2", cen=cell*Vec(0.125,0.000,0.250), axis=Vec(1,0,0), axis2=Vec(0,-1,1), col=(0,1,1) ),
# SymElem( "D3", cen=cell*Vec(-0.125,-0.125,-0.125), axis=Vec(1,1,1), axis2=Vec(1,-1,0), col=(1,0,0) ),
# SymElem( "D2", cen=cell*Vec(-0.125,0.000,-0.250), axis=Vec(1,0,0), axis2=Vec(0,-1,1), col=(1,1,0) ),
]
component_pos = [Vec(-8, -7, 6), Vec(-7, 0, -11), ]
test_xtal(G, cell, component_pos=component_pos, tag="I4132",
origin=cell * Vec(0.5, 0.5, 0.5), showshape=0, **kwargs)
# cube( cell*Vec(-0.5,-0.5,-0.5), cell*Vec(0.5,0.5,0.5) )
cube(cell * Vec(-0, -0, -0), cell * Vec(1, 1, 1))
def test_F432(depth=6, cell=100, maxrad=90):
# C3 and D2 at angle = 35.2644 offset = 0
# C3 axis=[0.57735,0.57735,0.57735] origin=[0,0,0]
# D2 axis=[1,0,0] axis2=[0,-0.707107,0.707107] origin=[0,0.25,0.25]
AXS = [Vec(1, 1, 1),
Vec(1, 0, 0)]
CEN = [cell * Vec(0, 0, 0),
cell * Vec(0, 0.25, 0.25)]
G = [
SymElem("C2", axis=Vec(1, 1, 0), cen=Vec(0, 0, 0)),
SymElem("C3", axis=AXS[0], cen=CEN[0]),
SymElem("C4", axis=Vec(1, 0, 0), cen=Vec(0, 0, 0)),
SymElem("D2", axis=AXS[1], axis2=Vec(0, -1, 1), cen=CEN[1])
]
symtrie = generate_sym_trie(G, depth=depth)
# buildcgo = BuildCGO( nodes=[ CEN1+Vec(2,3,4), CEN2+Vec(2,4,3), ] )
nodes = [
CEN[0] + projperp(AXS[0], randnorm()) * 8.0,
CEN[1] + projperp(AXS[1], randnorm()) * 8.0
]
buildcgo = BuildCGO(nodes=nodes, maxrad=maxrad,
origin=cell * Vec(0.5, 0.5, 0.5), showlinks=False)
symtrie.visit(buildcgo)
buildcgo.show()
cube(Vec(0, 0, 0), cell * Vec(1, 1, 1))
for g in G:
print "show", g
g.show(radius=2.0, sphereradius=4.0)
return AXS, CEN
def test_P4132(depth=8, cell=50, maxrad=80):
#**** P4132 ****
# C2 and C3 at angle = 35.2644 offset = 0.176777
# C2 axis=[-0.707107,0.707107,0] origin=[-0.125,-0.125,-0.125]
# C3 axis=[0.57735,-0.57735,0.57735] origin=[0,-0.5,-0.5]
AXS = [Vec(-1, 1, 0),
Vec(1, -1, 1)]
CEN = [cell * Vec(1, 1, 1) / -8.0,
cell * Vec(0, 1, 1) / -2.0]
# AXS = [ Vec(-1, 1, 0) ,
# Vec( 1, 1, 1) ]
# CEN = [ cell * Vec(1,1,1)/-8.0,
# cell * Vec(0,0,0) ]
G = [
SymElem("C2", axis=AXS[0], cen=CEN[0]),
SymElem("C3", axis=AXS[1], cen=CEN[1]),
]
symtrie = generate_sym_trie(G, depth=depth)
# buildcgo = BuildCGO( nodes=[ CEN1+Vec(2,3,4), CEN2+Vec(2,4,3), ] )
cencell = cell / 2.0 * Vec(1, 1, 1)
buildcgo = BuildCGO(nodes=[CEN[1] + randnorm() * 5.0, CEN[0] + randnorm() * 8.0],
origin=cencell, maxrad=maxrad, showlinks=False, showelems=True)
symtrie.visit(buildcgo)
buildcgo.show()
cube(Vec(0, 0, 0), cell * Vec(1, 1, 1))
for g in G:
print "show", g
g.show(radius=2.0, sphereradius=4.0)
return AXS, CEN
def test_P442(cell=80, **kwargs):
# delete all; run ~/pymol/symgen.py; test_P4( depth=4, cell=100,
# symdef_scale=0.000001, generic_names=1 )
G = [SymElem("C4", cen=cell * Vec(0.0, 0.0, 0.0)),
SymElem("C2", cen=cell * Vec(0.5, 0.0, 0.0)),
]
test_xtal(G, cell, tag='test_P4_42', **kwargs)
def test_T32(cell=100,**kwargs): print "========================================== T32 ==========================================" G = [ SymElem( "C3", axis=Vec(1,1,1) ), SymElem( "C2", axis=Vec(1,0,0), cen=Vec(0.00001,0,0) ), ] component_pos=[ Vec(8,6,5), Vec(7,2,1), ] test_xtal(G,cell,component_pos=component_pos,tag="T32",origin=cell*Vec(0.0,0.0,0.0),showshape=0,**kwargs)
def test_P23_TT(cell=100,**kwargs): # delete all; run ~/pymol/symgen.py; test_P23_TD2B( depth=2, cell=200, symdef_scale=0.000001, generic_names=1 ) G = [ SymElem( "C3" , axis=Vec( 1,-1,-1), cen=cell*Vec(0.0 , 0.0 ,0.0 ) ), SymElem( "C3" , axis=Vec( 1,-1, 1), cen=cell*Vec(0.25, 0.25,0.0 ) ), # SymElem( "T" , cen=cell*Vec(0.25,0.25,0.0) ), ] test_xtal(G,cell,tag="P23_TT",**kwargs) cube( cell*Vec(1,1,1)*-0.5, cell*Vec(1,1,1)*0.5 )
def test_F432_TD2(cell=150,**kwargs):
# delete all; run ~/pymol/symgen.py; test_F432_TD2( depth=2, cell=200, symdef_scale=0.000001, generic_names=1 )
G = [ SymElem( "D2", cen=cell*Vec(0.0,0.0,0.0) ), # , axis2=Vec(1,1,0) ),
SymElem( "T" , cen=cell*Vec(0.0,0.0,0.25), input_xform=RAD(Uz,45) ),
# SymElem( "O" , cen=cell*Vec(0.5,0.5,0.0) ),
]
component_pos=[ Vec(2,4,8), Vec(2,5,-12), Vec(4,6,8) ]
test_xtal(G,cell,component_pos=component_pos,tag="F432_TD2",**kwargs)
cube( cell*Vec(-0.5,-0.5,-0.25), cell*Vec(0.5,0.5,0.75), xform=RAD(Uz,45) )
def test_F432_OTD2(depth=3,cell=80,**kwargs): # delete all; run /Users/sheffler/pymol/symgen.py; test_P23(depth=1,mindepth=1) # ODT 96 # TDO 96 G = [ SymElem( "O" , cen=cell*Vec(0.5,0.5,0.0) ), SymElem( "D2", cen=cell*Vec(0.0,0.0,0.0), axis2=Vec(1,1,0) ), SymElem( "T" , cen=cell*Vec(0.0,0.0,-0.5) ), ] component_pos=[ Vec(2,4,8), Vec(2,5,-12), Vec(4,6,8) ] extranodes = [ cell*Vec(0.0,0.5,0.0)] test_xtal(G,cell,component_pos=component_pos,tag="F432_TD2",extranodes=extranodes,**kwargs) cube( cell*Vec(-1,-1,-0.5), cell*Vec(1,1,1.5) )
def test_I432_OD4(cell=80, **kwargs):
# delete all; run /Users/sheffler/pymol/symgen.py; test_F432_OD4( depth=3, cell=200, symdef_scale=0.000001, generic_names=1 )
# G = [ SymElem( "D2", cen=cell*Vec(0.0,0.0,0.0), axis2=Vec(1,1,0) ),
# # SymElem( "T" , cen=cell*Vec(0.0,0.0,-0.5) ),
# SymElem( "O" , cen=cell*Vec(0.5,0.5,0.0) ),
# ]
G = [SymElem("D4", cen=cell * Vec(0.0, 0.0, 0.0)),
# SymElem( "T" , cen=cell*Vec(0.0,0.0,-0.5) ),
SymElem("O", cen=cell * Vec(0.0, 0.0, 0.5), input_xform=RAD(Uz, 45)),
]
component_pos = [Vec(2, 4, 8), Vec(2, 5, -12), Vec(4, 6, 8)]
test_xtal(G, cell, component_pos=component_pos, tag="I432_OD4", **kwargs)
cube(cell * Vec(-1, -1, -0.5), cell * Vec(1, 1, 1.5))
def test_P213(cell=100,**kwargs): AXS = [ Vec( 1, 1, 1), Vec( 1, 1,-1) ] CEN = [ cell * Vec(0,0,0), cell * Vec(0.5,0,0.0) ] G = [ SymElem( "C3", axis=AXS[0], cen=CEN[0] ), SymElem( "C3", axis=AXS[1], cen=CEN[1] ), ] component_pos=[ Vec(-18,-17,-16), Vec(7,0,11), ] test_xtal(G,cell,tag="P213",origin=cell*Vec(0.0,0.0,0.0),showshape=0,**kwargs) cube( Vec(0,0,0), cell*Vec(1,1,1) )
def test_I432( depth=6, cell=50, **kwargs ): #**** I432 **** #C2 and D3 at angle = 35.2644 offset = 0.353553 # C2 axis=[-0.707107,0.707107,0] origin=[0.25,0.25,0.25] # D3 axis=[-0.57735,0.57735,0.57735] axis2=[0.707107,0.707107,0] origin=[0,0,0] G = [ SymElem( "C2", axis=Vec(-1,1,0), cen=Vec(1,1,1)/4.0*cell ), SymElem( "D3", axis=Vec(-1,1,1), axis2=Vec(1,1,0) ) ] symtrie = generate_sym_trie(G,depth=depth) # buildcgo = BuildCGO( nodes=[ CEN1+Vec(2,3,4), CEN2+Vec(2,4,3), ] ) nodes = [] buildcgo = BuildCGO( nodes=nodes, origin=cell*Vec(0.5,0.5,0.5), showlinks=False, **kwargs ) symtrie.visit(buildcgo) buildcgo.show() cube( Vec(0,0,0), cell*Vec(1,1,1) ) for g in G: print "show",g g.show(radius=2.0,sphereradius=4.0)
def test_D2TET(depth=6, cell=60, **kwargs):
G = [
# SymElem("C2",axis=Vec( 1,0,0),cen=Vec( 0 ,cell/2.0, cell/4.0)),
# SymElem("C3",axis=Vec(-1,1,1),cen=Vec(-cell/6.0,cell/6.0,-cell/3.0)),
# SymElem("C2",axis=Vec(1,1,0),cen=cell*Vec(0,0.0,0.0)),
# SymElem("C3",axis=Vec(-1,1,1),cen=Vec(0,0,0)),
# SymElem("C2",axis=Vec(0,1,0)),
SymElem("C3", axis=Vec(1, 1, 1)),
# SymElem("C2",axis=Vec(0,1,0),cen=Vec(1,1,1)*cell/2.0), # other T
# SymElem("C3",axis=Vec(1,1,1),cen=Vec(1,1,1)*cell/2.0), # other T
# SymElem("C4",axis=Vec(1,0,0),cen=Vec(1,1,1)*cell/2.0),
SymElem("D2", cen=Vec(0, 0, cell / 2.0)),
# SymElem("D2",cen=Vec(0,cell/2.0,cell/2.0)), # other D2
]
# for elem in G: print elem
symtrie = generate_sym_trie(G, depth=depth)
buildcgo = BuildCGO(nodes=[], origin=Vec(0.5, 0.5, 0.5) * cell, **kwargs)
# buildcgo = BuildCGO( nodes=[ Vec(6,6,30), ] )
symtrie.visit(buildcgo)
buildcgo.show()
cube(Vec(0, 0, 0), cell * Vec(1, 1, 1))
for g in G:
print "show", g
g.show(radius=2.0, sphereradius=4.0)
def test_quasi( depth=8, cell=20.0, maxrad=9e9 ): G = [ SymElem( "C2", axis=Vec(1,0,0) ), SymElem( "C2", axis=Vec(0,1,0) ), SymElem( "C2", axis=Vec(0,0,1) ), SymElem( "C3", axis=Vec(+1,+1,+1) ), SymElem( "C3", axis=Vec(+1,-1,-1) ), SymElem( "C3", axis=Vec(-1,+1,-1) ), SymElem( "C3", axis=Vec(-1,-1,+1) ), SymElem( "C2", axis=Vec(2,-1,-1), cen=cell*Vec(1,1,1) ), ] nodes = [ ] symtrie = generate_sym_trie(G,depth=depth) symtrie.visit(print_node) print symtrie buildcgo = BuildCGO( nodes=nodes, maxrad=maxrad, origin=cell*Vec(0.5,0.5,0.5), showlinks=False, showelems=True ) symtrie.visit(buildcgo) buildcgo.show()
def test_D4OCT(depth=4):
CELL = 30
G = [
# SymElem("C2",axis=Vec( 1,0,0),cen=Vec( 0 ,CELL/2.0, CELL/4.0)),
# SymElem("C3",axis=Vec(-1,1,1),cen=Vec(-CELL/6.0,CELL/6.0,-CELL/3.0)),
# SymElem("C2",axis=Vec(1,1,0),cen=CELL*Vec(0,0.0,0.0)),
# SymElem("C3",axis=Vec(-1,1,1),cen=Vec(0,0,0)),
SymElem("C2", axis=Vec(1, 1, 0), cen=Vec(0, 0, CELL)),
SymElem("C3", axis=Vec(1, 1, 1), cen=Vec(0, 0, CELL)),
SymElem("C4", axis=Vec(1, 0, 0), cen=Vec(0, 0, CELL)),
SymElem("C4", axis=Vec(0, 0, 1)),
SymElem("C2", axis=Vec(1, 0, 0)),
SymElem("C2", axis=Vec(0, 1, 0)),
]
# for elem in G: print elem
symtrie = generate_sym_trie(G, depth=depth)
# buildcgo = BuildCGO( nodes=[ Vec(2,4,3), Vec(-6,-2,35), ] )
buildcgo = BuildCGO(nodes=[Vec(-6, -2, CELL + 5), Vec(2, 4, 3), ])
# buildcgo = BuildCGO( nodes=[ Vec(-6,-2,35), ] )
# buildcgo = BuildCGO( nodes=[ Vec(2,4,3), ] )
symtrie.visit(buildcgo)
buildcgo.show()
def test_icos(depth=3, cell=30, **kwargs):
# dodec
# (+-1, +-1, +-1)
# (0, +-1/p, +-p)
# (+-1/p, +-p, 0)
# (+-p, 0, +-1/p)
# icos
# (0, +-1, +-p)
# (+-1, +-p, 0)
# (+-p, 0, +-1)
p = (1.0 + sqrt(5.0)) / 2.0
q = 1.0 / p
v33a = (Vec(1, 1, 1).normalized() - Vec(q, p, 0).normalized()).normalized()
v33b = (Vec(1, 1, 1).normalized() - Vec(p, 0, q).normalized()).normalized()
v33c = (Vec(1, 1, 1).normalized() - Vec(0, q, p).normalized()).normalized()
icsang = angle_degrees(Vec(1, 1, 1), V0, v33a)
tetang = 180.0 - math.acos(-1.0 / 3.0) * 180.0 / math.pi
print icsang, tetang
delta_deg = icsang - tetang
v33a = RAD(v33a.cross(Vec(1, 1, 1)), delta_deg) * v33a
v33b = RAD(v33b.cross(Vec(1, 1, 1)), delta_deg) * v33b
v33c = RAD(v33c.cross(Vec(1, 1, 1)), delta_deg) * v33c
print angle_degrees(Vec(1, 1, 1), V0, v33a)
print angle_degrees(Vec(1, 1, 1), V0, v33b)
print angle_degrees(Vec(1, 1, 1), V0, v33c)
G = [
# icos 3folds
SymElem("C3", Vec(+1, +1, +1)),
SymElem("C3", Vec(+1, +1, -1)),
SymElem("C3", Vec(+1, -1, +1)),
SymElem("C3", Vec(-1, +1, +1)),
SymElem("C3", Vec(0, +q, +p)),
SymElem("C3", Vec(0, +q, -p)),
SymElem("C3", Vec(+q, +p, 0)),
SymElem("C3", Vec(+q, -p, 0)),
SymElem("C3", Vec(+p, 0, +q)),
SymElem("C3", Vec(-p, 0, +q)),
SymElem("C5", Vec(0, +p, 1)),
SymElem("C5", Vec(0, -p, 1)),
SymElem("C5", Vec(+p, 1, 0)),
SymElem("C5", Vec(-p, 1, 0)),
SymElem("C5", Vec(1, 0, +p)),
SymElem("C5", Vec(1, 0, -p)),
# tet
SymElem("C3", Vec(1, 1, 1), cen=cell * Vec(1, 1, 1)),
SymElem("C3", v33a, cen=cell * Vec(1, 1, 1)),
SymElem("C3", v33b, cen=cell * Vec(1, 1, 1)),
SymElem("C3", v33c, cen=cell * Vec(1, 1, 1)),
SymElem("C2", v33a + v33b, cen=cell * Vec(1, 1, 1)),
SymElem("C2", v33b + v33c, cen=cell * Vec(1, 1, 1)),
SymElem("C2", v33c + v33a, cen=cell * Vec(1, 1, 1)),
]
symtrie = generate_sym_trie(G, depth=depth)
# symtrie.visit(print_node)
nodes = []
buildcgo = BuildCGO(nodes=nodes, origin=cell *
Vec(0.5, 0.5, 0.5), showelems=True, **kwargs)
symtrie.visit(buildcgo)
buildcgo.show()
def test_P4m_44(cell=80, **kwargs):
G = [SymElem("D4", cen=cell * Vec(0.0, 0.0, 0.0)),
SymElem("D4", cen=cell * Vec(0.5, 0.0, 0.0)), ]
test_xtal(G, cell, tag="P432_OD4", **kwargs)
def test_P4m44(cell=100, **kwargs):
G = [SymElem("D4", cen=cell * Vec(0.0, 0.0, 0.0)),
# moved lattice WRP C2!!!!!
SymElem("D4", cen=cell * Vec(0.5, 0.0, 0.0)),
]
test_xtal(G, cell, tag='test_P4_44', **kwargs)