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hex/triangle lattice generator internal constants 

Former-commit-id: 7c581b5e832ee91f0b1bde804233a635f4090975
This commit is contained in:
Marek Nečada 2017-02-05 18:46:36 +02:00
parent df90b7b440
commit af4eb887c4
1 changed files with 19 additions and 17 deletions
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36
qpms/hex.py
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@ -1,8 +1,12 @@
import math import math
import numpy as np import numpy as np
_s3 = math.sqrt(3)
_e6 = np.array([[math.cos(2*math.pi*i/6),math.sin(2*math.pi*i/6),0] if v3d else [math.cos(2*math.pi*i/6),math.sin(2*math.pi*i/6)] for i in range(6)])
_f6 = np.array([[-math.sin(2*math.pi*i/6),math.cos(2*math.pi*i/6),0] if v3d else [math.sin(2*math.pi*i/6),-math.cos(2*math.pi*i/6)] for i in range(6)])
def generate_trianglepoints(maxlayer, include_origin = False, v3d = True, circular = True, sixthindices = False, mirrorindices = False): def generate_trianglepoints(maxlayer, include_origin = False, v3d = True, circular = True, sixthindices = False, mirrorindices = False):
e6 = np.array([[math.cos(2*math.pi*i/6),math.sin(2*math.pi*i/6),0] if v3d else [math.cos(2*math.pi*i/6),math.sin(2*math.pi*i/6)] for i in range(6)])
points = np.empty((3*maxlayer*(maxlayer+1)+(1 if include_origin else 0), 3 if v3d else 2)) points = np.empty((3*maxlayer*(maxlayer+1)+(1 if include_origin else 0), 3 if v3d else 2))
point_i = 0 point_i = 0
if (include_origin): if (include_origin):
@ -35,8 +39,8 @@ def generate_trianglepoints(maxlayer, include_origin = False, v3d = True, circul
for layer in range(1,maxlayer+1): for layer in range(1,maxlayer+1):
for i in range(6): for i in range(6):
base = e6[i]*layer base = _e6[i]*layer
shift = e6[(i+2)%6] shift = _e6[(i+2)%6]
ar = np.arange(layer) ar = np.arange(layer)
points[point_i:(point_i+layer)] = base[nx,:] + ar[:,nx] * shift[nx,:] points[point_i:(point_i+layer)] = base[nx,:] + ar[:,nx] * shift[nx,:]
if sixthindices: if sixthindices:
@ -68,8 +72,6 @@ def generate_trianglepoints(maxlayer, include_origin = False, v3d = True, circul
'nmi' : nmi if mirrorindices else None} 'nmi' : nmi if mirrorindices else None}
def generate_trianglepoints_hexcomplement(maxlayer, v3d = True, circular = True, thirdindices = False, mirrorindices=False): def generate_trianglepoints_hexcomplement(maxlayer, v3d = True, circular = True, thirdindices = False, mirrorindices=False):
e6 = np.array([[math.cos(2*math.pi*i/6),math.sin(2*math.pi*i/6),0] if v3d else [math.cos(2*math.pi*i/6),math.sin(2*math.pi*i/6)] for i in range(6)])
f6 = np.array([[-math.sin(2*math.pi*i/6),math.cos(2*math.pi*i/6),0] if v3d else [math.sin(2*math.pi*i/6),-math.cos(2*math.pi*i/6)] for i in range(6)])
points = np.empty((3*maxlayer*maxlayer, 3 if v3d else 2)) points = np.empty((3*maxlayer*maxlayer, 3 if v3d else 2))
point_i = 0 point_i = 0
# 3 * layer ** 2 is the basis index for a layer, a layer contains 3 * (2*layer + 1) points # 3 * layer ** 2 is the basis index for a layer, a layer contains 3 * (2*layer + 1) points
@ -95,44 +97,44 @@ def generate_trianglepoints_hexcomplement(maxlayer, v3d = True, circular = True,
for layer in range(0,maxlayer): for layer in range(0,maxlayer):
if (layer % 2): # odd layer if (layer % 2): # odd layer
for i in range(3): for i in range(3):
base = f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / s3) base = _f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / _s3)
shift = e6[(2*i+2)%6] shift = _e6[(2*i+2)%6]
count = (layer + 1) // 2 count = (layer + 1) // 2
ar = np.arange(count) ar = np.arange(count)
points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
point_i += count point_i += count
base = e6[(2*i+1)%6]*layer + f6[(2*i)%6] / s3 base = _e6[(2*i+1)%6]*layer + _f6[(2*i)%6] / _s3
shift = e6[(2*i+3)%6] shift = _e6[(2*i+3)%6]
count = layer count = layer
ar = np.arange(count) ar = np.arange(count)
points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
point_i += count point_i += count
base = e6[(2*i+2)%6]*layer + f6[(2*i)%6] / s3 base = _e6[(2*i+2)%6]*layer + _f6[(2*i)%6] / _s3
shift = e6[(2*i+4)%6] shift = _e6[(2*i+4)%6]
count = (layer + 1) // 2 count = (layer + 1) // 2
ar = np.arange(count) ar = np.arange(count)
points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
point_i += count point_i += count
else: # even layer: else: # even layer:
for i in range(3): for i in range(3):
shift = e6[(2*i+2)%6] shift = _e6[(2*i+2)%6]
base = f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / s3) + shift / 2 base = _f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / _s3) + shift / 2
count = layer // 2 count = layer // 2
ar = np.arange(count) ar = np.arange(count)
points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
point_i += count point_i += count
base = e6[(2*i+1)%6]*layer + f6[(2*i)%6] / s3 base = _e6[(2*i+1)%6]*layer + _f6[(2*i)%6] / _s3
shift = e6[(2*i+3)%6] shift = _e6[(2*i+3)%6]
count = layer count = layer
ar = np.arange(count) ar = np.arange(count)
points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
point_i += count point_i += count
base = e6[(2*i+2)%6]*layer + f6[(2*i)%6] / s3 base = _e6[(2*i+2)%6]*layer + _f6[(2*i)%6] / _s3
shift = e6[(2*i+4)%6] shift = _e6[(2*i+4)%6]
count = (layer + 2) // 2 count = (layer + 2) // 2
ar = np.arange(count) ar = np.arange(count)
points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]