Functions for generating hexagonal/triangular lattices
Former-commit-id: 5139893ade0c5bfa46c712af3913218158038e37
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Marek Nečada
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import math
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import numpy as np
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def generate_trianglepoints(maxlayer, include_origin = False, v3d = True, circular = True, sixthindices = False, mirrorindices = False):
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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)])
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points = np.empty((3*maxlayer*(maxlayer+1)+(1 if include_origin else 0), 3 if v3d else 2))
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point_i = 0
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if (include_origin):
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points[0] = np.array((0,0,0) if v3d else (0,0))
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point_i = 1
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if sixthindices:
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si = np.empty((6,(maxlayer*(maxlayer+1))//2), dtype=int)
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sii = [0,0,0,0,0,0]
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if mirrorindices:
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#layer indices start from one!
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ilayer = np.arange(1, maxlayer+1) # We need first to "copy" layer indices to correspond to the Muster count
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mustercount = (ilayer - 1)//2
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mustercum = np.cumsum(mustercount)
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layerstart = np.zeros((mustercum[maxlayer - 1]), dtype=int)
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layerstart[mustercum[:(maxlayer-1)]] = 1
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print(mustercum, layerstart)
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layer = np.cumsum(layerstart) + 2 # That's it
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print(layer)
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lb = 3*layer*(layer-1) # layer base (lowest) index
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print(lb)
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li = np.arange(len(layer)) - mustercum[layer-2] # muster indices for each layers
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print(li)
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mi = np.empty((2, len(layer)), dtype=int)
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mi[0] = lb + 1 + li
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mi[1] = lb + layer - (1 + li)
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# there are two non-musters in each even layer, one non-muster in each odd
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layer = (2*np.arange(((3*maxlayer)//2))+1)//3 + 1
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nmi = 3*layer*(layer-1)
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nmi[2::3] += layer[2::3] // 2 # second non-musters in even layers
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for layer in range(1,maxlayer+1):
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for i in range(6):
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base = e6[i]*layer
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shift = e6[(i+2)%6]
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ar = np.arange(layer)
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points[point_i:(point_i+layer)] = base[nx,:] + ar[:,nx] * shift[nx,:]
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if sixthindices:
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si[i, sii[i]:sii[i]+layer] = point_i + ar
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sii[i] += layer
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point_i += layer
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if (circular):
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mask = (np.sum(points * points, axis = -1) <= maxlayer * maxlayer * 3/ 4 + 0.1) # UGLY FIX OF ASYMMETRY BECAUSE OF ROUNDING ERROR
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points = points[mask]
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if sixthindices:
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cum = np.cumsum(mask) - 1
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mask0 = mask[si[0]]
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si_ = si[:,mask0]
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si = cum[si_]
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if not (mirrorindices or sixthindices):
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return points
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else:
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return {'points': points,
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'si' : si if sixthindices else None,
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'mi' : mi if mirrorindices else None,
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'nmi' : nmi if mirrorindices else None}
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def generate_trianglepoints_hexcomplement(maxlayer, v3d = True, circular = True, thirdindices = False, mirrorindices=False):
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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)])
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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)])
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points = np.empty((3*maxlayer*maxlayer, 3 if v3d else 2))
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#print(len(points))
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point_i = 0
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# 3 * layer ** 2 is the basis index for a layer, a layer contains 3 * (2*layer + 1) points
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if thirdindices:
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ii = np.arange(maxlayer**2)
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layer = np.empty((maxlayer**2), dtype=int)
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layer = np.sqrt(ii, out=layer, casting='unsafe')
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#ti0 = 2*layer**2 + ii
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ti = np.arange(3)[:, nx] * (2*layer + 1)[nx, :] + (2*layer**2 + ii)[nx,:]
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if mirrorindices:
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ii = np.arange((maxlayer-1)*maxlayer/2)
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layer = np.empty(((maxlayer-1)*maxlayer//2), dtype=int)
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layer = (np.sqrt(1+8*ii, out=layer, casting='unsafe')+1)//2
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li = ii - ((layer - 1) * (layer-2))//2# numbers indices in a each layer
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lb = 3*layer **2 # base index of a layer
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mi = np.empty((2,len(layer)), dtype=int)
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mi[0] = lb + li + layer % 2
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mi[1] = lb + 2*layer - li
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# indices of non-mirrored/self-mirrored
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layer = np.arange(maxlayer)
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lb = 3 * layer**2
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nmi = lb + ((layer + 1) % 2) * layer
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for layer in range(0,maxlayer):
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#print(layer)
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if (layer % 2): # odd layer
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for i in range(3):
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base = f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / s3)
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shift = e6[(2*i+2)%6]
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count = (layer + 1) // 2
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#print(point_i, count)
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ar = np.arange(count)
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points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
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point_i += count
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base = e6[(2*i+1)%6]*layer + f6[(2*i)%6] / s3
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shift = e6[(2*i+3)%6]
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count = layer
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#print(point_i, count)
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ar = np.arange(count)
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points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
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point_i += count
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base = e6[(2*i+2)%6]*layer + f6[(2*i)%6] / s3
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shift = e6[(2*i+4)%6]
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count = (layer + 1) / 2
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#print(point_i, count)
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ar = np.arange(count)
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points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
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point_i += count
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else: # even layer:
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for i in range(3):
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shift = e6[(2*i+2)%6]
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base = f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / s3) + shift / 2
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count = layer / 2
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#print(point_i, count)
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ar = np.arange(count)
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points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
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point_i += count
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base = e6[(2*i+1)%6]*layer + f6[(2*i)%6] / s3
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shift = e6[(2*i+3)%6]
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count = layer
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#print(point_i, count)
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ar = np.arange(count)
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points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
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point_i += count
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base = e6[(2*i+2)%6]*layer + f6[(2*i)%6] / s3
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shift = e6[(2*i+4)%6]
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count = (layer + 2) / 2
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#print(point_i, count)
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ar = np.arange(count)
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points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]
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point_i += count
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#if (mirrorindices):
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if (circular):
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mask = (np.sum(points * points, axis = -1) <= maxlayer * maxlayer * 3/ 4 + 0.01) # UGLY FIX OF ASYMMETRY BECAUSE OF ROUNDING ERROR
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points = points[mask]
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if thirdindices:
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cum = np.cumsum(mask) - 1
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mask0 = mask[ti[0]]
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ti_ = ti[:,mask0]
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ti = cum[ti_]
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if mirrorindices:
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cum = np.cumsum(mask) - 1
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mask0 = mask[mi[0]]
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mi_ = mi[:,mask0]
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mi = cum[mi_]
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mask0 = mask[nmi]
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nmi_ = nmi[mask0]
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nmi = cum[nmi_]
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if not (mirrorindices or thirdindices):
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return points
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else:
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return {'points': points,
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'ti' : ti if thirdindices else None,
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'mi' : mi if mirrorindices else None,
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'nmi' : nmi if mirrorindices else None}
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