From af4eb887c45f1e05057d49cd8088f0739bd8e65b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Sun, 5 Feb 2017 18:46:36 +0200 Subject: [PATCH] hex/triangle lattice generator internal constants Former-commit-id: 7c581b5e832ee91f0b1bde804233a635f4090975 --- qpms/hex.py | 36 +++++++++++++++++++----------------- 1 file changed, 19 insertions(+), 17 deletions(-) diff --git a/qpms/hex.py b/qpms/hex.py index f2142c9..75af9ce 100644 --- a/qpms/hex.py +++ b/qpms/hex.py @@ -1,8 +1,12 @@ import math 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): - 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)) point_i = 0 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 i in range(6): - base = e6[i]*layer - shift = e6[(i+2)%6] + base = _e6[i]*layer + shift = _e6[(i+2)%6] ar = np.arange(layer) points[point_i:(point_i+layer)] = base[nx,:] + ar[:,nx] * shift[nx,:] if sixthindices: @@ -68,8 +72,6 @@ def generate_trianglepoints(maxlayer, include_origin = False, v3d = True, circul 'nmi' : nmi if mirrorindices else None} 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)) point_i = 0 # 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): if (layer % 2): # odd layer for i in range(3): - base = f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / s3) - shift = e6[(2*i+2)%6] + base = _f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / _s3) + shift = _e6[(2*i+2)%6] count = (layer + 1) // 2 ar = np.arange(count) points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] point_i += count - base = e6[(2*i+1)%6]*layer + f6[(2*i)%6] / s3 - shift = e6[(2*i+3)%6] + base = _e6[(2*i+1)%6]*layer + _f6[(2*i)%6] / _s3 + shift = _e6[(2*i+3)%6] count = layer ar = np.arange(count) points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] point_i += count - base = e6[(2*i+2)%6]*layer + f6[(2*i)%6] / s3 - shift = e6[(2*i+4)%6] + base = _e6[(2*i+2)%6]*layer + _f6[(2*i)%6] / _s3 + shift = _e6[(2*i+4)%6] count = (layer + 1) // 2 ar = np.arange(count) points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] point_i += count else: # even layer: for i in range(3): - shift = e6[(2*i+2)%6] - base = f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / s3) + shift / 2 + shift = _e6[(2*i+2)%6] + base = _f6[(2*i-1)%6] * ((0.5 + 1.5 * layer) / _s3) + shift / 2 count = layer // 2 ar = np.arange(count) points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] point_i += count - base = e6[(2*i+1)%6]*layer + f6[(2*i)%6] / s3 - shift = e6[(2*i+3)%6] + base = _e6[(2*i+1)%6]*layer + _f6[(2*i)%6] / _s3 + shift = _e6[(2*i+3)%6] count = layer ar = np.arange(count) points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:] point_i += count - base = e6[(2*i+2)%6]*layer + f6[(2*i)%6] / s3 - shift = e6[(2*i+4)%6] + base = _e6[(2*i+2)%6]*layer + _f6[(2*i)%6] / _s3 + shift = _e6[(2*i+4)%6] count = (layer + 2) // 2 ar = np.arange(count) points[point_i:point_i+count,:] = base + ar[:,nx]*shift[nx,:]