1 | #!/usr/bin/env python |
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2 | # -*- coding: utf-8 -*- |
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3 | """ |
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4 | Jitter Explorer |
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5 | =============== |
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6 | |
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7 | Application to explore orientation angle and angular dispersity. |
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8 | |
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9 | From the command line:: |
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10 | |
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11 | # Show docs |
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12 | python -m sasmodels.jitter --help |
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13 | |
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14 | # Guyou projection jitter, uniform over 20 degree theta and 10 in phi |
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15 | python -m sasmodels.jitter --projection=guyou --dist=uniform --jitter=20,10,0 |
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16 | |
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17 | From a jupyter cell:: |
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18 | |
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19 | import ipyvolume as ipv |
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20 | from sasmodels import jitter |
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21 | import importlib; importlib.reload(jitter) |
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22 | jitter.set_plotter("ipv") |
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23 | |
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24 | size = (10, 40, 100) |
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25 | view = (20, 0, 0) |
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26 | |
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27 | #size = (15, 15, 100) |
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28 | #view = (60, 60, 0) |
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29 | |
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30 | dview = (0, 0, 0) |
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31 | #dview = (5, 5, 0) |
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32 | #dview = (15, 180, 0) |
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33 | #dview = (180, 15, 0) |
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34 | |
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35 | projection = 'equirectangular' |
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36 | #projection = 'azimuthal_equidistance' |
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37 | #projection = 'guyou' |
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38 | #projection = 'sinusoidal' |
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39 | #projection = 'azimuthal_equal_area' |
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40 | |
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41 | dist = 'uniform' |
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42 | #dist = 'gaussian' |
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43 | |
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44 | jitter.run(size=size, view=view, jitter=dview, dist=dist, projection=projection) |
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45 | #filename = projection+('_theta' if dview[0] == 180 else '_phi' if dview[1] == 180 else '') |
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46 | #ipv.savefig(filename+'.png') |
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47 | """ |
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48 | from __future__ import division, print_function |
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49 | |
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50 | import argparse |
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51 | |
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52 | import numpy as np |
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53 | from numpy import pi, cos, sin, sqrt, exp, degrees, radians |
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54 | |
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55 | def draw_beam(axes, view=(0, 0), alpha=0.5, steps=25): |
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56 | """ |
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57 | Draw the beam going from source at (0, 0, 1) to detector at (0, 0, -1) |
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58 | """ |
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59 | #axes.plot([0,0],[0,0],[1,-1]) |
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60 | #axes.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=alpha) |
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61 | |
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62 | u = np.linspace(0, 2 * np.pi, steps) |
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63 | v = np.linspace(-1, 1, 2) |
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64 | |
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65 | r = 0.02 |
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66 | x = r*np.outer(np.cos(u), np.ones_like(v)) |
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67 | y = r*np.outer(np.sin(u), np.ones_like(v)) |
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68 | z = 1.3*np.outer(np.ones_like(u), v) |
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69 | |
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70 | theta, phi = view |
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71 | shape = x.shape |
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72 | points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) |
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73 | points = Rz(phi)*Ry(theta)*points |
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74 | x, y, z = [v.reshape(shape) for v in points] |
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75 | axes.plot_surface(x, y, z, color='yellow', alpha=alpha) |
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76 | |
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77 | # TODO: draw endcaps on beam |
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78 | ## Drawing tiny balls on the end will work |
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79 | #draw_sphere(axes, radius=0.02, center=(0, 0, 1.3), color='yellow', alpha=alpha) |
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80 | #draw_sphere(axes, radius=0.02, center=(0, 0, -1.3), color='yellow', alpha=alpha) |
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81 | ## The following does not work |
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82 | #triangles = [(0, i+1, i+2) for i in range(steps-2)] |
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83 | #x_cap, y_cap = x[:, 0], y[:, 0] |
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84 | #for z_cap in z[:, 0], z[:, -1]: |
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85 | # axes.plot_trisurf(x_cap, y_cap, z_cap, triangles, |
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86 | # color='yellow', alpha=alpha) |
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87 | |
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88 | |
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89 | def draw_ellipsoid(axes, size, view, jitter, steps=25, alpha=1): |
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90 | """Draw an ellipsoid.""" |
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91 | a, b, c = size |
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92 | u = np.linspace(0, 2 * np.pi, steps) |
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93 | v = np.linspace(0, np.pi, steps) |
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94 | x = a*np.outer(np.cos(u), np.sin(v)) |
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95 | y = b*np.outer(np.sin(u), np.sin(v)) |
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96 | z = c*np.outer(np.ones_like(u), np.cos(v)) |
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97 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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98 | |
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99 | axes.plot_surface(x, y, z, color='w', alpha=alpha) |
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100 | |
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101 | draw_labels(axes, view, jitter, [ |
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102 | ('c+', [+0, +0, +c], [+1, +0, +0]), |
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103 | ('c-', [+0, +0, -c], [+0, +0, -1]), |
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104 | ('a+', [+a, +0, +0], [+0, +0, +1]), |
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105 | ('a-', [-a, +0, +0], [+0, +0, -1]), |
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106 | ('b+', [+0, +b, +0], [-1, +0, +0]), |
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107 | ('b-', [+0, -b, +0], [-1, +0, +0]), |
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108 | ]) |
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109 | |
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110 | def draw_sc(axes, size, view, jitter, steps=None, alpha=1): |
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111 | """Draw points for simple cubic paracrystal""" |
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112 | atoms = _build_sc() |
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113 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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114 | |
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115 | def draw_fcc(axes, size, view, jitter, steps=None, alpha=1): |
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116 | """Draw points for face-centered cubic paracrystal""" |
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117 | # Build the simple cubic crystal |
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118 | atoms = _build_sc() |
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119 | # Define the centers for each face |
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120 | # x planes at -1, 0, 1 have four centers per plane, at +/- 0.5 in y and z |
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121 | x, y, z = ( |
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122 | [-1]*4 + [0]*4 + [1]*4, |
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123 | ([-0.5]*2 + [0.5]*2)*3, |
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124 | [-0.5, 0.5]*12, |
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125 | ) |
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126 | # y and z planes can be generated by substituting x for y and z respectively |
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127 | atoms.extend(zip(x+y+z, y+z+x, z+x+y)) |
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128 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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129 | |
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130 | def draw_bcc(axes, size, view, jitter, steps=None, alpha=1): |
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131 | """Draw points for body-centered cubic paracrystal""" |
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132 | # Build the simple cubic crystal |
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133 | atoms = _build_sc() |
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134 | # Define the centers for each octant |
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135 | # x plane at +/- 0.5 have four centers per plane at +/- 0.5 in y and z |
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136 | x, y, z = ( |
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137 | [-0.5]*4 + [0.5]*4, |
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138 | ([-0.5]*2 + [0.5]*2)*2, |
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139 | [-0.5, 0.5]*8, |
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140 | ) |
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141 | atoms.extend(zip(x, y, z)) |
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142 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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143 | |
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144 | def _draw_crystal(axes, size, view, jitter, atoms=None): |
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145 | atoms, size = np.asarray(atoms, 'd').T, np.asarray(size, 'd') |
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146 | x, y, z = atoms*size[:, None] |
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147 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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148 | axes.scatter([x[0]], [y[0]], [z[0]], c='yellow', marker='o') |
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149 | axes.scatter(x[1:], y[1:], z[1:], c='r', marker='o') |
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150 | |
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151 | def _build_sc(): |
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152 | # three planes of 9 dots for x at -1, 0 and 1 |
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153 | x, y, z = ( |
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154 | [-1]*9 + [0]*9 + [1]*9, |
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155 | ([-1]*3 + [0]*3 + [1]*3)*3, |
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156 | [-1, 0, 1]*9, |
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157 | ) |
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158 | atoms = list(zip(x, y, z)) |
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159 | #print(list(enumerate(atoms))) |
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160 | # Pull the dot at (0, 0, 1) to the front of the list |
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161 | # It will be highlighted in the view |
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162 | index = 14 |
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163 | highlight = atoms[index] |
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164 | del atoms[index] |
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165 | atoms.insert(0, highlight) |
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166 | return atoms |
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167 | |
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168 | def draw_box(axes, size, view): |
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169 | a, b, c = size |
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170 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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171 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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172 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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173 | x, y, z = transform_xyz(view, None, x, y, z) |
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174 | def draw(i, j): |
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175 | axes.plot([x[i],x[j]], [y[i], y[j]], [z[i], z[j]], color='black') |
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176 | draw(0, 1) |
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177 | draw(0, 2) |
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178 | draw(0, 3) |
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179 | draw(7, 4) |
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180 | draw(7, 5) |
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181 | draw(7, 6) |
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182 | |
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183 | def draw_parallelepiped(axes, size, view, jitter, steps=None, |
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184 | color=(0.6, 1.0, 0.6), alpha=1): |
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185 | """Draw a parallelepiped.""" |
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186 | a, b, c = size |
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187 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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188 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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189 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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190 | tri = np.array([ |
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191 | # counter clockwise triangles |
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192 | # z: up/down, x: right/left, y: front/back |
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193 | [0, 1, 2], [3, 2, 1], # top face |
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194 | [6, 5, 4], [5, 6, 7], # bottom face |
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195 | [0, 2, 6], [6, 4, 0], # right face |
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196 | [1, 5, 7], [7, 3, 1], # left face |
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197 | [2, 3, 6], [7, 6, 3], # front face |
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198 | [4, 1, 0], [5, 1, 4], # back face |
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199 | ]) |
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200 | |
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201 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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202 | axes.plot_trisurf(x, y, triangles=tri, Z=z, color=color, alpha=alpha, |
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203 | linewidth=0) |
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204 | |
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205 | # Colour the c+ face of the box. |
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206 | # Since I can't control face color, instead draw a thin box situated just |
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207 | # in front of the "c+" face. Use the c face so that rotations about psi |
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208 | # rotate that face. |
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209 | if 0: |
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210 | color = (1, 0.6, 0.6) # pink |
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211 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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212 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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213 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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214 | x, y, z = transform_xyz(view, jitter, x, y, abs(z)+0.001) |
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215 | axes.plot_trisurf(x, y, triangles=tri, Z=z, color=color, alpha=alpha) |
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216 | |
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217 | draw_labels(axes, view, jitter, [ |
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218 | ('c+', [+0, +0, +c], [+1, +0, +0]), |
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219 | ('c-', [+0, +0, -c], [+0, +0, -1]), |
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220 | ('a+', [+a, +0, +0], [+0, +0, +1]), |
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221 | ('a-', [-a, +0, +0], [+0, +0, -1]), |
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222 | ('b+', [+0, +b, +0], [-1, +0, +0]), |
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223 | ('b-', [+0, -b, +0], [-1, +0, +0]), |
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224 | ]) |
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225 | |
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226 | def draw_sphere(axes, radius=0.5, steps=25, center=(0,0,0), color='w', alpha=1.): |
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227 | """Draw a sphere""" |
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228 | u = np.linspace(0, 2 * np.pi, steps) |
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229 | v = np.linspace(0, np.pi, steps) |
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230 | |
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231 | x = radius * np.outer(np.cos(u), np.sin(v)) + center[0] |
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232 | y = radius * np.outer(np.sin(u), np.sin(v)) + center[1] |
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233 | z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) + center[2] |
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234 | axes.plot_surface(x, y, z, color=color, alpha=alpha) |
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235 | #axes.plot_wireframe(x, y, z) |
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236 | |
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237 | def draw_axes(axes, origin=(-1, -1, -1), length=(2, 2, 2)): |
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238 | x, y, z = origin |
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239 | dx, dy, dz = length |
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240 | axes.plot([x, x+dx], [y, y], [z, z], color='black') |
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241 | axes.plot([x, x], [y, y+dy], [z, z], color='black') |
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242 | axes.plot([x, x], [y, y], [z, z+dz], color='black') |
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243 | |
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244 | def draw_person_on_sphere(axes, view, height=0.5, radius=0.5): |
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245 | limb_offset = height * 0.05 |
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246 | head_radius = height * 0.10 |
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247 | head_height = height - head_radius |
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248 | neck_length = head_radius * 0.50 |
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249 | shoulder_height = height - 2*head_radius - neck_length |
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250 | torso_length = shoulder_height * 0.55 |
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251 | torso_radius = torso_length * 0.30 |
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252 | leg_length = shoulder_height - torso_length |
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253 | arm_length = torso_length * 0.90 |
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254 | |
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255 | def _draw_part(x, z): |
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256 | y = np.zeros_like(x) |
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257 | xp, yp, zp = transform_xyz(view, None, x, y, z + radius) |
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258 | axes.plot(xp, yp, zp, color='k') |
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259 | |
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260 | # circle for head |
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261 | u = np.linspace(0, 2 * np.pi, 40) |
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262 | x = head_radius * np.cos(u) |
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263 | z = head_radius * np.sin(u) + head_height |
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264 | _draw_part(x, z) |
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265 | |
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266 | # rectangle for body |
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267 | x = np.array([-torso_radius, torso_radius, torso_radius, -torso_radius, -torso_radius]) |
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268 | z = np.array([0., 0, torso_length, torso_length, 0]) + leg_length |
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269 | _draw_part(x, z) |
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270 | |
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271 | # arms |
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272 | x = np.array([-torso_radius - limb_offset, -torso_radius - limb_offset, -torso_radius]) |
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273 | z = np.array([shoulder_height - arm_length, shoulder_height, shoulder_height]) |
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274 | _draw_part(x, z) |
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275 | _draw_part(-x, z) |
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276 | |
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277 | # legs |
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278 | x = np.array([-torso_radius + limb_offset, -torso_radius + limb_offset]) |
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279 | z = np.array([0, leg_length]) |
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280 | _draw_part(x, z) |
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281 | _draw_part(-x, z) |
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282 | |
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283 | limits = [-radius-height, radius+height] |
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284 | axes.set_xlim(limits) |
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285 | axes.set_ylim(limits) |
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286 | axes.set_zlim(limits) |
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287 | axes.set_axis_off() |
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288 | |
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289 | def draw_jitter(axes, view, jitter, dist='gaussian', |
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290 | size=(0.1, 0.4, 1.0), |
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291 | draw_shape=draw_parallelepiped, |
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292 | projection='equirectangular', |
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293 | alpha=0.8, |
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294 | views=None): |
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295 | """ |
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296 | Represent jitter as a set of shapes at different orientations. |
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297 | """ |
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298 | project, project_weight = get_projection(projection) |
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299 | |
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300 | # set max diagonal to 0.95 |
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301 | scale = 0.95/sqrt(sum(v**2 for v in size)) |
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302 | size = tuple(scale*v for v in size) |
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303 | |
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304 | dtheta, dphi, dpsi = jitter |
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305 | base = {'gaussian':3, 'rectangle':sqrt(3), 'uniform':1}[dist] |
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306 | def steps(delta): |
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307 | if views is None: |
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308 | n = max(3, min(25, 2*int(base*delta/5))) |
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309 | else: |
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310 | n = views |
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311 | return base*delta*np.linspace(-1, 1, n) if delta > 0 else [0.] |
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312 | for theta in steps(dtheta): |
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313 | for phi in steps(dphi): |
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314 | for psi in steps(dpsi): |
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315 | w = project_weight(theta, phi, 1.0, 1.0) |
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316 | if w > 0: |
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317 | dview = project(theta, phi, psi) |
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318 | draw_shape(axes, size, view, dview, alpha=alpha) |
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319 | for v in 'xyz': |
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320 | a, b, c = size |
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321 | lim = np.sqrt(a**2 + b**2 + c**2) |
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322 | getattr(axes, 'set_'+v+'lim')([-lim, lim]) |
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323 | #getattr(axes, v+'axis').label.set_text(v) |
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324 | |
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325 | PROJECTIONS = [ |
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326 | # in order of PROJECTION number; do not change without updating the |
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327 | # constants in kernel_iq.c |
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328 | 'equirectangular', 'sinusoidal', 'guyou', 'azimuthal_equidistance', |
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329 | 'azimuthal_equal_area', |
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330 | ] |
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331 | def get_projection(projection): |
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332 | |
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333 | """ |
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334 | jitter projections |
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335 | <https://en.wikipedia.org/wiki/List_of_map_projections> |
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336 | |
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337 | equirectangular (standard latitude-longitude mesh) |
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338 | <https://en.wikipedia.org/wiki/Equirectangular_projection> |
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339 | Allows free movement in phi (around the equator), but theta is |
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340 | limited to +/- 90, and points are cos-weighted. Jitter in phi is |
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341 | uniform in weight along a line of latitude. With small theta and |
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342 | phi ranging over +/- 180 this forms a wobbling disk. With small |
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343 | phi and theta ranging over +/- 90 this forms a wedge like a slice |
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344 | of an orange. |
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345 | azimuthal_equidistance (Postel) |
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346 | <https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection> |
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347 | Preserves distance from center, and so is an excellent map for |
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348 | representing a bivariate gaussian on the surface. Theta and phi |
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349 | operate identically, cutting wegdes from the antipode of the viewing |
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350 | angle. This unfortunately does not allow free movement in either |
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351 | theta or phi since the orthogonal wobble decreases to 0 as the body |
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352 | rotates through 180 degrees. |
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353 | sinusoidal (Sanson-Flamsteed, Mercator equal-area) |
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354 | <https://en.wikipedia.org/wiki/Sinusoidal_projection> |
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355 | Preserves arc length with latitude, giving bad behaviour at |
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356 | theta near +/- 90. Theta and phi operate somewhat differently, |
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357 | so a system with a-b-c dtheta-dphi-dpsi will not give the same |
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358 | value as one with b-a-c dphi-dtheta-dpsi, as would be the case |
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359 | for azimuthal equidistance. Free movement using theta or phi |
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360 | uniform over +/- 180 will work, but not as well as equirectangular |
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361 | phi, with theta being slightly worse. Computationally it is much |
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362 | cheaper for wide theta-phi meshes since it excludes points which |
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363 | lie outside the sinusoid near theta +/- 90 rather than packing |
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364 | them close together as in equirectangle. Note that the poles |
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365 | will be slightly overweighted for theta > 90 with the circle |
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366 | from theta at 90+dt winding backwards around the pole, overlapping |
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367 | the circle from theta at 90-dt. |
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368 | Guyou (hemisphere-in-a-square) **not weighted** |
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369 | <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection> |
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370 | With tiling, allows rotation in phi or theta through +/- 180, with |
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371 | uniform spacing. Both theta and phi allow free rotation, with wobble |
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372 | in the orthogonal direction reasonably well behaved (though not as |
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373 | good as equirectangular phi). The forward/reverse transformations |
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374 | relies on elliptic integrals that are somewhat expensive, so the |
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375 | behaviour has to be very good to justify the cost and complexity. |
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376 | The weighting function for each point has not yet been computed. |
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377 | Note: run the module *guyou.py* directly and it will show the forward |
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378 | and reverse mappings. |
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379 | azimuthal_equal_area **incomplete** |
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380 | <https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection> |
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381 | Preserves the relative density of the surface patches. Not that |
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382 | useful and not completely implemented |
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383 | Gauss-Kreuger **not implemented** |
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384 | <https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Ellipsoidal_transverse_Mercator> |
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385 | Should allow free movement in theta, but phi is distorted. |
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386 | """ |
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387 | # TODO: try Kent distribution instead of a gaussian warped by projection |
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388 | |
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389 | if projection == 'equirectangular': #define PROJECTION 1 |
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390 | def _project(theta_i, phi_j, psi): |
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391 | latitude, longitude = theta_i, phi_j |
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392 | return latitude, longitude, psi |
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393 | #return Rx(phi_j)*Ry(theta_i) |
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394 | def _weight(theta_i, phi_j, w_i, w_j): |
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395 | return w_i*w_j*abs(cos(radians(theta_i))) |
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396 | elif projection == 'sinusoidal': #define PROJECTION 2 |
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397 | def _project(theta_i, phi_j, psi): |
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398 | latitude = theta_i |
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399 | scale = cos(radians(latitude)) |
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400 | longitude = phi_j/scale if abs(phi_j) < abs(scale)*180 else 0 |
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401 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
---|
402 | return latitude, longitude, psi |
---|
403 | #return Rx(longitude)*Ry(latitude) |
---|
404 | def _project(theta_i, phi_j, w_i, w_j): |
---|
405 | latitude = theta_i |
---|
406 | scale = cos(radians(latitude)) |
---|
407 | active = 1 if abs(phi_j) < abs(scale)*180 else 0 |
---|
408 | return active*w_i*w_j |
---|
409 | elif projection == 'guyou': #define PROJECTION 3 (eventually?) |
---|
410 | def _project(theta_i, phi_j, psi): |
---|
411 | from .guyou import guyou_invert |
---|
412 | #latitude, longitude = guyou_invert([theta_i], [phi_j]) |
---|
413 | longitude, latitude = guyou_invert([phi_j], [theta_i]) |
---|
414 | return latitude, longitude, psi |
---|
415 | #return Rx(longitude[0])*Ry(latitude[0]) |
---|
416 | def _weight(theta_i, phi_j, w_i, w_j): |
---|
417 | return w_i*w_j |
---|
418 | elif projection == 'azimuthal_equidistance': |
---|
419 | # Note that calculates angles for Rz Ry rather than Rx Ry |
---|
420 | def _project(theta_i, phi_j, psi): |
---|
421 | latitude = sqrt(theta_i**2 + phi_j**2) |
---|
422 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
---|
423 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
---|
424 | return latitude, longitude, psi-longitude, 'zyz' |
---|
425 | #R = Rz(longitude)*Ry(latitude)*Rz(psi) |
---|
426 | #return R_to_xyz(R) |
---|
427 | #return Rz(longitude)*Ry(latitude) |
---|
428 | def _weight(theta_i, phi_j, w_i, w_j): |
---|
429 | # Weighting for each point comes from the integral: |
---|
430 | # \int\int I(q, lat, log) sin(lat) dlat dlog |
---|
431 | # We are doing a conformal mapping from disk to sphere, so we need |
---|
432 | # a change of variables g(theta, phi) -> (lat, long): |
---|
433 | # lat, long = sqrt(theta^2 + phi^2), arctan(phi/theta) |
---|
434 | # giving: |
---|
435 | # dtheta dphi = det(J) dlat dlong |
---|
436 | # where J is the jacobian from the partials of g. Using |
---|
437 | # R = sqrt(theta^2 + phi^2), |
---|
438 | # then |
---|
439 | # J = [[x/R, Y/R], -y/R^2, x/R^2]] |
---|
440 | # and |
---|
441 | # det(J) = 1/R |
---|
442 | # with the final integral being: |
---|
443 | # \int\int I(q, theta, phi) sin(R)/R dtheta dphi |
---|
444 | # |
---|
445 | # This does approximately the right thing, decreasing the weight |
---|
446 | # of each point as you go farther out on the disk, but it hasn't |
---|
447 | # yet been checked against the 1D integral results. Prior |
---|
448 | # to declaring this "good enough" and checking that integrals |
---|
449 | # work in practice, we will examine alternative mappings. |
---|
450 | # |
---|
451 | # The issue is that the mapping does not support the case of free |
---|
452 | # rotation about a single axis correctly, with a small deviation |
---|
453 | # in the orthogonal axis independent of the first axis. Like the |
---|
454 | # usual polar coordiates integration, the integrated sections |
---|
455 | # form wedges, though at least in this case the wedge cuts through |
---|
456 | # the entire sphere, and treats theta and phi identically. |
---|
457 | latitude = sqrt(theta_i**2 + phi_j**2) |
---|
458 | weight = sin(radians(latitude))/latitude if latitude != 0 else 1 |
---|
459 | return weight*w_i*w_j if latitude < 180 else 0 |
---|
460 | elif projection == 'azimuthal_equal_area': |
---|
461 | # Note that calculates angles for Rz Ry rather than Rx Ry |
---|
462 | def _project(theta_i, phi_j, psi): |
---|
463 | radius = min(1, sqrt(theta_i**2 + phi_j**2)/180) |
---|
464 | latitude = 180-degrees(2*np.arccos(radius)) |
---|
465 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
---|
466 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
---|
467 | return latitude, longitude, psi, "zyz" |
---|
468 | #R = Rz(longitude)*Ry(latitude)*Rz(psi) |
---|
469 | #return R_to_xyz(R) |
---|
470 | #return Rz(longitude)*Ry(latitude) |
---|
471 | def _weight(theta_i, phi_j, w_i, w_j): |
---|
472 | latitude = sqrt(theta_i**2 + phi_j**2) |
---|
473 | weight = sin(radians(latitude))/latitude if latitude != 0 else 1 |
---|
474 | return weight*w_i*w_j if latitude < 180 else 0 |
---|
475 | else: |
---|
476 | raise ValueError("unknown projection %r"%projection) |
---|
477 | |
---|
478 | return _project, _weight |
---|
479 | |
---|
480 | def R_to_xyz(R): |
---|
481 | """ |
---|
482 | Return phi, theta, psi Tait-Bryan angles corresponding to the given rotation matrix. |
---|
483 | |
---|
484 | Extracting Euler Angles from a Rotation Matrix |
---|
485 | Mike Day, Insomniac Games |
---|
486 | https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2012/07/euler-angles1.pdf |
---|
487 | Based on: Shoemakeâs "Euler Angle Conversion", Graphics Gems IV, pp. 222-229 |
---|
488 | """ |
---|
489 | phi = np.arctan2(R[1, 2], R[2, 2]) |
---|
490 | theta = np.arctan2(-R[0, 2], np.sqrt(R[0, 0]**2 + R[0, 1]**2)) |
---|
491 | psi = np.arctan2(R[0, 1], R[0, 0]) |
---|
492 | return np.degrees(phi), np.degrees(theta), np.degrees(psi) |
---|
493 | |
---|
494 | def draw_mesh(axes, view, jitter, radius=1.2, n=11, dist='gaussian', |
---|
495 | projection='equirectangular'): |
---|
496 | """ |
---|
497 | Draw the dispersion mesh showing the theta-phi orientations at which |
---|
498 | the model will be evaluated. |
---|
499 | """ |
---|
500 | |
---|
501 | _project, _weight = get_projection(projection) |
---|
502 | def _rotate(theta, phi, z): |
---|
503 | dview = _project(theta, phi, 0.) |
---|
504 | if len(dview) == 4: # hack for zyz coords |
---|
505 | return Rz(dview[1])*Ry(dview[0])*z |
---|
506 | else: |
---|
507 | return Rx(dview[1])*Ry(dview[0])*z |
---|
508 | |
---|
509 | |
---|
510 | dist_x = np.linspace(-1, 1, n) |
---|
511 | weights = np.ones_like(dist_x) |
---|
512 | if dist == 'gaussian': |
---|
513 | dist_x *= 3 |
---|
514 | weights = exp(-0.5*dist_x**2) |
---|
515 | elif dist == 'rectangle': |
---|
516 | # Note: uses sasmodels ridiculous definition of rectangle width |
---|
517 | dist_x *= sqrt(3) |
---|
518 | elif dist == 'uniform': |
---|
519 | pass |
---|
520 | else: |
---|
521 | raise ValueError("expected dist to be gaussian, rectangle or uniform") |
---|
522 | |
---|
523 | # mesh in theta, phi formed by rotating z |
---|
524 | dtheta, dphi, dpsi = jitter |
---|
525 | z = np.matrix([[0], [0], [radius]]) |
---|
526 | points = np.hstack([_rotate(theta_i, phi_j, z) |
---|
527 | for theta_i in dtheta*dist_x |
---|
528 | for phi_j in dphi*dist_x]) |
---|
529 | dist_w = np.array([_weight(theta_i, phi_j, w_i, w_j) |
---|
530 | for w_i, theta_i in zip(weights, dtheta*dist_x) |
---|
531 | for w_j, phi_j in zip(weights, dphi*dist_x)]) |
---|
532 | #print(max(dist_w), min(dist_w), min(dist_w[dist_w > 0])) |
---|
533 | points = points[:, dist_w > 0] |
---|
534 | dist_w = dist_w[dist_w > 0] |
---|
535 | dist_w /= max(dist_w) |
---|
536 | |
---|
537 | # rotate relative to beam |
---|
538 | points = orient_relative_to_beam(view, points) |
---|
539 | |
---|
540 | x, y, z = [np.array(v).flatten() for v in points] |
---|
541 | #plt.figure(2); plt.clf(); plt.hist(z, bins=np.linspace(-1, 1, 51)) |
---|
542 | axes.scatter(x, y, z, c=dist_w, marker='o', vmin=0., vmax=1.) |
---|
543 | |
---|
544 | def draw_labels(axes, view, jitter, text): |
---|
545 | """ |
---|
546 | Draw text at a particular location. |
---|
547 | """ |
---|
548 | labels, locations, orientations = zip(*text) |
---|
549 | px, py, pz = zip(*locations) |
---|
550 | dx, dy, dz = zip(*orientations) |
---|
551 | |
---|
552 | px, py, pz = transform_xyz(view, jitter, px, py, pz) |
---|
553 | dx, dy, dz = transform_xyz(view, jitter, dx, dy, dz) |
---|
554 | |
---|
555 | # TODO: zdir for labels is broken, and labels aren't appearing. |
---|
556 | for label, p, zdir in zip(labels, zip(px, py, pz), zip(dx, dy, dz)): |
---|
557 | zdir = np.asarray(zdir).flatten() |
---|
558 | axes.text(p[0], p[1], p[2], label, zdir=zdir) |
---|
559 | |
---|
560 | # Definition of rotation matrices comes from wikipedia: |
---|
561 | # https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations |
---|
562 | def Rx(angle): |
---|
563 | """Construct a matrix to rotate points about *x* by *angle* degrees.""" |
---|
564 | angle = radians(angle) |
---|
565 | rot = [[1, 0, 0], |
---|
566 | [0, +cos(angle), -sin(angle)], |
---|
567 | [0, +sin(angle), +cos(angle)]] |
---|
568 | return np.matrix(rot) |
---|
569 | |
---|
570 | def Ry(angle): |
---|
571 | """Construct a matrix to rotate points about *y* by *angle* degrees.""" |
---|
572 | angle = radians(angle) |
---|
573 | rot = [[+cos(angle), 0, +sin(angle)], |
---|
574 | [0, 1, 0], |
---|
575 | [-sin(angle), 0, +cos(angle)]] |
---|
576 | return np.matrix(rot) |
---|
577 | |
---|
578 | def Rz(angle): |
---|
579 | """Construct a matrix to rotate points about *z* by *angle* degrees.""" |
---|
580 | angle = radians(angle) |
---|
581 | rot = [[+cos(angle), -sin(angle), 0], |
---|
582 | [+sin(angle), +cos(angle), 0], |
---|
583 | [0, 0, 1]] |
---|
584 | return np.matrix(rot) |
---|
585 | |
---|
586 | def transform_xyz(view, jitter, x, y, z): |
---|
587 | """ |
---|
588 | Send a set of (x,y,z) points through the jitter and view transforms. |
---|
589 | """ |
---|
590 | x, y, z = [np.asarray(v) for v in (x, y, z)] |
---|
591 | shape = x.shape |
---|
592 | points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) |
---|
593 | points = apply_jitter(jitter, points) |
---|
594 | points = orient_relative_to_beam(view, points) |
---|
595 | x, y, z = [np.array(v).reshape(shape) for v in points] |
---|
596 | return x, y, z |
---|
597 | |
---|
598 | def apply_jitter(jitter, points): |
---|
599 | """ |
---|
600 | Apply the jitter transform to a set of points. |
---|
601 | |
---|
602 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
603 | """ |
---|
604 | if jitter is None: |
---|
605 | return points |
---|
606 | # Hack to deal with the fact that azimuthal_equidistance uses euler angles |
---|
607 | if len(jitter) == 4: |
---|
608 | dtheta, dphi, dpsi, _ = jitter |
---|
609 | points = Rz(dphi)*Ry(dtheta)*Rz(dpsi)*points |
---|
610 | else: |
---|
611 | dtheta, dphi, dpsi = jitter |
---|
612 | points = Rx(dphi)*Ry(dtheta)*Rz(dpsi)*points |
---|
613 | return points |
---|
614 | |
---|
615 | def orient_relative_to_beam(view, points): |
---|
616 | """ |
---|
617 | Apply the view transform to a set of points. |
---|
618 | |
---|
619 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
620 | """ |
---|
621 | theta, phi, psi = view |
---|
622 | points = Rz(phi)*Ry(theta)*Rz(psi)*points # viewing angle |
---|
623 | #points = Rz(psi)*Ry(pi/2-theta)*Rz(phi)*points # 1-D integration angles |
---|
624 | #points = Rx(phi)*Ry(theta)*Rz(psi)*points # angular dispersion angle |
---|
625 | return points |
---|
626 | |
---|
627 | def orient_relative_to_beam_quaternion(view, points): |
---|
628 | """ |
---|
629 | Apply the view transform to a set of points. |
---|
630 | |
---|
631 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
632 | |
---|
633 | This variant uses quaternions rather than rotation matrices for the |
---|
634 | computation. It works but it is not used because it doesn't solve |
---|
635 | any problems. The challenge of mapping theta/phi/psi to SO(3) does |
---|
636 | not disappear by calculating the transform differently. |
---|
637 | """ |
---|
638 | theta, phi, psi = view |
---|
639 | x, y, z = [1, 0, 0], [0, 1, 0], [0, 0, 1] |
---|
640 | q = Quaternion(1, [0, 0, 0]) |
---|
641 | ## Compose a rotation about the three axes by rotating |
---|
642 | ## the unit vectors before applying the rotation. |
---|
643 | #q = Quaternion.from_angle_axis(theta, q.rot(x)) * q |
---|
644 | #q = Quaternion.from_angle_axis(phi, q.rot(y)) * q |
---|
645 | #q = Quaternion.from_angle_axis(psi, q.rot(z)) * q |
---|
646 | ## The above turns out to be equivalent to reversing |
---|
647 | ## the order of application, so ignore it and use below. |
---|
648 | q = q * Quaternion.from_angle_axis(theta, x) |
---|
649 | q = q * Quaternion.from_angle_axis(phi, y) |
---|
650 | q = q * Quaternion.from_angle_axis(psi, z) |
---|
651 | ## Reverse the order by post-multiply rather than pre-multiply |
---|
652 | #q = Quaternion.from_angle_axis(theta, x) * q |
---|
653 | #q = Quaternion.from_angle_axis(phi, y) * q |
---|
654 | #q = Quaternion.from_angle_axis(psi, z) * q |
---|
655 | #print("axes psi", q.rot(np.matrix([x, y, z]).T)) |
---|
656 | return q.rot(points) |
---|
657 | #orient_relative_to_beam = orient_relative_to_beam_quaternion |
---|
658 | |
---|
659 | # Simple stand-alone quaternion class |
---|
660 | import numpy as np |
---|
661 | from copy import copy |
---|
662 | class Quaternion(object): |
---|
663 | def __init__(self, w, r): |
---|
664 | self.w = w |
---|
665 | self.r = np.asarray(r, dtype='d') |
---|
666 | @staticmethod |
---|
667 | def from_angle_axis(theta, r): |
---|
668 | theta = np.radians(theta)/2 |
---|
669 | r = np.asarray(r) |
---|
670 | w = np.cos(theta) |
---|
671 | r = np.sin(theta)*r/np.dot(r,r) |
---|
672 | return Quaternion(w, r) |
---|
673 | def __mul__(self, other): |
---|
674 | if isinstance(other, Quaternion): |
---|
675 | w = self.w*other.w - np.dot(self.r, other.r) |
---|
676 | r = self.w*other.r + other.w*self.r + np.cross(self.r, other.r) |
---|
677 | return Quaternion(w, r) |
---|
678 | def rot(self, v): |
---|
679 | v = np.asarray(v).T |
---|
680 | use_transpose = (v.shape[-1] != 3) |
---|
681 | if use_transpose: v = v.T |
---|
682 | v = v + np.cross(2*self.r, np.cross(self.r, v) + self.w*v) |
---|
683 | #v = v + 2*self.w*np.cross(self.r, v) + np.cross(2*self.r, np.cross(self.r, v)) |
---|
684 | if use_transpose: v = v.T |
---|
685 | return v.T |
---|
686 | def conj(self): |
---|
687 | return Quaternion(self.w, -self.r) |
---|
688 | def inv(self): |
---|
689 | return self.conj()/self.norm()**2 |
---|
690 | def norm(self): |
---|
691 | return np.sqrt(self.w**2 + np.sum(self.r**2)) |
---|
692 | def __str__(self): |
---|
693 | return "%g%+gi%+gj%+gk"%(self.w, self.r[0], self.r[1], self.r[2]) |
---|
694 | def test_qrot(): |
---|
695 | # Define rotation of 60 degrees around an axis in y-z that is 60 degrees from y. |
---|
696 | # The rotation axis is determined by rotating the point [0, 1, 0] about x. |
---|
697 | ax = Quaternion.from_angle_axis(60, [1, 0, 0]).rot([0, 1, 0]) |
---|
698 | q = Quaternion.from_angle_axis(60, ax) |
---|
699 | # Set the point to be rotated, and its expected rotated position. |
---|
700 | p = [1, -1, 2] |
---|
701 | target = [(10+4*np.sqrt(3))/8, (1+2*np.sqrt(3))/8, (14-3*np.sqrt(3))/8] |
---|
702 | #print(q, q.rot(p) - target) |
---|
703 | assert max(abs(q.rot(p) - target)) < 1e-14 |
---|
704 | #test_qrot() |
---|
705 | #import sys; sys.exit() |
---|
706 | |
---|
707 | # translate between number of dimension of dispersity and the number of |
---|
708 | # points along each dimension. |
---|
709 | PD_N_TABLE = { |
---|
710 | (0, 0, 0): (0, 0, 0), # 0 |
---|
711 | (1, 0, 0): (100, 0, 0), # 100 |
---|
712 | (0, 1, 0): (0, 100, 0), |
---|
713 | (0, 0, 1): (0, 0, 100), |
---|
714 | (1, 1, 0): (30, 30, 0), # 900 |
---|
715 | (1, 0, 1): (30, 0, 30), |
---|
716 | (0, 1, 1): (0, 30, 30), |
---|
717 | (1, 1, 1): (15, 15, 15), # 3375 |
---|
718 | } |
---|
719 | |
---|
720 | def clipped_range(data, portion=1.0, mode='central'): |
---|
721 | """ |
---|
722 | Determine range from data. |
---|
723 | |
---|
724 | If *portion* is 1, use full range, otherwise use the center of the range |
---|
725 | or the top of the range, depending on whether *mode* is 'central' or 'top'. |
---|
726 | """ |
---|
727 | if portion == 1.0: |
---|
728 | return data.min(), data.max() |
---|
729 | elif mode == 'central': |
---|
730 | data = np.sort(data.flatten()) |
---|
731 | offset = int(portion*len(data)/2 + 0.5) |
---|
732 | return data[offset], data[-offset] |
---|
733 | elif mode == 'top': |
---|
734 | data = np.sort(data.flatten()) |
---|
735 | offset = int(portion*len(data) + 0.5) |
---|
736 | return data[offset], data[-1] |
---|
737 | |
---|
738 | def draw_scattering(calculator, axes, view, jitter, dist='gaussian'): |
---|
739 | """ |
---|
740 | Plot the scattering for the particular view. |
---|
741 | |
---|
742 | *calculator* is returned from :func:`build_model`. *axes* are the 3D axes |
---|
743 | on which the data will be plotted. *view* and *jitter* are the current |
---|
744 | orientation and orientation dispersity. *dist* is one of the sasmodels |
---|
745 | weight distributions. |
---|
746 | """ |
---|
747 | if dist == 'uniform': # uniform is not yet in this branch |
---|
748 | dist, scale = 'rectangle', 1/sqrt(3) |
---|
749 | else: |
---|
750 | scale = 1 |
---|
751 | |
---|
752 | # add the orientation parameters to the model parameters |
---|
753 | theta, phi, psi = view |
---|
754 | theta_pd, phi_pd, psi_pd = [scale*v for v in jitter] |
---|
755 | theta_pd_n, phi_pd_n, psi_pd_n = PD_N_TABLE[(theta_pd > 0, phi_pd > 0, psi_pd > 0)] |
---|
756 | ## increase pd_n for testing jitter integration rather than simple viz |
---|
757 | #theta_pd_n, phi_pd_n, psi_pd_n = [5*v for v in (theta_pd_n, phi_pd_n, psi_pd_n)] |
---|
758 | |
---|
759 | pars = dict( |
---|
760 | theta=theta, theta_pd=theta_pd, theta_pd_type=dist, theta_pd_n=theta_pd_n, |
---|
761 | phi=phi, phi_pd=phi_pd, phi_pd_type=dist, phi_pd_n=phi_pd_n, |
---|
762 | psi=psi, psi_pd=psi_pd, psi_pd_type=dist, psi_pd_n=psi_pd_n, |
---|
763 | ) |
---|
764 | pars.update(calculator.pars) |
---|
765 | |
---|
766 | # compute the pattern |
---|
767 | qx, qy = calculator._data.x_bins, calculator._data.y_bins |
---|
768 | Iqxy = calculator(**pars).reshape(len(qx), len(qy)) |
---|
769 | |
---|
770 | # scale it and draw it |
---|
771 | Iqxy = np.log(Iqxy) |
---|
772 | if calculator.limits: |
---|
773 | # use limits from orientation (0,0,0) |
---|
774 | vmin, vmax = calculator.limits |
---|
775 | else: |
---|
776 | vmax = Iqxy.max() |
---|
777 | vmin = vmax*10**-7 |
---|
778 | #vmin, vmax = clipped_range(Iqxy, portion=portion, mode='top') |
---|
779 | #vmin, vmax = Iqxy.min(), Iqxy.max() |
---|
780 | #print("range",(vmin,vmax)) |
---|
781 | #qx, qy = np.meshgrid(qx, qy) |
---|
782 | if 0: |
---|
783 | from matplotlib import cm |
---|
784 | level = np.asarray(255*(Iqxy - vmin)/(vmax - vmin), 'i') |
---|
785 | level[level < 0] = 0 |
---|
786 | colors = plt.get_cmap()(level) |
---|
787 | #colors = cm.coolwarm(level) |
---|
788 | #colors = cm.gist_yarg(level) |
---|
789 | #colors = cm.Wistia(level) |
---|
790 | colors[level<=0, 3] = 0. # set floor to transparent |
---|
791 | x, y = np.meshgrid(qx/qx.max(), qy/qy.max()) |
---|
792 | axes.plot_surface(x, y, -1.1*np.ones_like(x), facecolors=colors) |
---|
793 | elif 1: |
---|
794 | axes.contourf(qx/qx.max(), qy/qy.max(), Iqxy, zdir='z', offset=-1.1, |
---|
795 | levels=np.linspace(vmin, vmax, 24)) |
---|
796 | else: |
---|
797 | axes.pcolormesh(qx, qy, Iqxy) |
---|
798 | |
---|
799 | def build_model(model_name, n=150, qmax=0.5, **pars): |
---|
800 | """ |
---|
801 | Build a calculator for the given shape. |
---|
802 | |
---|
803 | *model_name* is any sasmodels model. *n* and *qmax* define an n x n mesh |
---|
804 | on which to evaluate the model. The remaining parameters are stored in |
---|
805 | the returned calculator as *calculator.pars*. They are used by |
---|
806 | :func:`draw_scattering` to set the non-orientation parameters in the |
---|
807 | calculation. |
---|
808 | |
---|
809 | Returns a *calculator* function which takes a dictionary or parameters and |
---|
810 | produces Iqxy. The Iqxy value needs to be reshaped to an n x n matrix |
---|
811 | for plotting. See the :class:`sasmodels.direct_model.DirectModel` class |
---|
812 | for details. |
---|
813 | """ |
---|
814 | from sasmodels.core import load_model_info, build_model as build_sasmodel |
---|
815 | from sasmodels.data import empty_data2D |
---|
816 | from sasmodels.direct_model import DirectModel |
---|
817 | |
---|
818 | model_info = load_model_info(model_name) |
---|
819 | model = build_sasmodel(model_info) #, dtype='double!') |
---|
820 | q = np.linspace(-qmax, qmax, n) |
---|
821 | data = empty_data2D(q, q) |
---|
822 | calculator = DirectModel(data, model) |
---|
823 | |
---|
824 | # stuff the values for non-orientation parameters into the calculator |
---|
825 | calculator.pars = pars.copy() |
---|
826 | calculator.pars.setdefault('backgound', 1e-3) |
---|
827 | |
---|
828 | # fix the data limits so that we can see if the pattern fades |
---|
829 | # under rotation or angular dispersion |
---|
830 | Iqxy = calculator(theta=0, phi=0, psi=0, **calculator.pars) |
---|
831 | Iqxy = np.log(Iqxy) |
---|
832 | vmin, vmax = clipped_range(Iqxy, 0.95, mode='top') |
---|
833 | calculator.limits = vmin, vmax+1 |
---|
834 | |
---|
835 | return calculator |
---|
836 | |
---|
837 | def select_calculator(model_name, n=150, size=(10, 40, 100)): |
---|
838 | """ |
---|
839 | Create a model calculator for the given shape. |
---|
840 | |
---|
841 | *model_name* is one of sphere, cylinder, ellipsoid, triaxial_ellipsoid, |
---|
842 | parallelepiped or bcc_paracrystal. *n* is the number of points to use |
---|
843 | in the q range. *qmax* is chosen based on model parameters for the |
---|
844 | given model to show something intersting. |
---|
845 | |
---|
846 | Returns *calculator* and tuple *size* (a,b,c) giving minor and major |
---|
847 | equitorial axes and polar axis respectively. See :func:`build_model` |
---|
848 | for details on the returned calculator. |
---|
849 | """ |
---|
850 | a, b, c = size |
---|
851 | d_factor = 0.06 # for paracrystal models |
---|
852 | if model_name == 'sphere': |
---|
853 | calculator = build_model('sphere', n=n, radius=c) |
---|
854 | a = b = c |
---|
855 | elif model_name == 'sc_paracrystal': |
---|
856 | a = b = c |
---|
857 | dnn = c |
---|
858 | radius = 0.5*c |
---|
859 | calculator = build_model('sc_paracrystal', n=n, dnn=dnn, |
---|
860 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
861 | background=0) |
---|
862 | elif model_name == 'fcc_paracrystal': |
---|
863 | a = b = c |
---|
864 | # nearest neigbour distance dnn should be 2 radius, but I think the |
---|
865 | # model uses lattice spacing rather than dnn in its calculations |
---|
866 | dnn = 0.5*c |
---|
867 | radius = sqrt(2)/4 * c |
---|
868 | calculator = build_model('fcc_paracrystal', n=n, dnn=dnn, |
---|
869 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
870 | background=0) |
---|
871 | elif model_name == 'bcc_paracrystal': |
---|
872 | a = b = c |
---|
873 | # nearest neigbour distance dnn should be 2 radius, but I think the |
---|
874 | # model uses lattice spacing rather than dnn in its calculations |
---|
875 | dnn = 0.5*c |
---|
876 | radius = sqrt(3)/2 * c |
---|
877 | calculator = build_model('bcc_paracrystal', n=n, dnn=dnn, |
---|
878 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
879 | background=0) |
---|
880 | elif model_name == 'cylinder': |
---|
881 | calculator = build_model('cylinder', n=n, qmax=0.3, radius=b, length=c) |
---|
882 | a = b |
---|
883 | elif model_name == 'ellipsoid': |
---|
884 | calculator = build_model('ellipsoid', n=n, qmax=1.0, |
---|
885 | radius_polar=c, radius_equatorial=b) |
---|
886 | a = b |
---|
887 | elif model_name == 'triaxial_ellipsoid': |
---|
888 | calculator = build_model('triaxial_ellipsoid', n=n, qmax=0.5, |
---|
889 | radius_equat_minor=a, |
---|
890 | radius_equat_major=b, |
---|
891 | radius_polar=c) |
---|
892 | elif model_name == 'parallelepiped': |
---|
893 | calculator = build_model('parallelepiped', n=n, a=a, b=b, c=c) |
---|
894 | else: |
---|
895 | raise ValueError("unknown model %s"%model_name) |
---|
896 | |
---|
897 | return calculator, (a, b, c) |
---|
898 | |
---|
899 | SHAPES = [ |
---|
900 | 'parallelepiped', |
---|
901 | 'sphere', 'ellipsoid', 'triaxial_ellipsoid', |
---|
902 | 'cylinder', |
---|
903 | 'fcc_paracrystal', 'bcc_paracrystal', 'sc_paracrystal', |
---|
904 | ] |
---|
905 | |
---|
906 | DRAW_SHAPES = { |
---|
907 | 'fcc_paracrystal': draw_fcc, |
---|
908 | 'bcc_paracrystal': draw_bcc, |
---|
909 | 'sc_paracrystal': draw_sc, |
---|
910 | 'parallelepiped': draw_parallelepiped, |
---|
911 | } |
---|
912 | |
---|
913 | DISTRIBUTIONS = [ |
---|
914 | 'gaussian', 'rectangle', 'uniform', |
---|
915 | ] |
---|
916 | DIST_LIMITS = { |
---|
917 | 'gaussian': 30, |
---|
918 | 'rectangle': 90/sqrt(3), |
---|
919 | 'uniform': 90, |
---|
920 | } |
---|
921 | |
---|
922 | |
---|
923 | def run(model_name='parallelepiped', size=(10, 40, 100), |
---|
924 | view=(0, 0, 0), jitter=(0, 0, 0), |
---|
925 | dist='gaussian', mesh=30, |
---|
926 | projection='equirectangular'): |
---|
927 | """ |
---|
928 | Show an interactive orientation and jitter demo. |
---|
929 | |
---|
930 | *model_name* is one of: sphere, ellipsoid, triaxial_ellipsoid, |
---|
931 | parallelepiped, cylinder, or sc/fcc/bcc_paracrystal |
---|
932 | |
---|
933 | *size* gives the dimensions (a, b, c) of the shape. |
---|
934 | |
---|
935 | *view* gives the initial view (theta, phi, psi) of the shape. |
---|
936 | |
---|
937 | *view* gives the initial jitter (dtheta, dphi, dpsi) of the shape. |
---|
938 | |
---|
939 | *dist* is the type of dispersition: gaussian, rectangle, or uniform. |
---|
940 | |
---|
941 | *mesh* is the number of points in the dispersion mesh. |
---|
942 | |
---|
943 | *projection* is the map projection to use for the mesh: equirectangular, |
---|
944 | sinusoidal, guyou, azimuthal_equidistance, or azimuthal_equal_area. |
---|
945 | """ |
---|
946 | # projection number according to 1-order position in list, but |
---|
947 | # only 1 and 2 are implemented so far. |
---|
948 | from sasmodels import generate |
---|
949 | generate.PROJECTION = PROJECTIONS.index(projection) + 1 |
---|
950 | if generate.PROJECTION > 2: |
---|
951 | print("*** PROJECTION %s not implemented in scattering function ***"%projection) |
---|
952 | generate.PROJECTION = 2 |
---|
953 | |
---|
954 | # set up calculator |
---|
955 | calculator, size = select_calculator(model_name, n=150, size=size) |
---|
956 | draw_shape = DRAW_SHAPES.get(model_name, draw_parallelepiped) |
---|
957 | #draw_shape = draw_fcc |
---|
958 | |
---|
959 | ## uncomment to set an independent the colour range for every view |
---|
960 | ## If left commented, the colour range is fixed for all views |
---|
961 | calculator.limits = None |
---|
962 | |
---|
963 | PLOT_ENGINE(calculator, draw_shape, size, view, jitter, dist, mesh, projection) |
---|
964 | |
---|
965 | def mpl_plot(calculator, draw_shape, size, view, jitter, dist, mesh, projection): |
---|
966 | import mpl_toolkits.mplot3d # Adds projection='3d' option to subplot |
---|
967 | import matplotlib.pyplot as plt |
---|
968 | from matplotlib.widgets import Slider |
---|
969 | |
---|
970 | ## create the plot window |
---|
971 | #plt.hold(True) |
---|
972 | plt.subplots(num=None, figsize=(5.5, 5.5)) |
---|
973 | plt.set_cmap('gist_earth') |
---|
974 | plt.clf() |
---|
975 | plt.gcf().canvas.set_window_title(projection) |
---|
976 | #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) |
---|
977 | #axes = plt.subplot(gs[0], projection='3d') |
---|
978 | axes = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') |
---|
979 | try: # CRUFT: not all versions of matplotlib accept 'square' 3d projection |
---|
980 | axes.axis('square') |
---|
981 | except Exception: |
---|
982 | pass |
---|
983 | |
---|
984 | #axcolor = {'facecolor': 'lightgoldenrodyellow'} |
---|
985 | axcolor = {} |
---|
986 | |
---|
987 | ## add control widgets to plot |
---|
988 | axes_theta = plt.axes([0.1, 0.15, 0.45, 0.04], **axcolor) |
---|
989 | axes_phi = plt.axes([0.1, 0.1, 0.45, 0.04], **axcolor) |
---|
990 | axes_psi = plt.axes([0.1, 0.05, 0.45, 0.04], **axcolor) |
---|
991 | stheta = Slider(axes_theta, u'Ξ', -90, 90, valinit=0) |
---|
992 | sphi = Slider(axes_phi, u'Ï', -180, 180, valinit=0) |
---|
993 | spsi = Slider(axes_psi, u'Ï', -180, 180, valinit=0) |
---|
994 | |
---|
995 | axes_dtheta = plt.axes([0.75, 0.15, 0.15, 0.04], **axcolor) |
---|
996 | axes_dphi = plt.axes([0.75, 0.1, 0.15, 0.04], **axcolor) |
---|
997 | axes_dpsi = plt.axes([0.75, 0.05, 0.15, 0.04], **axcolor) |
---|
998 | # Note: using ridiculous definition of rectangle distribution, whose width |
---|
999 | # in sasmodels is sqrt(3) times the given width. Divide by sqrt(3) to keep |
---|
1000 | # the maximum width to 90. |
---|
1001 | dlimit = DIST_LIMITS[dist] |
---|
1002 | sdtheta = Slider(axes_dtheta, u'ÎΞ', 0, 2*dlimit, valinit=0) |
---|
1003 | sdphi = Slider(axes_dphi, u'ÎÏ', 0, 2*dlimit, valinit=0) |
---|
1004 | sdpsi = Slider(axes_dpsi, u'ÎÏ', 0, 2*dlimit, valinit=0) |
---|
1005 | |
---|
1006 | ## initial view and jitter |
---|
1007 | theta, phi, psi = view |
---|
1008 | stheta.set_val(theta) |
---|
1009 | sphi.set_val(phi) |
---|
1010 | spsi.set_val(psi) |
---|
1011 | dtheta, dphi, dpsi = jitter |
---|
1012 | sdtheta.set_val(dtheta) |
---|
1013 | sdphi.set_val(dphi) |
---|
1014 | sdpsi.set_val(dpsi) |
---|
1015 | |
---|
1016 | ## callback to draw the new view |
---|
1017 | def update(val, axis=None): |
---|
1018 | view = stheta.val, sphi.val, spsi.val |
---|
1019 | jitter = sdtheta.val, sdphi.val, sdpsi.val |
---|
1020 | # set small jitter as 0 if multiple pd dims |
---|
1021 | dims = sum(v > 0 for v in jitter) |
---|
1022 | limit = [0, 0.5, 5, 5][dims] |
---|
1023 | jitter = [0 if v < limit else v for v in jitter] |
---|
1024 | axes.cla() |
---|
1025 | |
---|
1026 | ## Visualize as person on globe |
---|
1027 | #draw_sphere(axes) |
---|
1028 | #draw_person_on_sphere(axes, view) |
---|
1029 | |
---|
1030 | ## Move beam instead of shape |
---|
1031 | #draw_beam(axes, -view[:2]) |
---|
1032 | #draw_jitter(axes, (0,0,0), (0,0,0), views=3) |
---|
1033 | |
---|
1034 | ## Move shape and draw scattering |
---|
1035 | draw_beam(axes, (0, 0), alpha=1.) |
---|
1036 | draw_jitter(axes, view, jitter, dist=dist, size=size, alpha=1., |
---|
1037 | draw_shape=draw_shape, projection=projection, views=3) |
---|
1038 | draw_mesh(axes, view, jitter, dist=dist, n=mesh, projection=projection) |
---|
1039 | draw_scattering(calculator, axes, view, jitter, dist=dist) |
---|
1040 | |
---|
1041 | plt.gcf().canvas.draw() |
---|
1042 | |
---|
1043 | ## bind control widgets to view updater |
---|
1044 | stheta.on_changed(lambda v: update(v, 'theta')) |
---|
1045 | sphi.on_changed(lambda v: update(v, 'phi')) |
---|
1046 | spsi.on_changed(lambda v: update(v, 'psi')) |
---|
1047 | sdtheta.on_changed(lambda v: update(v, 'dtheta')) |
---|
1048 | sdphi.on_changed(lambda v: update(v, 'dphi')) |
---|
1049 | sdpsi.on_changed(lambda v: update(v, 'dpsi')) |
---|
1050 | |
---|
1051 | ## initialize view |
---|
1052 | update(None, 'phi') |
---|
1053 | |
---|
1054 | ## go interactive |
---|
1055 | plt.show() |
---|
1056 | |
---|
1057 | |
---|
1058 | def map_colors(z, kw): |
---|
1059 | from matplotlib import cm |
---|
1060 | |
---|
1061 | cmap = kw.pop('cmap', cm.coolwarm) |
---|
1062 | alpha = kw.pop('alpha', None) |
---|
1063 | vmin = kw.pop('vmin', z.min()) |
---|
1064 | vmax = kw.pop('vmax', z.max()) |
---|
1065 | c = kw.pop('c', None) |
---|
1066 | color = kw.pop('color', c) |
---|
1067 | if color is None: |
---|
1068 | znorm = ((z - vmin) / (vmax - vmin)).clip(0, 1) |
---|
1069 | color = cmap(znorm) |
---|
1070 | elif isinstance(color, np.ndarray) and color.shape == z.shape: |
---|
1071 | color = cmap(color) |
---|
1072 | if alpha is None: |
---|
1073 | if isinstance(color, np.ndarray): |
---|
1074 | color = color[..., :3] |
---|
1075 | else: |
---|
1076 | color[..., 3] = alpha |
---|
1077 | kw['color'] = color |
---|
1078 | |
---|
1079 | def make_vec(*args): |
---|
1080 | #return [np.asarray(v, 'd').flatten() for v in args] |
---|
1081 | return [np.asarray(v, 'd') for v in args] |
---|
1082 | |
---|
1083 | def make_image(z, kw): |
---|
1084 | import PIL.Image |
---|
1085 | from matplotlib import cm |
---|
1086 | |
---|
1087 | cmap = kw.pop('cmap', cm.coolwarm) |
---|
1088 | |
---|
1089 | znorm = (z-z.min())/z.ptp() |
---|
1090 | c = cmap(znorm) |
---|
1091 | c = c[..., :3] |
---|
1092 | rgb = np.asarray(c*255, 'u1') |
---|
1093 | image = PIL.Image.fromarray(rgb, mode='RGB') |
---|
1094 | return image |
---|
1095 | |
---|
1096 | |
---|
1097 | _IPV_MARKERS = { |
---|
1098 | 'o': 'sphere', |
---|
1099 | } |
---|
1100 | _IPV_COLORS = { |
---|
1101 | 'w': 'white', |
---|
1102 | 'k': 'black', |
---|
1103 | 'c': 'cyan', |
---|
1104 | 'm': 'magenta', |
---|
1105 | 'y': 'yellow', |
---|
1106 | 'r': 'red', |
---|
1107 | 'g': 'green', |
---|
1108 | 'b': 'blue', |
---|
1109 | } |
---|
1110 | def ipv_fix_color(kw): |
---|
1111 | alpha = kw.pop('alpha', None) |
---|
1112 | color = kw.get('color', None) |
---|
1113 | if isinstance(color, str): |
---|
1114 | color = _IPV_COLORS.get(color, color) |
---|
1115 | kw['color'] = color |
---|
1116 | if alpha is not None: |
---|
1117 | color = kw['color'] |
---|
1118 | #TODO: convert color to [r, g, b, a] if not already |
---|
1119 | if isinstance(color, (tuple, list)): |
---|
1120 | if len(color) == 3: |
---|
1121 | color = (color[0], color[1], color[2], alpha) |
---|
1122 | else: |
---|
1123 | color = (color[0], color[1], color[2], alpha*color[3]) |
---|
1124 | color = np.array(color) |
---|
1125 | if isinstance(color, np.ndarray) and color.shape[-1] == 4: |
---|
1126 | color[..., 3] = alpha |
---|
1127 | kw['color'] = color |
---|
1128 | |
---|
1129 | def ipv_set_transparency(kw, obj): |
---|
1130 | color = kw.get('color', None) |
---|
1131 | if (isinstance(color, np.ndarray) |
---|
1132 | and color.shape[-1] == 4 |
---|
1133 | and (color[..., 3] != 1.0).any()): |
---|
1134 | obj.material.transparent = True |
---|
1135 | obj.material.side = "FrontSide" |
---|
1136 | |
---|
1137 | def ipv_axes(): |
---|
1138 | import ipyvolume as ipv |
---|
1139 | |
---|
1140 | class Plotter: |
---|
1141 | # transparency can be achieved by setting the following: |
---|
1142 | # mesh.color = [r, g, b, alpha] |
---|
1143 | # mesh.material.transparent = True |
---|
1144 | # mesh.material.side = "FrontSide" |
---|
1145 | # smooth(ish) rotation can be achieved by setting: |
---|
1146 | # slide.continuous_update = True |
---|
1147 | # figure.animation = 0. |
---|
1148 | # mesh.material.x = x |
---|
1149 | # mesh.material.y = y |
---|
1150 | # mesh.material.z = z |
---|
1151 | # maybe need to synchronize update of x/y/z to avoid shimmy when moving |
---|
1152 | def plot(self, x, y, z, **kw): |
---|
1153 | ipv_fix_color(kw) |
---|
1154 | x, y, z = make_vec(x, y, z) |
---|
1155 | ipv.plot(x, y, z, **kw) |
---|
1156 | def plot_surface(self, x, y, z, **kw): |
---|
1157 | facecolors = kw.pop('facecolors', None) |
---|
1158 | if facecolors is not None: |
---|
1159 | kw['color'] = facecolors |
---|
1160 | ipv_fix_color(kw) |
---|
1161 | x, y, z = make_vec(x, y, z) |
---|
1162 | h = ipv.plot_surface(x, y, z, **kw) |
---|
1163 | ipv_set_transparency(kw, h) |
---|
1164 | #h.material.side = "DoubleSide" |
---|
1165 | return h |
---|
1166 | def plot_trisurf(self, x, y, triangles=None, Z=None, **kw): |
---|
1167 | kw.pop('linewidth', None) |
---|
1168 | ipv_fix_color(kw) |
---|
1169 | x, y, z = make_vec(x, y, Z) |
---|
1170 | if triangles is not None: |
---|
1171 | triangles = np.asarray(triangles) |
---|
1172 | h = ipv.plot_trisurf(x, y, z, triangles=triangles, **kw) |
---|
1173 | ipv_set_transparency(kw, h) |
---|
1174 | return h |
---|
1175 | def scatter(self, x, y, z, **kw): |
---|
1176 | x, y, z = make_vec(x, y, z) |
---|
1177 | map_colors(z, kw) |
---|
1178 | marker = kw.get('marker', None) |
---|
1179 | kw['marker'] = _IPV_MARKERS.get(marker, marker) |
---|
1180 | h = ipv.scatter(x, y, z, **kw) |
---|
1181 | ipv_set_transparency(kw, h) |
---|
1182 | return h |
---|
1183 | def contourf(self, x, y, v, zdir='z', offset=0, levels=None, **kw): |
---|
1184 | # Don't use contour for now (although we might want to later) |
---|
1185 | self.pcolor(x, y, v, zdir='z', offset=offset, **kw) |
---|
1186 | def pcolor(self, x, y, v, zdir='z', offset=0, **kw): |
---|
1187 | x, y, v = make_vec(x, y, v) |
---|
1188 | image = make_image(v, kw) |
---|
1189 | xmin, xmax = x.min(), x.max() |
---|
1190 | ymin, ymax = y.min(), y.max() |
---|
1191 | x = np.array([[xmin, xmax], [xmin, xmax]]) |
---|
1192 | y = np.array([[ymin, ymin], [ymax, ymax]]) |
---|
1193 | z = x*0 + offset |
---|
1194 | u = np.array([[0., 1], [0, 1]]) |
---|
1195 | v = np.array([[0., 0], [1, 1]]) |
---|
1196 | h = ipv.plot_mesh(x, y, z, u=u, v=v, texture=image, wireframe=False) |
---|
1197 | ipv_set_transparency(kw, h) |
---|
1198 | h.material.side = "DoubleSide" |
---|
1199 | return h |
---|
1200 | def text(self, *args, **kw): |
---|
1201 | pass |
---|
1202 | def set_xlim(self, limits): |
---|
1203 | ipv.xlim(*limits) |
---|
1204 | def set_ylim(self, limits): |
---|
1205 | ipv.ylim(*limits) |
---|
1206 | def set_zlim(self, limits): |
---|
1207 | ipv.zlim(*limits) |
---|
1208 | def set_axes_on(self): |
---|
1209 | ipv.style.axis_on() |
---|
1210 | def set_axis_off(self): |
---|
1211 | ipv.style.axes_off() |
---|
1212 | return Plotter() |
---|
1213 | |
---|
1214 | def ipv_plot(calculator, draw_shape, size, view, jitter, dist, mesh, projection): |
---|
1215 | import ipywidgets as widgets |
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1216 | import ipyvolume as ipv |
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1217 | |
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1218 | axes = ipv_axes() |
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1219 | |
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1220 | def draw(view, jitter): |
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1221 | camera = ipv.gcf().camera |
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1222 | #print(ipv.gcf().__dict__.keys()) |
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1223 | #print(dir(ipv.gcf())) |
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1224 | ipv.figure(animation=0.) # no animation when updating object mesh |
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1225 | |
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1226 | # set small jitter as 0 if multiple pd dims |
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1227 | dims = sum(v > 0 for v in jitter) |
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1228 | limit = [0, 0.5, 5, 5][dims] |
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1229 | jitter = [0 if v < limit else v for v in jitter] |
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1230 | |
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1231 | ## Visualize as person on globe |
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1232 | #draw_beam(axes, (0, 0)) |
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1233 | #draw_sphere(axes) |
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1234 | #draw_person_on_sphere(axes, view) |
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1235 | |
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1236 | ## Move beam instead of shape |
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1237 | #draw_beam(axes, view=(-view[0], -view[1])) |
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1238 | #draw_jitter(axes, view=(0,0,0), jitter=(0,0,0)) |
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1239 | |
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1240 | ## Move shape and draw scattering |
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1241 | draw_beam(axes, (0, 0), steps=25) |
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1242 | draw_jitter(axes, view, jitter, dist=dist, size=size, alpha=1.0, |
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1243 | draw_shape=draw_shape, projection=projection) |
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1244 | draw_mesh(axes, view, jitter, dist=dist, n=mesh, radius=0.95, |
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1245 | projection=projection) |
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1246 | draw_scattering(calculator, axes, view, jitter, dist=dist) |
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1247 | |
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1248 | draw_axes(axes, origin=(-1, -1, -1.1)) |
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1249 | ipv.style.box_off() |
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1250 | ipv.style.axes_off() |
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1251 | ipv.xyzlabel(" ", " ", " ") |
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1252 | |
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1253 | ipv.gcf().camera = camera |
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1254 | ipv.show() |
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1255 | |
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1256 | |
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1257 | trange, prange = (-180., 180., 1.), (-180., 180., 1.) |
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1258 | dtrange, dprange = (0., 180., 1.), (0., 180., 1.) |
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1259 | |
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1260 | ## Super simple interfaca, but uses non-ascii variable namese |
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1261 | # Ξ Ï Ï ÎΞ ÎÏ ÎÏ |
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1262 | #def update(**kw): |
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1263 | # view = kw['Ξ'], kw['Ï'], kw['Ï'] |
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1264 | # jitter = kw['ÎΞ'], kw['ÎÏ'], kw['ÎÏ'] |
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1265 | # draw(view, jitter) |
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1266 | #widgets.interact(update, Ξ=trange, Ï=prange, Ï=prange, ÎΞ=dtrange, ÎÏ=dprange, ÎÏ=dprange) |
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1267 | |
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1268 | def update(theta, phi, psi, dtheta, dphi, dpsi): |
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1269 | draw(view=(theta, phi, psi), jitter=(dtheta, dphi, dpsi)) |
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1270 | |
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1271 | def slider(name, slice, init=0.): |
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1272 | return widgets.FloatSlider( |
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1273 | value=init, |
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1274 | min=slice[0], |
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1275 | max=slice[1], |
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1276 | step=slice[2], |
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1277 | description=name, |
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1278 | disabled=False, |
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1279 | #continuous_update=True, |
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1280 | continuous_update=False, |
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1281 | orientation='horizontal', |
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1282 | readout=True, |
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1283 | readout_format='.1f', |
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1284 | ) |
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1285 | theta = slider(u'Ξ', trange, view[0]) |
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1286 | phi = slider(u'Ï', prange, view[1]) |
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1287 | psi = slider(u'Ï', prange, view[2]) |
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1288 | dtheta = slider(u'ÎΞ', dtrange, jitter[0]) |
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1289 | dphi = slider(u'ÎÏ', dprange, jitter[1]) |
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1290 | dpsi = slider(u'ÎÏ', dprange, jitter[2]) |
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1291 | fields = { |
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1292 | 'theta': theta, 'phi': phi, 'psi': psi, |
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1293 | 'dtheta': dtheta, 'dphi': dphi, 'dpsi': dpsi, |
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1294 | } |
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1295 | ui = widgets.HBox([ |
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1296 | widgets.VBox([theta, phi, psi]), |
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1297 | widgets.VBox([dtheta, dphi, dpsi]) |
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1298 | ]) |
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1299 | |
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1300 | out = widgets.interactive_output(update, fields) |
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1301 | display(ui, out) |
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1302 | |
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1303 | |
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1304 | _ENGINES = { |
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1305 | "matplotlib": mpl_plot, |
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1306 | "mpl": mpl_plot, |
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1307 | #"plotly": plotly_plot, |
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1308 | "ipvolume": ipv_plot, |
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1309 | "ipv": ipv_plot, |
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1310 | } |
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1311 | PLOT_ENGINE = _ENGINES["matplotlib"] |
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1312 | def set_plotter(name): |
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1313 | global PLOT_ENGINE |
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1314 | PLOT_ENGINE = _ENGINES[name] |
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1315 | |
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1316 | def main(): |
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1317 | parser = argparse.ArgumentParser( |
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1318 | description="Display jitter", |
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1319 | formatter_class=argparse.ArgumentDefaultsHelpFormatter, |
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1320 | ) |
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1321 | parser.add_argument('-p', '--projection', choices=PROJECTIONS, |
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1322 | default=PROJECTIONS[0], |
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1323 | help='coordinate projection') |
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1324 | parser.add_argument('-s', '--size', type=str, default='10,40,100', |
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1325 | help='a,b,c lengths') |
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1326 | parser.add_argument('-v', '--view', type=str, default='0,0,0', |
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1327 | help='initial view angles') |
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1328 | parser.add_argument('-j', '--jitter', type=str, default='0,0,0', |
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1329 | help='initial angular dispersion') |
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1330 | parser.add_argument('-d', '--distribution', choices=DISTRIBUTIONS, |
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1331 | default=DISTRIBUTIONS[0], |
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1332 | help='jitter distribution') |
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1333 | parser.add_argument('-m', '--mesh', type=int, default=30, |
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1334 | help='#points in theta-phi mesh') |
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1335 | parser.add_argument('shape', choices=SHAPES, nargs='?', default=SHAPES[0], |
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1336 | help='oriented shape') |
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1337 | opts = parser.parse_args() |
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1338 | size = tuple(float(v) for v in opts.size.split(',')) |
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1339 | view = tuple(float(v) for v in opts.view.split(',')) |
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1340 | jitter = tuple(float(v) for v in opts.jitter.split(',')) |
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1341 | run(opts.shape, size=size, view=view, jitter=jitter, |
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1342 | mesh=opts.mesh, dist=opts.distribution, |
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1343 | projection=opts.projection) |
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1344 | |
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1345 | if __name__ == "__main__": |
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1346 | main() |
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