[aa6989b] | 1 | #!/usr/bin/env python |
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[782dd1f] | 2 | """ |
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[0d5a655] | 3 | Jitter Explorer |
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| 4 | =============== |
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| 5 | |
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| 6 | Application to explore orientation angle and angular dispersity. |
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[5f12750] | 7 | |
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| 8 | From the command line:: |
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| 9 | |
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| 10 | # Show docs |
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| 11 | python -m sasmodels.jitter --help |
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| 12 | |
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| 13 | # Guyou projection jitter, uniform over 20 degree theta and 10 in phi |
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| 14 | python -m sasmodels.jitter --projection=guyou --dist=uniform --jitter=20,10,0 |
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| 15 | |
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| 16 | From a jupyter cell:: |
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| 17 | |
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| 18 | import ipyvolume as ipv |
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| 19 | from sasmodels import jitter |
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| 20 | import importlib; importlib.reload(jitter) |
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| 21 | jitter.set_plotter("ipv") |
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| 22 | |
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| 23 | size = (10, 40, 100) |
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| 24 | view = (20, 0, 0) |
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| 25 | |
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| 26 | #size = (15, 15, 100) |
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| 27 | #view = (60, 60, 0) |
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| 28 | |
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| 29 | dview = (0, 0, 0) |
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| 30 | #dview = (5, 5, 0) |
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| 31 | #dview = (15, 180, 0) |
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| 32 | #dview = (180, 15, 0) |
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| 33 | |
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| 34 | projection = 'equirectangular' |
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| 35 | #projection = 'azimuthal_equidistance' |
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| 36 | #projection = 'guyou' |
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| 37 | #projection = 'sinusoidal' |
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| 38 | #projection = 'azimuthal_equal_area' |
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| 39 | |
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| 40 | dist = 'uniform' |
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| 41 | #dist = 'gaussian' |
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| 42 | |
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| 43 | jitter.run(size=size, view=view, jitter=dview, dist=dist, projection=projection) |
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| 44 | #filename = projection+('_theta' if dview[0] == 180 else '_phi' if dview[1] == 180 else '') |
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| 45 | #ipv.savefig(filename+'.png') |
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[782dd1f] | 46 | """ |
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[aa6989b] | 47 | from __future__ import division, print_function |
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| 48 | |
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[bcb5594] | 49 | import argparse |
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| 50 | |
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[782dd1f] | 51 | import numpy as np |
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| 52 | from numpy import pi, cos, sin, sqrt, exp, degrees, radians |
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| 53 | |
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[5f12750] | 54 | def draw_beam(axes, view=(0, 0), alpha=0.5): |
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[aa6989b] | 55 | """ |
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| 56 | Draw the beam going from source at (0, 0, 1) to detector at (0, 0, -1) |
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| 57 | """ |
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[802c412] | 58 | #axes.plot([0,0],[0,0],[1,-1]) |
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[5f12750] | 59 | #axes.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=alpha) |
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[782dd1f] | 60 | |
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[5f12750] | 61 | steps = [6, 6] |
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| 62 | u = np.linspace(0, 2 * np.pi, steps[0]) |
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| 63 | v = np.linspace(-1, 1, steps[1]) |
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[782dd1f] | 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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[8678a34] | 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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[782dd1f] | 75 | |
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[5f12750] | 76 | axes.plot_surface(x, y, z, color='yellow', alpha=alpha) |
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[85190c2] | 77 | |
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[802c412] | 78 | def draw_ellipsoid(axes, size, view, jitter, steps=25, alpha=1): |
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[aa6989b] | 79 | """Draw an ellipsoid.""" |
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[d86f0fc] | 80 | a, b, c = size |
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[782dd1f] | 81 | u = np.linspace(0, 2 * np.pi, steps) |
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| 82 | v = np.linspace(0, np.pi, steps) |
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| 83 | x = a*np.outer(np.cos(u), np.sin(v)) |
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| 84 | y = b*np.outer(np.sin(u), np.sin(v)) |
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| 85 | z = c*np.outer(np.ones_like(u), np.cos(v)) |
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[8678a34] | 86 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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[782dd1f] | 87 | |
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[5f12750] | 88 | axes.plot_surface(x, y, z, color='w', alpha=alpha) |
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[782dd1f] | 89 | |
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[802c412] | 90 | draw_labels(axes, view, jitter, [ |
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[d86f0fc] | 91 | ('c+', [+0, +0, +c], [+1, +0, +0]), |
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| 92 | ('c-', [+0, +0, -c], [+0, +0, -1]), |
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| 93 | ('a+', [+a, +0, +0], [+0, +0, +1]), |
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| 94 | ('a-', [-a, +0, +0], [+0, +0, -1]), |
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| 95 | ('b+', [+0, +b, +0], [-1, +0, +0]), |
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| 96 | ('b-', [+0, -b, +0], [-1, +0, +0]), |
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[8678a34] | 97 | ]) |
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[782dd1f] | 98 | |
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[802c412] | 99 | def draw_sc(axes, size, view, jitter, steps=None, alpha=1): |
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[d86f0fc] | 100 | """Draw points for simple cubic paracrystal""" |
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[58a1be9] | 101 | atoms = _build_sc() |
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[802c412] | 102 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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[58a1be9] | 103 | |
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[802c412] | 104 | def draw_fcc(axes, size, view, jitter, steps=None, alpha=1): |
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[d86f0fc] | 105 | """Draw points for face-centered cubic paracrystal""" |
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[58a1be9] | 106 | # Build the simple cubic crystal |
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| 107 | atoms = _build_sc() |
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| 108 | # Define the centers for each face |
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| 109 | # x planes at -1, 0, 1 have four centers per plane, at +/- 0.5 in y and z |
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| 110 | x, y, z = ( |
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| 111 | [-1]*4 + [0]*4 + [1]*4, |
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| 112 | ([-0.5]*2 + [0.5]*2)*3, |
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| 113 | [-0.5, 0.5]*12, |
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| 114 | ) |
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| 115 | # y and z planes can be generated by substituting x for y and z respectively |
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| 116 | atoms.extend(zip(x+y+z, y+z+x, z+x+y)) |
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[802c412] | 117 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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[58a1be9] | 118 | |
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[802c412] | 119 | def draw_bcc(axes, size, view, jitter, steps=None, alpha=1): |
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[d86f0fc] | 120 | """Draw points for body-centered cubic paracrystal""" |
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[58a1be9] | 121 | # Build the simple cubic crystal |
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| 122 | atoms = _build_sc() |
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| 123 | # Define the centers for each octant |
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| 124 | # x plane at +/- 0.5 have four centers per plane at +/- 0.5 in y and z |
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| 125 | x, y, z = ( |
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| 126 | [-0.5]*4 + [0.5]*4, |
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| 127 | ([-0.5]*2 + [0.5]*2)*2, |
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| 128 | [-0.5, 0.5]*8, |
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| 129 | ) |
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| 130 | atoms.extend(zip(x, y, z)) |
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[802c412] | 131 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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[58a1be9] | 132 | |
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[b3703f5] | 133 | def _draw_crystal(axes, size, view, jitter, atoms=None): |
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[58a1be9] | 134 | atoms, size = np.asarray(atoms, 'd').T, np.asarray(size, 'd') |
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| 135 | x, y, z = atoms*size[:, None] |
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| 136 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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[802c412] | 137 | axes.scatter([x[0]], [y[0]], [z[0]], c='yellow', marker='o') |
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| 138 | axes.scatter(x[1:], y[1:], z[1:], c='r', marker='o') |
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[58a1be9] | 139 | |
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| 140 | def _build_sc(): |
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| 141 | # three planes of 9 dots for x at -1, 0 and 1 |
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| 142 | x, y, z = ( |
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| 143 | [-1]*9 + [0]*9 + [1]*9, |
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| 144 | ([-1]*3 + [0]*3 + [1]*3)*3, |
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| 145 | [-1, 0, 1]*9, |
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| 146 | ) |
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| 147 | atoms = list(zip(x, y, z)) |
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| 148 | #print(list(enumerate(atoms))) |
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[199bd07] | 149 | # Pull the dot at (0, 0, 1) to the front of the list |
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[58a1be9] | 150 | # It will be highlighted in the view |
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[199bd07] | 151 | index = 14 |
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[58a1be9] | 152 | highlight = atoms[index] |
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| 153 | del atoms[index] |
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| 154 | atoms.insert(0, highlight) |
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| 155 | return atoms |
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| 156 | |
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[802c412] | 157 | def draw_parallelepiped(axes, size, view, jitter, steps=None, alpha=1): |
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[aa6989b] | 158 | """Draw a parallelepiped.""" |
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[31a02f1] | 159 | a, b, c = size |
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[d86f0fc] | 160 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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| 161 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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| 162 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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[782dd1f] | 163 | tri = np.array([ |
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| 164 | # counter clockwise triangles |
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| 165 | # z: up/down, x: right/left, y: front/back |
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[d86f0fc] | 166 | [0, 1, 2], [3, 2, 1], # top face |
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| 167 | [6, 5, 4], [5, 6, 7], # bottom face |
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| 168 | [0, 2, 6], [6, 4, 0], # right face |
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| 169 | [1, 5, 7], [7, 3, 1], # left face |
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| 170 | [2, 3, 6], [7, 6, 3], # front face |
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| 171 | [4, 1, 0], [5, 1, 4], # back face |
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[782dd1f] | 172 | ]) |
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| 173 | |
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[8678a34] | 174 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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[5f12750] | 175 | color = [0.6, 1, 0.6] # pale green |
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| 176 | axes.plot_trisurf(x, y, triangles=tri, Z=z, color=color, alpha=alpha) |
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[782dd1f] | 177 | |
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[5f12750] | 178 | # Colour the c+ face of the box. |
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[31a02f1] | 179 | # Since I can't control face color, instead draw a thin box situated just |
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[58a1be9] | 180 | # in front of the "c+" face. Use the c face so that rotations about psi |
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| 181 | # rotate that face. |
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[5f12750] | 182 | if 0: |
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| 183 | #color = [1, 0.6, 0.6] # pink |
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[d86f0fc] | 184 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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| 185 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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| 186 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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[58a1be9] | 187 | x, y, z = transform_xyz(view, jitter, x, y, abs(z)+0.001) |
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[5f12750] | 188 | axes.plot_trisurf(x, y, triangles=tri, Z=z, color=color, alpha=alpha) |
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[31a02f1] | 189 | |
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[802c412] | 190 | draw_labels(axes, view, jitter, [ |
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[d86f0fc] | 191 | ('c+', [+0, +0, +c], [+1, +0, +0]), |
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| 192 | ('c-', [+0, +0, -c], [+0, +0, -1]), |
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| 193 | ('a+', [+a, +0, +0], [+0, +0, +1]), |
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| 194 | ('a-', [-a, +0, +0], [+0, +0, -1]), |
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| 195 | ('b+', [+0, +b, +0], [-1, +0, +0]), |
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| 196 | ('b-', [+0, -b, +0], [-1, +0, +0]), |
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[8678a34] | 197 | ]) |
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[782dd1f] | 198 | |
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[5f12750] | 199 | def draw_sphere(axes, radius=0.5, steps=25): |
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[aa6989b] | 200 | """Draw a sphere""" |
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| 201 | u = np.linspace(0, 2 * np.pi, steps) |
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| 202 | v = np.linspace(0, np.pi, steps) |
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| 203 | |
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| 204 | x = radius * np.outer(np.cos(u), np.sin(v)) |
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| 205 | y = radius * np.outer(np.sin(u), np.sin(v)) |
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| 206 | z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) |
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[5f12750] | 207 | axes.plot_surface(x, y, z, color='w') |
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| 208 | #axes.plot_wireframe(x, y, z) |
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| 209 | |
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| 210 | def draw_person_on_sphere(axes, view, height=0.5, radius=0.5): |
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| 211 | limb_offset = height * 0.05 |
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| 212 | head_radius = height * 0.10 |
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| 213 | head_height = height - head_radius |
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| 214 | neck_length = head_radius * 0.50 |
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| 215 | shoulder_height = height - 2*head_radius - neck_length |
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| 216 | torso_length = shoulder_height * 0.55 |
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| 217 | torso_radius = torso_length * 0.30 |
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| 218 | leg_length = shoulder_height - torso_length |
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| 219 | arm_length = torso_length * 0.90 |
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| 220 | |
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| 221 | def _draw_part(x, z): |
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| 222 | y = np.zeros_like(x) |
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| 223 | xp, yp, zp = transform_xyz(view, None, x, y, z + radius) |
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| 224 | axes.plot(xp, yp, zp, color='k') |
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| 225 | |
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| 226 | # circle for head |
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| 227 | u = np.linspace(0, 2 * np.pi, 40) |
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| 228 | x = head_radius * np.cos(u) |
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| 229 | z = head_radius * np.sin(u) + head_height |
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| 230 | _draw_part(x, z) |
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| 231 | |
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| 232 | # rectangle for body |
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| 233 | x = np.array([-torso_radius, torso_radius, torso_radius, -torso_radius, -torso_radius]) |
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| 234 | z = np.array([0., 0, torso_length, torso_length, 0]) + leg_length |
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| 235 | _draw_part(x, z) |
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| 236 | |
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| 237 | # arms |
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| 238 | x = np.array([-torso_radius - limb_offset, -torso_radius - limb_offset, -torso_radius]) |
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| 239 | z = np.array([shoulder_height - arm_length, shoulder_height, shoulder_height]) |
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| 240 | _draw_part(x, z) |
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| 241 | _draw_part(-x, z) |
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| 242 | |
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| 243 | # legs |
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| 244 | x = np.array([-torso_radius + limb_offset, -torso_radius + limb_offset]) |
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| 245 | z = np.array([0, leg_length]) |
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| 246 | _draw_part(x, z) |
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| 247 | _draw_part(-x, z) |
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| 248 | |
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| 249 | limits = [-radius-height, radius+height] |
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| 250 | axes.set_xlim(limits) |
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| 251 | axes.set_ylim(limits) |
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| 252 | axes.set_zlim(limits) |
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| 253 | axes.set_axis_off() |
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| 254 | |
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| 255 | def draw_jitter(axes, view, jitter, dist='gaussian', |
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| 256 | size=(0.1, 0.4, 1.0), |
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| 257 | draw_shape=draw_parallelepiped, |
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| 258 | projection='equirectangular', |
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| 259 | alpha=0.8, |
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| 260 | views=None): |
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[58a1be9] | 261 | """ |
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| 262 | Represent jitter as a set of shapes at different orientations. |
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| 263 | """ |
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[5f12750] | 264 | project, weight = get_projection(projection) |
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| 265 | |
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[58a1be9] | 266 | # set max diagonal to 0.95 |
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| 267 | scale = 0.95/sqrt(sum(v**2 for v in size)) |
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| 268 | size = tuple(scale*v for v in size) |
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| 269 | |
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| 270 | dtheta, dphi, dpsi = jitter |
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[5f12750] | 271 | base = {'gaussian':3, 'rectangle':sqrt(3), 'uniform':1}[dist] |
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| 272 | def steps(delta): |
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| 273 | limit = base*delta |
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| 274 | if views is None: |
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| 275 | n = max(3, min(25, 2*int(base*delta/15))) |
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| 276 | else: |
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| 277 | n = views |
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| 278 | s = base*delta*np.linspace(-1, 1, n) if delta > 0 else [0] |
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| 279 | return s |
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| 280 | stheta = steps(dtheta) |
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| 281 | sphi = steps(dphi) |
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| 282 | spsi = steps(dpsi) |
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| 283 | #print(stheta, sphi, spsi) |
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| 284 | for theta in stheta: |
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| 285 | for phi in sphi: |
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| 286 | for psi in spsi: |
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| 287 | w = weight(theta, phi, 1.0, 1.0) |
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| 288 | if w > 0: |
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| 289 | dview = project(theta, phi, psi) |
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| 290 | draw_shape(axes, size, view, dview, alpha=alpha) |
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[58a1be9] | 291 | for v in 'xyz': |
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| 292 | a, b, c = size |
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[d86f0fc] | 293 | lim = np.sqrt(a**2 + b**2 + c**2) |
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[802c412] | 294 | getattr(axes, 'set_'+v+'lim')([-lim, lim]) |
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[5f12750] | 295 | #getattr(axes, v+'axis').label.set_text(v) |
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[58a1be9] | 296 | |
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[bcb5594] | 297 | PROJECTIONS = [ |
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[4991048] | 298 | # in order of PROJECTION number; do not change without updating the |
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| 299 | # constants in kernel_iq.c |
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| 300 | 'equirectangular', 'sinusoidal', 'guyou', 'azimuthal_equidistance', |
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[8cfb486] | 301 | 'azimuthal_equal_area', |
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[bcb5594] | 302 | ] |
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[5f12750] | 303 | def get_projection(projection): |
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[bcb5594] | 304 | |
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[5f12750] | 305 | """ |
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[bcb5594] | 306 | jitter projections |
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| 307 | <https://en.wikipedia.org/wiki/List_of_map_projections> |
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| 308 | |
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| 309 | equirectangular (standard latitude-longitude mesh) |
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| 310 | <https://en.wikipedia.org/wiki/Equirectangular_projection> |
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| 311 | Allows free movement in phi (around the equator), but theta is |
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| 312 | limited to +/- 90, and points are cos-weighted. Jitter in phi is |
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| 313 | uniform in weight along a line of latitude. With small theta and |
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| 314 | phi ranging over +/- 180 this forms a wobbling disk. With small |
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| 315 | phi and theta ranging over +/- 90 this forms a wedge like a slice |
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| 316 | of an orange. |
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| 317 | azimuthal_equidistance (Postel) |
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| 318 | <https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection> |
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| 319 | Preserves distance from center, and so is an excellent map for |
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| 320 | representing a bivariate gaussian on the surface. Theta and phi |
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| 321 | operate identically, cutting wegdes from the antipode of the viewing |
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| 322 | angle. This unfortunately does not allow free movement in either |
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| 323 | theta or phi since the orthogonal wobble decreases to 0 as the body |
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| 324 | rotates through 180 degrees. |
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| 325 | sinusoidal (Sanson-Flamsteed, Mercator equal-area) |
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| 326 | <https://en.wikipedia.org/wiki/Sinusoidal_projection> |
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| 327 | Preserves arc length with latitude, giving bad behaviour at |
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| 328 | theta near +/- 90. Theta and phi operate somewhat differently, |
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| 329 | so a system with a-b-c dtheta-dphi-dpsi will not give the same |
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| 330 | value as one with b-a-c dphi-dtheta-dpsi, as would be the case |
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| 331 | for azimuthal equidistance. Free movement using theta or phi |
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| 332 | uniform over +/- 180 will work, but not as well as equirectangular |
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| 333 | phi, with theta being slightly worse. Computationally it is much |
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| 334 | cheaper for wide theta-phi meshes since it excludes points which |
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| 335 | lie outside the sinusoid near theta +/- 90 rather than packing |
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[d73a5ac] | 336 | them close together as in equirectangle. Note that the poles |
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| 337 | will be slightly overweighted for theta > 90 with the circle |
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| 338 | from theta at 90+dt winding backwards around the pole, overlapping |
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| 339 | the circle from theta at 90-dt. |
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[0f65169] | 340 | Guyou (hemisphere-in-a-square) **not weighted** |
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[bcb5594] | 341 | <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection> |
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[0f65169] | 342 | With tiling, allows rotation in phi or theta through +/- 180, with |
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| 343 | uniform spacing. Both theta and phi allow free rotation, with wobble |
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| 344 | in the orthogonal direction reasonably well behaved (though not as |
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| 345 | good as equirectangular phi). The forward/reverse transformations |
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| 346 | relies on elliptic integrals that are somewhat expensive, so the |
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| 347 | behaviour has to be very good to justify the cost and complexity. |
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| 348 | The weighting function for each point has not yet been computed. |
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| 349 | Note: run the module *guyou.py* directly and it will show the forward |
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| 350 | and reverse mappings. |
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[bcb5594] | 351 | azimuthal_equal_area **incomplete** |
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| 352 | <https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection> |
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| 353 | Preserves the relative density of the surface patches. Not that |
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| 354 | useful and not completely implemented |
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| 355 | Gauss-Kreuger **not implemented** |
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| 356 | <https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Ellipsoidal_transverse_Mercator> |
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| 357 | Should allow free movement in theta, but phi is distorted. |
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[aa6989b] | 358 | """ |
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[802c412] | 359 | # TODO: try Kent distribution instead of a gaussian warped by projection |
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| 360 | |
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[4991048] | 361 | if projection == 'equirectangular': #define PROJECTION 1 |
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[5f12750] | 362 | def _project(theta_i, phi_j, psi): |
---|
| 363 | latitude, longitude = theta_i, phi_j |
---|
| 364 | return latitude, longitude, psi |
---|
| 365 | #return Rx(phi_j)*Ry(theta_i) |
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[802c412] | 366 | def _weight(theta_i, phi_j, w_i, w_j): |
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| 367 | return w_i*w_j*abs(cos(radians(theta_i))) |
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[4991048] | 368 | elif projection == 'sinusoidal': #define PROJECTION 2 |
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[5f12750] | 369 | def _project(theta_i, phi_j, psi): |
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[4991048] | 370 | latitude = theta_i |
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| 371 | scale = cos(radians(latitude)) |
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| 372 | longitude = phi_j/scale if abs(phi_j) < abs(scale)*180 else 0 |
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| 373 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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[5f12750] | 374 | return latitude, longitude, psi |
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| 375 | #return Rx(longitude)*Ry(latitude) |
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| 376 | def _project(theta_i, phi_j, w_i, w_j): |
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[4991048] | 377 | latitude = theta_i |
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| 378 | scale = cos(radians(latitude)) |
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[802c412] | 379 | active = 1 if abs(phi_j) < abs(scale)*180 else 0 |
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| 380 | return active*w_i*w_j |
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[4991048] | 381 | elif projection == 'guyou': #define PROJECTION 3 (eventually?) |
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[5f12750] | 382 | def _project(theta_i, phi_j, psi): |
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[802c412] | 383 | from .guyou import guyou_invert |
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[4991048] | 384 | #latitude, longitude = guyou_invert([theta_i], [phi_j]) |
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| 385 | longitude, latitude = guyou_invert([phi_j], [theta_i]) |
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[5f12750] | 386 | return latitude, longitude, psi |
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| 387 | #return Rx(longitude[0])*Ry(latitude[0]) |
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[802c412] | 388 | def _weight(theta_i, phi_j, w_i, w_j): |
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| 389 | return w_i*w_j |
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[5f12750] | 390 | elif projection == 'azimuthal_equidistance': |
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| 391 | # Note that calculates angles for Rz Ry rather than Rx Ry |
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| 392 | def _project(theta_i, phi_j, psi): |
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[87a6591] | 393 | latitude = sqrt(theta_i**2 + phi_j**2) |
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| 394 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
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| 395 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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[5f12750] | 396 | return latitude, longitude, psi-longitude, 'zyz' |
---|
| 397 | #R = Rz(longitude)*Ry(latitude)*Rz(psi) |
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| 398 | #return R_to_xyz(R) |
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| 399 | #return Rz(longitude)*Ry(latitude) |
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[802c412] | 400 | def _weight(theta_i, phi_j, w_i, w_j): |
---|
[5b5ea20] | 401 | # Weighting for each point comes from the integral: |
---|
| 402 | # \int\int I(q, lat, log) sin(lat) dlat dlog |
---|
| 403 | # We are doing a conformal mapping from disk to sphere, so we need |
---|
| 404 | # a change of variables g(theta, phi) -> (lat, long): |
---|
| 405 | # lat, long = sqrt(theta^2 + phi^2), arctan(phi/theta) |
---|
| 406 | # giving: |
---|
| 407 | # dtheta dphi = det(J) dlat dlong |
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| 408 | # where J is the jacobian from the partials of g. Using |
---|
| 409 | # R = sqrt(theta^2 + phi^2), |
---|
| 410 | # then |
---|
| 411 | # J = [[x/R, Y/R], -y/R^2, x/R^2]] |
---|
| 412 | # and |
---|
| 413 | # det(J) = 1/R |
---|
| 414 | # with the final integral being: |
---|
| 415 | # \int\int I(q, theta, phi) sin(R)/R dtheta dphi |
---|
| 416 | # |
---|
| 417 | # This does approximately the right thing, decreasing the weight |
---|
| 418 | # of each point as you go farther out on the disk, but it hasn't |
---|
| 419 | # yet been checked against the 1D integral results. Prior |
---|
| 420 | # to declaring this "good enough" and checking that integrals |
---|
| 421 | # work in practice, we will examine alternative mappings. |
---|
| 422 | # |
---|
| 423 | # The issue is that the mapping does not support the case of free |
---|
| 424 | # rotation about a single axis correctly, with a small deviation |
---|
| 425 | # in the orthogonal axis independent of the first axis. Like the |
---|
| 426 | # usual polar coordiates integration, the integrated sections |
---|
| 427 | # form wedges, though at least in this case the wedge cuts through |
---|
| 428 | # the entire sphere, and treats theta and phi identically. |
---|
[87a6591] | 429 | latitude = sqrt(theta_i**2 + phi_j**2) |
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[802c412] | 430 | weight = sin(radians(latitude))/latitude if latitude != 0 else 1 |
---|
| 431 | return weight*w_i*w_j if latitude < 180 else 0 |
---|
[bcb5594] | 432 | elif projection == 'azimuthal_equal_area': |
---|
[5f12750] | 433 | # Note that calculates angles for Rz Ry rather than Rx Ry |
---|
| 434 | def _project(theta_i, phi_j, psi): |
---|
[802c412] | 435 | radius = min(1, sqrt(theta_i**2 + phi_j**2)/180) |
---|
| 436 | latitude = 180-degrees(2*np.arccos(radius)) |
---|
[87a6591] | 437 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
---|
| 438 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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[5f12750] | 439 | return latitude, longitude, psi, "zyz" |
---|
| 440 | #R = Rz(longitude)*Ry(latitude)*Rz(psi) |
---|
| 441 | #return R_to_xyz(R) |
---|
| 442 | #return Rz(longitude)*Ry(latitude) |
---|
[802c412] | 443 | def _weight(theta_i, phi_j, w_i, w_j): |
---|
[5b5ea20] | 444 | latitude = sqrt(theta_i**2 + phi_j**2) |
---|
[802c412] | 445 | weight = sin(radians(latitude))/latitude if latitude != 0 else 1 |
---|
| 446 | return weight*w_i*w_j if latitude < 180 else 0 |
---|
[b9578fc] | 447 | else: |
---|
[bcb5594] | 448 | raise ValueError("unknown projection %r"%projection) |
---|
[b9578fc] | 449 | |
---|
[5f12750] | 450 | return _project, _weight |
---|
| 451 | |
---|
| 452 | def R_to_xyz(R): |
---|
| 453 | """ |
---|
| 454 | Return phi, theta, psi Tait-Bryan angles corresponding to the given rotation matrix. |
---|
| 455 | |
---|
| 456 | Extracting Euler Angles from a Rotation Matrix |
---|
| 457 | Mike Day, Insomniac Games |
---|
| 458 | https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2012/07/euler-angles1.pdf |
---|
| 459 | Based on: Shoemakeâs âEuler Angle Conversionâ, Graphics Gems IV, pp. 222-229 |
---|
| 460 | """ |
---|
| 461 | phi = np.arctan2(R[1, 2], R[2, 2]) |
---|
| 462 | theta = np.arctan2(-R[0, 2], np.sqrt(R[0, 0]**2 + R[0, 1]**2)) |
---|
| 463 | psi = np.arctan2(R[0, 1], R[0, 0]) |
---|
| 464 | return np.degrees(phi), np.degrees(theta), np.degrees(psi) |
---|
| 465 | |
---|
| 466 | def draw_mesh(axes, view, jitter, radius=1.2, n=11, dist='gaussian', |
---|
| 467 | projection='equirectangular'): |
---|
| 468 | """ |
---|
| 469 | Draw the dispersion mesh showing the theta-phi orientations at which |
---|
| 470 | the model will be evaluated. |
---|
| 471 | """ |
---|
| 472 | |
---|
| 473 | _project, _weight = get_projection(projection) |
---|
| 474 | def _rotate(theta, phi, z): |
---|
| 475 | dview = _project(theta, phi, 0.) |
---|
| 476 | if len(dview) == 4: # hack for zyz coords |
---|
| 477 | return Rz(dview[1])*Ry(dview[0])*z |
---|
| 478 | else: |
---|
| 479 | return Rx(dview[1])*Ry(dview[0])*z |
---|
| 480 | |
---|
| 481 | |
---|
| 482 | dist_x = np.linspace(-1, 1, n) |
---|
| 483 | weights = np.ones_like(dist_x) |
---|
| 484 | if dist == 'gaussian': |
---|
| 485 | dist_x *= 3 |
---|
| 486 | weights = exp(-0.5*dist_x**2) |
---|
| 487 | elif dist == 'rectangle': |
---|
| 488 | # Note: uses sasmodels ridiculous definition of rectangle width |
---|
| 489 | dist_x *= sqrt(3) |
---|
| 490 | elif dist == 'uniform': |
---|
| 491 | pass |
---|
| 492 | else: |
---|
| 493 | raise ValueError("expected dist to be gaussian, rectangle or uniform") |
---|
| 494 | |
---|
[8678a34] | 495 | # mesh in theta, phi formed by rotating z |
---|
[d86f0fc] | 496 | dtheta, dphi, dpsi = jitter |
---|
[8678a34] | 497 | z = np.matrix([[0], [0], [radius]]) |
---|
[5f12750] | 498 | points = np.hstack([_rotate(theta_i, phi_j, z) |
---|
[b3703f5] | 499 | for theta_i in dtheta*dist_x |
---|
| 500 | for phi_j in dphi*dist_x]) |
---|
| 501 | dist_w = np.array([_weight(theta_i, phi_j, w_i, w_j) |
---|
| 502 | for w_i, theta_i in zip(weights, dtheta*dist_x) |
---|
| 503 | for w_j, phi_j in zip(weights, dphi*dist_x)]) |
---|
| 504 | #print(max(dist_w), min(dist_w), min(dist_w[dist_w > 0])) |
---|
| 505 | points = points[:, dist_w > 0] |
---|
| 506 | dist_w = dist_w[dist_w > 0] |
---|
| 507 | dist_w /= max(dist_w) |
---|
[87a6591] | 508 | |
---|
[8678a34] | 509 | # rotate relative to beam |
---|
| 510 | points = orient_relative_to_beam(view, points) |
---|
[782dd1f] | 511 | |
---|
[8678a34] | 512 | x, y, z = [np.array(v).flatten() for v in points] |
---|
[87a6591] | 513 | #plt.figure(2); plt.clf(); plt.hist(z, bins=np.linspace(-1, 1, 51)) |
---|
[b3703f5] | 514 | axes.scatter(x, y, z, c=dist_w, marker='o', vmin=0., vmax=1.) |
---|
[782dd1f] | 515 | |
---|
[802c412] | 516 | def draw_labels(axes, view, jitter, text): |
---|
[aa6989b] | 517 | """ |
---|
| 518 | Draw text at a particular location. |
---|
| 519 | """ |
---|
| 520 | labels, locations, orientations = zip(*text) |
---|
| 521 | px, py, pz = zip(*locations) |
---|
| 522 | dx, dy, dz = zip(*orientations) |
---|
| 523 | |
---|
| 524 | px, py, pz = transform_xyz(view, jitter, px, py, pz) |
---|
| 525 | dx, dy, dz = transform_xyz(view, jitter, dx, dy, dz) |
---|
| 526 | |
---|
| 527 | # TODO: zdir for labels is broken, and labels aren't appearing. |
---|
| 528 | for label, p, zdir in zip(labels, zip(px, py, pz), zip(dx, dy, dz)): |
---|
| 529 | zdir = np.asarray(zdir).flatten() |
---|
[802c412] | 530 | axes.text(p[0], p[1], p[2], label, zdir=zdir) |
---|
[aa6989b] | 531 | |
---|
| 532 | # Definition of rotation matrices comes from wikipedia: |
---|
| 533 | # https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations |
---|
[782dd1f] | 534 | def Rx(angle): |
---|
[aa6989b] | 535 | """Construct a matrix to rotate points about *x* by *angle* degrees.""" |
---|
[802c412] | 536 | angle = radians(angle) |
---|
[b3703f5] | 537 | rot = [[1, 0, 0], |
---|
| 538 | [0, +cos(angle), -sin(angle)], |
---|
| 539 | [0, +sin(angle), +cos(angle)]] |
---|
| 540 | return np.matrix(rot) |
---|
[782dd1f] | 541 | |
---|
| 542 | def Ry(angle): |
---|
[aa6989b] | 543 | """Construct a matrix to rotate points about *y* by *angle* degrees.""" |
---|
[802c412] | 544 | angle = radians(angle) |
---|
[b3703f5] | 545 | rot = [[+cos(angle), 0, +sin(angle)], |
---|
| 546 | [0, 1, 0], |
---|
| 547 | [-sin(angle), 0, +cos(angle)]] |
---|
| 548 | return np.matrix(rot) |
---|
[782dd1f] | 549 | |
---|
| 550 | def Rz(angle): |
---|
[aa6989b] | 551 | """Construct a matrix to rotate points about *z* by *angle* degrees.""" |
---|
[802c412] | 552 | angle = radians(angle) |
---|
[b3703f5] | 553 | rot = [[+cos(angle), -sin(angle), 0], |
---|
| 554 | [+sin(angle), +cos(angle), 0], |
---|
| 555 | [0, 0, 1]] |
---|
| 556 | return np.matrix(rot) |
---|
[782dd1f] | 557 | |
---|
[8678a34] | 558 | def transform_xyz(view, jitter, x, y, z): |
---|
[aa6989b] | 559 | """ |
---|
| 560 | Send a set of (x,y,z) points through the jitter and view transforms. |
---|
| 561 | """ |
---|
[8678a34] | 562 | x, y, z = [np.asarray(v) for v in (x, y, z)] |
---|
| 563 | shape = x.shape |
---|
[d86f0fc] | 564 | points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) |
---|
[8678a34] | 565 | points = apply_jitter(jitter, points) |
---|
| 566 | points = orient_relative_to_beam(view, points) |
---|
| 567 | x, y, z = [np.array(v).reshape(shape) for v in points] |
---|
| 568 | return x, y, z |
---|
| 569 | |
---|
| 570 | def apply_jitter(jitter, points): |
---|
[aa6989b] | 571 | """ |
---|
| 572 | Apply the jitter transform to a set of points. |
---|
| 573 | |
---|
| 574 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
| 575 | """ |
---|
[5f12750] | 576 | if jitter is None: |
---|
| 577 | return points |
---|
| 578 | # Hack to deal with the fact that azimuthal_equidistance uses euler angles |
---|
| 579 | if len(jitter) == 4: |
---|
| 580 | dtheta, dphi, dpsi, _ = jitter |
---|
| 581 | points = Rz(dphi)*Ry(dtheta)*Rz(dpsi)*points |
---|
| 582 | else: |
---|
| 583 | dtheta, dphi, dpsi = jitter |
---|
| 584 | points = Rx(dphi)*Ry(dtheta)*Rz(dpsi)*points |
---|
[8678a34] | 585 | return points |
---|
| 586 | |
---|
| 587 | def orient_relative_to_beam(view, points): |
---|
[aa6989b] | 588 | """ |
---|
| 589 | Apply the view transform to a set of points. |
---|
| 590 | |
---|
| 591 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
| 592 | """ |
---|
[8678a34] | 593 | theta, phi, psi = view |
---|
[5f12750] | 594 | points = Rz(phi)*Ry(theta)*Rz(psi)*points # viewing angle |
---|
| 595 | #points = Rz(psi)*Ry(pi/2-theta)*Rz(phi)*points # 1-D integration angles |
---|
| 596 | #points = Rx(phi)*Ry(theta)*Rz(psi)*points # angular dispersion angle |
---|
[8678a34] | 597 | return points |
---|
| 598 | |
---|
[5f12750] | 599 | def orient_relative_to_beam_quaternion(view, points): |
---|
| 600 | """ |
---|
| 601 | Apply the view transform to a set of points. |
---|
| 602 | |
---|
| 603 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
| 604 | |
---|
| 605 | This variant uses quaternions rather than rotation matrices for the |
---|
| 606 | computation. It works but it is not used because it doesn't solve |
---|
| 607 | any problems. The challenge of mapping theta/phi/psi to SO(3) does |
---|
| 608 | not disappear by calculating the transform differently. |
---|
| 609 | """ |
---|
| 610 | theta, phi, psi = view |
---|
| 611 | x, y, z = [1, 0, 0], [0, 1, 0], [0, 0, 1] |
---|
| 612 | q = Quaternion(1, [0, 0, 0]) |
---|
| 613 | ## Compose a rotation about the three axes by rotating |
---|
| 614 | ## the unit vectors before applying the rotation. |
---|
| 615 | #q = Quaternion.from_angle_axis(theta, q.rot(x)) * q |
---|
| 616 | #q = Quaternion.from_angle_axis(phi, q.rot(y)) * q |
---|
| 617 | #q = Quaternion.from_angle_axis(psi, q.rot(z)) * q |
---|
| 618 | ## The above turns out to be equivalent to reversing |
---|
| 619 | ## the order of application, so ignore it and use below. |
---|
| 620 | q = q * Quaternion.from_angle_axis(theta, x) |
---|
| 621 | q = q * Quaternion.from_angle_axis(phi, y) |
---|
| 622 | q = q * Quaternion.from_angle_axis(psi, z) |
---|
| 623 | ## Reverse the order by post-multiply rather than pre-multiply |
---|
| 624 | #q = Quaternion.from_angle_axis(theta, x) * q |
---|
| 625 | #q = Quaternion.from_angle_axis(phi, y) * q |
---|
| 626 | #q = Quaternion.from_angle_axis(psi, z) * q |
---|
| 627 | #print("axes psi", q.rot(np.matrix([x, y, z]).T)) |
---|
| 628 | return q.rot(points) |
---|
| 629 | #orient_relative_to_beam = orient_relative_to_beam_quaternion |
---|
| 630 | |
---|
| 631 | # Simple stand-alone quaternion class |
---|
| 632 | import numpy as np |
---|
| 633 | from copy import copy |
---|
| 634 | class Quaternion(object): |
---|
| 635 | def __init__(self, w, r): |
---|
| 636 | self.w = w |
---|
| 637 | self.r = np.asarray(r, dtype='d') |
---|
| 638 | @staticmethod |
---|
| 639 | def from_angle_axis(theta, r): |
---|
| 640 | theta = np.radians(theta)/2 |
---|
| 641 | r = np.asarray(r) |
---|
| 642 | w = np.cos(theta) |
---|
| 643 | r = np.sin(theta)*r/np.dot(r,r) |
---|
| 644 | return Quaternion(w, r) |
---|
| 645 | def __mul__(self, other): |
---|
| 646 | if isinstance(other, Quaternion): |
---|
| 647 | w = self.w*other.w - np.dot(self.r, other.r) |
---|
| 648 | r = self.w*other.r + other.w*self.r + np.cross(self.r, other.r) |
---|
| 649 | return Quaternion(w, r) |
---|
| 650 | def rot(self, v): |
---|
| 651 | v = np.asarray(v).T |
---|
| 652 | use_transpose = (v.shape[-1] != 3) |
---|
| 653 | if use_transpose: v = v.T |
---|
| 654 | v = v + np.cross(2*self.r, np.cross(self.r, v) + self.w*v) |
---|
| 655 | #v = v + 2*self.w*np.cross(self.r, v) + np.cross(2*self.r, np.cross(self.r, v)) |
---|
| 656 | if use_transpose: v = v.T |
---|
| 657 | return v.T |
---|
| 658 | def conj(self): |
---|
| 659 | return Quaternion(self.w, -self.r) |
---|
| 660 | def inv(self): |
---|
| 661 | return self.conj()/self.norm()**2 |
---|
| 662 | def norm(self): |
---|
| 663 | return np.sqrt(self.w**2 + np.sum(self.r**2)) |
---|
| 664 | def __str__(self): |
---|
| 665 | return "%g%+gi%+gj%+gk"%(self.w, self.r[0], self.r[1], self.r[2]) |
---|
| 666 | def test_qrot(): |
---|
| 667 | # Define rotation of 60 degrees around an axis in y-z that is 60 degrees from y. |
---|
| 668 | # The rotation axis is determined by rotating the point [0, 1, 0] about x. |
---|
| 669 | ax = Quaternion.from_angle_axis(60, [1, 0, 0]).rot([0, 1, 0]) |
---|
| 670 | q = Quaternion.from_angle_axis(60, ax) |
---|
| 671 | # Set the point to be rotated, and its expected rotated position. |
---|
| 672 | p = [1, -1, 2] |
---|
| 673 | target = [(10+4*np.sqrt(3))/8, (1+2*np.sqrt(3))/8, (14-3*np.sqrt(3))/8] |
---|
| 674 | #print(q, q.rot(p) - target) |
---|
| 675 | assert max(abs(q.rot(p) - target)) < 1e-14 |
---|
| 676 | #test_qrot() |
---|
| 677 | #import sys; sys.exit() |
---|
| 678 | |
---|
[aa6989b] | 679 | # translate between number of dimension of dispersity and the number of |
---|
| 680 | # points along each dimension. |
---|
| 681 | PD_N_TABLE = { |
---|
| 682 | (0, 0, 0): (0, 0, 0), # 0 |
---|
| 683 | (1, 0, 0): (100, 0, 0), # 100 |
---|
| 684 | (0, 1, 0): (0, 100, 0), |
---|
| 685 | (0, 0, 1): (0, 0, 100), |
---|
| 686 | (1, 1, 0): (30, 30, 0), # 900 |
---|
| 687 | (1, 0, 1): (30, 0, 30), |
---|
| 688 | (0, 1, 1): (0, 30, 30), |
---|
| 689 | (1, 1, 1): (15, 15, 15), # 3375 |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | def clipped_range(data, portion=1.0, mode='central'): |
---|
| 693 | """ |
---|
| 694 | Determine range from data. |
---|
| 695 | |
---|
| 696 | If *portion* is 1, use full range, otherwise use the center of the range |
---|
| 697 | or the top of the range, depending on whether *mode* is 'central' or 'top'. |
---|
| 698 | """ |
---|
| 699 | if portion == 1.0: |
---|
| 700 | return data.min(), data.max() |
---|
| 701 | elif mode == 'central': |
---|
| 702 | data = np.sort(data.flatten()) |
---|
| 703 | offset = int(portion*len(data)/2 + 0.5) |
---|
| 704 | return data[offset], data[-offset] |
---|
| 705 | elif mode == 'top': |
---|
| 706 | data = np.sort(data.flatten()) |
---|
| 707 | offset = int(portion*len(data) + 0.5) |
---|
| 708 | return data[offset], data[-1] |
---|
| 709 | |
---|
[802c412] | 710 | def draw_scattering(calculator, axes, view, jitter, dist='gaussian'): |
---|
[aa6989b] | 711 | """ |
---|
| 712 | Plot the scattering for the particular view. |
---|
| 713 | |
---|
[802c412] | 714 | *calculator* is returned from :func:`build_model`. *axes* are the 3D axes |
---|
[aa6989b] | 715 | on which the data will be plotted. *view* and *jitter* are the current |
---|
| 716 | orientation and orientation dispersity. *dist* is one of the sasmodels |
---|
| 717 | weight distributions. |
---|
| 718 | """ |
---|
[bcb5594] | 719 | if dist == 'uniform': # uniform is not yet in this branch |
---|
| 720 | dist, scale = 'rectangle', 1/sqrt(3) |
---|
| 721 | else: |
---|
| 722 | scale = 1 |
---|
[aa6989b] | 723 | |
---|
| 724 | # add the orientation parameters to the model parameters |
---|
| 725 | theta, phi, psi = view |
---|
| 726 | theta_pd, phi_pd, psi_pd = [scale*v for v in jitter] |
---|
[d86f0fc] | 727 | theta_pd_n, phi_pd_n, psi_pd_n = PD_N_TABLE[(theta_pd > 0, phi_pd > 0, psi_pd > 0)] |
---|
[aa6989b] | 728 | ## increase pd_n for testing jitter integration rather than simple viz |
---|
| 729 | #theta_pd_n, phi_pd_n, psi_pd_n = [5*v for v in (theta_pd_n, phi_pd_n, psi_pd_n)] |
---|
| 730 | |
---|
| 731 | pars = dict( |
---|
| 732 | theta=theta, theta_pd=theta_pd, theta_pd_type=dist, theta_pd_n=theta_pd_n, |
---|
| 733 | phi=phi, phi_pd=phi_pd, phi_pd_type=dist, phi_pd_n=phi_pd_n, |
---|
| 734 | psi=psi, psi_pd=psi_pd, psi_pd_type=dist, psi_pd_n=psi_pd_n, |
---|
| 735 | ) |
---|
| 736 | pars.update(calculator.pars) |
---|
| 737 | |
---|
| 738 | # compute the pattern |
---|
| 739 | qx, qy = calculator._data.x_bins, calculator._data.y_bins |
---|
| 740 | Iqxy = calculator(**pars).reshape(len(qx), len(qy)) |
---|
| 741 | |
---|
| 742 | # scale it and draw it |
---|
| 743 | Iqxy = np.log(Iqxy) |
---|
| 744 | if calculator.limits: |
---|
| 745 | # use limits from orientation (0,0,0) |
---|
| 746 | vmin, vmax = calculator.limits |
---|
| 747 | else: |
---|
[4991048] | 748 | vmax = Iqxy.max() |
---|
| 749 | vmin = vmax*10**-7 |
---|
| 750 | #vmin, vmax = clipped_range(Iqxy, portion=portion, mode='top') |
---|
[aa6989b] | 751 | #print("range",(vmin,vmax)) |
---|
| 752 | #qx, qy = np.meshgrid(qx, qy) |
---|
| 753 | if 0: |
---|
| 754 | level = np.asarray(255*(Iqxy - vmin)/(vmax - vmin), 'i') |
---|
[d86f0fc] | 755 | level[level < 0] = 0 |
---|
[aa6989b] | 756 | colors = plt.get_cmap()(level) |
---|
[5f12750] | 757 | axes.plot_surface(qx, qy, -1.1, facecolors=colors) |
---|
[aa6989b] | 758 | elif 1: |
---|
[802c412] | 759 | axes.contourf(qx/qx.max(), qy/qy.max(), Iqxy, zdir='z', offset=-1.1, |
---|
[b3703f5] | 760 | levels=np.linspace(vmin, vmax, 24)) |
---|
[aa6989b] | 761 | else: |
---|
[802c412] | 762 | axes.pcolormesh(qx, qy, Iqxy) |
---|
[aa6989b] | 763 | |
---|
| 764 | def build_model(model_name, n=150, qmax=0.5, **pars): |
---|
| 765 | """ |
---|
| 766 | Build a calculator for the given shape. |
---|
| 767 | |
---|
| 768 | *model_name* is any sasmodels model. *n* and *qmax* define an n x n mesh |
---|
| 769 | on which to evaluate the model. The remaining parameters are stored in |
---|
| 770 | the returned calculator as *calculator.pars*. They are used by |
---|
| 771 | :func:`draw_scattering` to set the non-orientation parameters in the |
---|
| 772 | calculation. |
---|
| 773 | |
---|
| 774 | Returns a *calculator* function which takes a dictionary or parameters and |
---|
| 775 | produces Iqxy. The Iqxy value needs to be reshaped to an n x n matrix |
---|
| 776 | for plotting. See the :class:`sasmodels.direct_model.DirectModel` class |
---|
| 777 | for details. |
---|
| 778 | """ |
---|
[b3703f5] | 779 | from sasmodels.core import load_model_info, build_model as build_sasmodel |
---|
[aa6989b] | 780 | from sasmodels.data import empty_data2D |
---|
| 781 | from sasmodels.direct_model import DirectModel |
---|
| 782 | |
---|
| 783 | model_info = load_model_info(model_name) |
---|
[b3703f5] | 784 | model = build_sasmodel(model_info) #, dtype='double!') |
---|
[aa6989b] | 785 | q = np.linspace(-qmax, qmax, n) |
---|
| 786 | data = empty_data2D(q, q) |
---|
| 787 | calculator = DirectModel(data, model) |
---|
| 788 | |
---|
| 789 | # stuff the values for non-orientation parameters into the calculator |
---|
| 790 | calculator.pars = pars.copy() |
---|
| 791 | calculator.pars.setdefault('backgound', 1e-3) |
---|
| 792 | |
---|
| 793 | # fix the data limits so that we can see if the pattern fades |
---|
| 794 | # under rotation or angular dispersion |
---|
| 795 | Iqxy = calculator(theta=0, phi=0, psi=0, **calculator.pars) |
---|
| 796 | Iqxy = np.log(Iqxy) |
---|
| 797 | vmin, vmax = clipped_range(Iqxy, 0.95, mode='top') |
---|
| 798 | calculator.limits = vmin, vmax+1 |
---|
| 799 | |
---|
| 800 | return calculator |
---|
| 801 | |
---|
[d86f0fc] | 802 | def select_calculator(model_name, n=150, size=(10, 40, 100)): |
---|
[aa6989b] | 803 | """ |
---|
| 804 | Create a model calculator for the given shape. |
---|
| 805 | |
---|
| 806 | *model_name* is one of sphere, cylinder, ellipsoid, triaxial_ellipsoid, |
---|
| 807 | parallelepiped or bcc_paracrystal. *n* is the number of points to use |
---|
| 808 | in the q range. *qmax* is chosen based on model parameters for the |
---|
| 809 | given model to show something intersting. |
---|
| 810 | |
---|
| 811 | Returns *calculator* and tuple *size* (a,b,c) giving minor and major |
---|
| 812 | equitorial axes and polar axis respectively. See :func:`build_model` |
---|
| 813 | for details on the returned calculator. |
---|
| 814 | """ |
---|
[59e537a] | 815 | a, b, c = size |
---|
[58a1be9] | 816 | d_factor = 0.06 # for paracrystal models |
---|
[aa6989b] | 817 | if model_name == 'sphere': |
---|
| 818 | calculator = build_model('sphere', n=n, radius=c) |
---|
| 819 | a = b = c |
---|
[58a1be9] | 820 | elif model_name == 'sc_paracrystal': |
---|
| 821 | a = b = c |
---|
| 822 | dnn = c |
---|
| 823 | radius = 0.5*c |
---|
| 824 | calculator = build_model('sc_paracrystal', n=n, dnn=dnn, |
---|
[d86f0fc] | 825 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
| 826 | background=0) |
---|
[58a1be9] | 827 | elif model_name == 'fcc_paracrystal': |
---|
| 828 | a = b = c |
---|
| 829 | # nearest neigbour distance dnn should be 2 radius, but I think the |
---|
| 830 | # model uses lattice spacing rather than dnn in its calculations |
---|
| 831 | dnn = 0.5*c |
---|
| 832 | radius = sqrt(2)/4 * c |
---|
| 833 | calculator = build_model('fcc_paracrystal', n=n, dnn=dnn, |
---|
[d86f0fc] | 834 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
| 835 | background=0) |
---|
[aa6989b] | 836 | elif model_name == 'bcc_paracrystal': |
---|
| 837 | a = b = c |
---|
[58a1be9] | 838 | # nearest neigbour distance dnn should be 2 radius, but I think the |
---|
| 839 | # model uses lattice spacing rather than dnn in its calculations |
---|
| 840 | dnn = 0.5*c |
---|
| 841 | radius = sqrt(3)/2 * c |
---|
| 842 | calculator = build_model('bcc_paracrystal', n=n, dnn=dnn, |
---|
[d86f0fc] | 843 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
| 844 | background=0) |
---|
[aa6989b] | 845 | elif model_name == 'cylinder': |
---|
| 846 | calculator = build_model('cylinder', n=n, qmax=0.3, radius=b, length=c) |
---|
| 847 | a = b |
---|
| 848 | elif model_name == 'ellipsoid': |
---|
| 849 | calculator = build_model('ellipsoid', n=n, qmax=1.0, |
---|
| 850 | radius_polar=c, radius_equatorial=b) |
---|
| 851 | a = b |
---|
| 852 | elif model_name == 'triaxial_ellipsoid': |
---|
| 853 | calculator = build_model('triaxial_ellipsoid', n=n, qmax=0.5, |
---|
| 854 | radius_equat_minor=a, |
---|
| 855 | radius_equat_major=b, |
---|
| 856 | radius_polar=c) |
---|
| 857 | elif model_name == 'parallelepiped': |
---|
| 858 | calculator = build_model('parallelepiped', n=n, a=a, b=b, c=c) |
---|
| 859 | else: |
---|
| 860 | raise ValueError("unknown model %s"%model_name) |
---|
[8678a34] | 861 | |
---|
[aa6989b] | 862 | return calculator, (a, b, c) |
---|
[8678a34] | 863 | |
---|
[bcb5594] | 864 | SHAPES = [ |
---|
[58a1be9] | 865 | 'parallelepiped', |
---|
| 866 | 'sphere', 'ellipsoid', 'triaxial_ellipsoid', |
---|
| 867 | 'cylinder', |
---|
| 868 | 'fcc_paracrystal', 'bcc_paracrystal', 'sc_paracrystal', |
---|
[d86f0fc] | 869 | ] |
---|
[bcb5594] | 870 | |
---|
[58a1be9] | 871 | DRAW_SHAPES = { |
---|
| 872 | 'fcc_paracrystal': draw_fcc, |
---|
| 873 | 'bcc_paracrystal': draw_bcc, |
---|
| 874 | 'sc_paracrystal': draw_sc, |
---|
| 875 | 'parallelepiped': draw_parallelepiped, |
---|
| 876 | } |
---|
| 877 | |
---|
[bcb5594] | 878 | DISTRIBUTIONS = [ |
---|
| 879 | 'gaussian', 'rectangle', 'uniform', |
---|
| 880 | ] |
---|
| 881 | DIST_LIMITS = { |
---|
| 882 | 'gaussian': 30, |
---|
| 883 | 'rectangle': 90/sqrt(3), |
---|
| 884 | 'uniform': 90, |
---|
| 885 | } |
---|
| 886 | |
---|
[5f12750] | 887 | |
---|
| 888 | def run(model_name='parallelepiped', size=(10, 40, 100), |
---|
| 889 | view=(0, 0, 0), jitter=(0, 0, 0), |
---|
[bcb5594] | 890 | dist='gaussian', mesh=30, |
---|
| 891 | projection='equirectangular'): |
---|
[aa6989b] | 892 | """ |
---|
| 893 | Show an interactive orientation and jitter demo. |
---|
[8678a34] | 894 | |
---|
[58a1be9] | 895 | *model_name* is one of: sphere, ellipsoid, triaxial_ellipsoid, |
---|
| 896 | parallelepiped, cylinder, or sc/fcc/bcc_paracrystal |
---|
[0d5a655] | 897 | |
---|
| 898 | *size* gives the dimensions (a, b, c) of the shape. |
---|
| 899 | |
---|
[5f12750] | 900 | *view* gives the initial view (theta, phi, psi) of the shape. |
---|
| 901 | |
---|
| 902 | *view* gives the initial jitter (dtheta, dphi, dpsi) of the shape. |
---|
| 903 | |
---|
[0d5a655] | 904 | *dist* is the type of dispersition: gaussian, rectangle, or uniform. |
---|
| 905 | |
---|
| 906 | *mesh* is the number of points in the dispersion mesh. |
---|
| 907 | |
---|
| 908 | *projection* is the map projection to use for the mesh: equirectangular, |
---|
| 909 | sinusoidal, guyou, azimuthal_equidistance, or azimuthal_equal_area. |
---|
[aa6989b] | 910 | """ |
---|
[4991048] | 911 | # projection number according to 1-order position in list, but |
---|
| 912 | # only 1 and 2 are implemented so far. |
---|
| 913 | from sasmodels import generate |
---|
| 914 | generate.PROJECTION = PROJECTIONS.index(projection) + 1 |
---|
| 915 | if generate.PROJECTION > 2: |
---|
| 916 | print("*** PROJECTION %s not implemented in scattering function ***"%projection) |
---|
| 917 | generate.PROJECTION = 2 |
---|
| 918 | |
---|
[aa6989b] | 919 | # set up calculator |
---|
[59e537a] | 920 | calculator, size = select_calculator(model_name, n=150, size=size) |
---|
[58a1be9] | 921 | draw_shape = DRAW_SHAPES.get(model_name, draw_parallelepiped) |
---|
[5f12750] | 922 | #draw_shape = draw_fcc |
---|
[8678a34] | 923 | |
---|
[aa6989b] | 924 | ## uncomment to set an independent the colour range for every view |
---|
| 925 | ## If left commented, the colour range is fixed for all views |
---|
| 926 | calculator.limits = None |
---|
| 927 | |
---|
[5f12750] | 928 | PLOT_ENGINE(calculator, draw_shape, size, view, jitter, dist, mesh, projection) |
---|
| 929 | |
---|
| 930 | def mpl_plot(calculator, draw_shape, size, view, jitter, dist, mesh, projection): |
---|
| 931 | import mpl_toolkits.mplot3d # Adds projection='3d' option to subplot |
---|
| 932 | import matplotlib.pyplot as plt |
---|
| 933 | from matplotlib.widgets import Slider |
---|
[aa6989b] | 934 | |
---|
| 935 | ## create the plot window |
---|
[782dd1f] | 936 | #plt.hold(True) |
---|
[de71632] | 937 | plt.subplots(num=None, figsize=(5.5, 5.5)) |
---|
[782dd1f] | 938 | plt.set_cmap('gist_earth') |
---|
| 939 | plt.clf() |
---|
[de71632] | 940 | plt.gcf().canvas.set_window_title(projection) |
---|
[782dd1f] | 941 | #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) |
---|
[802c412] | 942 | #axes = plt.subplot(gs[0], projection='3d') |
---|
| 943 | axes = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') |
---|
[36b3154] | 944 | try: # CRUFT: not all versions of matplotlib accept 'square' 3d projection |
---|
[802c412] | 945 | axes.axis('square') |
---|
[36b3154] | 946 | except Exception: |
---|
| 947 | pass |
---|
[782dd1f] | 948 | |
---|
| 949 | axcolor = 'lightgoldenrodyellow' |
---|
[8678a34] | 950 | |
---|
[aa6989b] | 951 | ## add control widgets to plot |
---|
[5f12750] | 952 | axes_theta = plt.axes([0.1, 0.15, 0.45, 0.04], facecolor=axcolor) |
---|
| 953 | axes_phi = plt.axes([0.1, 0.1, 0.45, 0.04], facecolor=axcolor) |
---|
| 954 | axes_psi = plt.axes([0.1, 0.05, 0.45, 0.04], facecolor=axcolor) |
---|
| 955 | stheta = Slider(axes_theta, 'Theta', -90, 90, valinit=0) |
---|
| 956 | sphi = Slider(axes_phi, 'Phi', -180, 180, valinit=0) |
---|
| 957 | spsi = Slider(axes_psi, 'Psi', -180, 180, valinit=0) |
---|
| 958 | |
---|
| 959 | axes_dtheta = plt.axes([0.75, 0.15, 0.15, 0.04], facecolor=axcolor) |
---|
| 960 | axes_dphi = plt.axes([0.75, 0.1, 0.15, 0.04], facecolor=axcolor) |
---|
| 961 | axes_dpsi = plt.axes([0.75, 0.05, 0.15, 0.04], facecolor=axcolor) |
---|
[aa6989b] | 962 | # Note: using ridiculous definition of rectangle distribution, whose width |
---|
| 963 | # in sasmodels is sqrt(3) times the given width. Divide by sqrt(3) to keep |
---|
| 964 | # the maximum width to 90. |
---|
[bcb5594] | 965 | dlimit = DIST_LIMITS[dist] |
---|
[5f12750] | 966 | sdtheta = Slider(axes_dtheta, 'dTheta', 0, 2*dlimit, valinit=0) |
---|
| 967 | sdphi = Slider(axes_dphi, 'dPhi', 0, 2*dlimit, valinit=0) |
---|
| 968 | sdpsi = Slider(axes_dpsi, 'dPsi', 0, 2*dlimit, valinit=0) |
---|
[aa6989b] | 969 | |
---|
[5f12750] | 970 | ## initial view and jitter |
---|
| 971 | theta, phi, psi = view |
---|
| 972 | stheta.set_val(theta) |
---|
| 973 | sphi.set_val(phi) |
---|
| 974 | spsi.set_val(psi) |
---|
| 975 | dtheta, dphi, dpsi = jitter |
---|
| 976 | sdtheta.set_val(dtheta) |
---|
| 977 | sdphi.set_val(dphi) |
---|
| 978 | sdpsi.set_val(dpsi) |
---|
[58a1be9] | 979 | |
---|
[aa6989b] | 980 | ## callback to draw the new view |
---|
[782dd1f] | 981 | def update(val, axis=None): |
---|
[8678a34] | 982 | view = stheta.val, sphi.val, spsi.val |
---|
| 983 | jitter = sdtheta.val, sdphi.val, sdpsi.val |
---|
[aa6989b] | 984 | # set small jitter as 0 if multiple pd dims |
---|
| 985 | dims = sum(v > 0 for v in jitter) |
---|
[5f12750] | 986 | limit = [0, 0.5, 5, 5][dims] |
---|
[aa6989b] | 987 | jitter = [0 if v < limit else v for v in jitter] |
---|
[802c412] | 988 | axes.cla() |
---|
[5f12750] | 989 | |
---|
| 990 | ## Visualize as person on globe |
---|
| 991 | #draw_sphere(axes) |
---|
| 992 | #draw_person_on_sphere(axes, view) |
---|
| 993 | |
---|
| 994 | ## Move beam instead of shape |
---|
| 995 | #draw_beam(axes, -view[:2]) |
---|
| 996 | #draw_jitter(axes, (0,0,0), (0,0,0), views=3) |
---|
| 997 | |
---|
| 998 | ## Move shape and draw scattering |
---|
[802c412] | 999 | draw_beam(axes, (0, 0)) |
---|
[5f12750] | 1000 | draw_jitter(axes, view, jitter, dist=dist, size=size, |
---|
| 1001 | draw_shape=draw_shape, projection=projection, views=3) |
---|
[802c412] | 1002 | draw_mesh(axes, view, jitter, dist=dist, n=mesh, projection=projection) |
---|
| 1003 | draw_scattering(calculator, axes, view, jitter, dist=dist) |
---|
[5f12750] | 1004 | |
---|
[782dd1f] | 1005 | plt.gcf().canvas.draw() |
---|
| 1006 | |
---|
[aa6989b] | 1007 | ## bind control widgets to view updater |
---|
[d86f0fc] | 1008 | stheta.on_changed(lambda v: update(v, 'theta')) |
---|
[782dd1f] | 1009 | sphi.on_changed(lambda v: update(v, 'phi')) |
---|
| 1010 | spsi.on_changed(lambda v: update(v, 'psi')) |
---|
| 1011 | sdtheta.on_changed(lambda v: update(v, 'dtheta')) |
---|
| 1012 | sdphi.on_changed(lambda v: update(v, 'dphi')) |
---|
| 1013 | sdpsi.on_changed(lambda v: update(v, 'dpsi')) |
---|
| 1014 | |
---|
[aa6989b] | 1015 | ## initialize view |
---|
[782dd1f] | 1016 | update(None, 'phi') |
---|
| 1017 | |
---|
[aa6989b] | 1018 | ## go interactive |
---|
[782dd1f] | 1019 | plt.show() |
---|
| 1020 | |
---|
[5f12750] | 1021 | |
---|
| 1022 | def map_colors(z, kw): |
---|
| 1023 | from matplotlib import cm |
---|
| 1024 | |
---|
| 1025 | cmap = kw.pop('cmap', cm.coolwarm) |
---|
| 1026 | alpha = kw.pop('alpha', None) |
---|
| 1027 | vmin = kw.pop('vmin', z.min()) |
---|
| 1028 | vmax = kw.pop('vmax', z.max()) |
---|
| 1029 | c = kw.pop('c', None) |
---|
| 1030 | color = kw.pop('color', c) |
---|
| 1031 | if color is None: |
---|
| 1032 | znorm = ((z - vmin) / (vmax - vmin)).clip(0, 1) |
---|
| 1033 | color = cmap(znorm) |
---|
| 1034 | elif isinstance(color, np.ndarray) and color.shape == z.shape: |
---|
| 1035 | color = cmap(color) |
---|
| 1036 | if alpha is None: |
---|
| 1037 | if isinstance(color, np.ndarray): |
---|
| 1038 | color = color[..., :3] |
---|
| 1039 | else: |
---|
| 1040 | color[..., 3] = alpha |
---|
| 1041 | kw['color'] = color |
---|
| 1042 | |
---|
| 1043 | def make_vec(*args, flat=False): |
---|
| 1044 | if flat: |
---|
| 1045 | return [np.asarray(v, 'd').flatten() for v in args] |
---|
| 1046 | else: |
---|
| 1047 | return [np.asarray(v, 'd') for v in args] |
---|
| 1048 | |
---|
| 1049 | def make_image(z, kw): |
---|
| 1050 | import PIL.Image |
---|
| 1051 | from matplotlib import cm |
---|
| 1052 | |
---|
| 1053 | cmap = kw.pop('cmap', cm.coolwarm) |
---|
| 1054 | |
---|
| 1055 | znorm = (z-z.min())/z.ptp() |
---|
| 1056 | c = cmap(znorm) |
---|
| 1057 | c = c[..., :3] |
---|
| 1058 | rgb = np.asarray(c*255, 'u1') |
---|
| 1059 | image = PIL.Image.fromarray(rgb, mode='RGB') |
---|
| 1060 | return image |
---|
| 1061 | |
---|
| 1062 | |
---|
| 1063 | _IPV_MARKERS = { |
---|
| 1064 | 'o': 'sphere', |
---|
| 1065 | } |
---|
| 1066 | _IPV_COLORS = { |
---|
| 1067 | 'w': 'white', |
---|
| 1068 | 'k': 'black', |
---|
| 1069 | 'c': 'cyan', |
---|
| 1070 | 'm': 'magenta', |
---|
| 1071 | 'y': 'yellow', |
---|
| 1072 | 'r': 'red', |
---|
| 1073 | 'g': 'green', |
---|
| 1074 | 'b': 'blue', |
---|
| 1075 | } |
---|
| 1076 | def ipv_fix_color(kw): |
---|
| 1077 | kw.pop('alpha', None) |
---|
| 1078 | color = kw.get('color', None) |
---|
| 1079 | if isinstance(color, str): |
---|
| 1080 | color = _IPV_COLORS.get(color, color) |
---|
| 1081 | kw['color'] = color |
---|
| 1082 | |
---|
| 1083 | |
---|
| 1084 | def ipv_plot(calculator, draw_shape, size, view, jitter, dist, mesh, projection): |
---|
| 1085 | import ipywidgets as widgets |
---|
| 1086 | import ipyvolume as ipv |
---|
| 1087 | |
---|
| 1088 | class Plotter: |
---|
| 1089 | def plot(self, x, y, z, **kw): |
---|
| 1090 | ipv_fix_color(kw) |
---|
| 1091 | x, y, z = make_vec(x, y, z) |
---|
| 1092 | ipv.plot(x, y, z, **kw) |
---|
| 1093 | def plot_surface(self, x, y, z, **kw): |
---|
| 1094 | ipv_fix_color(kw) |
---|
| 1095 | x, y, z = make_vec(x, y, z) |
---|
| 1096 | ipv.plot_surface(x, y, z, **kw) |
---|
| 1097 | def plot_trisurf(self, x, y, triangles=None, Z=None, **kw): |
---|
| 1098 | ipv_fix_color(kw) |
---|
| 1099 | x, y, z = make_vec(x, y, Z) |
---|
| 1100 | if triangles is not None: |
---|
| 1101 | triangles = np.asarray(triangles) |
---|
| 1102 | ipv.plot_trisurf(x, y, z, triangles=triangles, **kw) |
---|
| 1103 | def scatter(self, x, y, z, **kw): |
---|
| 1104 | x, y, z = make_vec(x, y, z) |
---|
| 1105 | map_colors(z, kw) |
---|
| 1106 | marker = kw.get('marker', None) |
---|
| 1107 | kw['marker'] = _IPV_MARKERS.get(marker, marker) |
---|
| 1108 | ipv.scatter(x, y, z, **kw) |
---|
| 1109 | def contourf(self, x, y, v, zdir='z', offset=0, levels=None, **kw): |
---|
| 1110 | # Don't use contour for now (although we might want to later) |
---|
| 1111 | self.pcolor(x, y, v, zdir='z', offset=offset, **kw) |
---|
| 1112 | def pcolor(self, x, y, v, zdir='z', offset=0, **kw): |
---|
| 1113 | x, y, v = make_vec(x, y, v) |
---|
| 1114 | image = make_image(v, kw) |
---|
| 1115 | xmin, xmax = x.min(), x.max() |
---|
| 1116 | ymin, ymax = y.min(), y.max() |
---|
| 1117 | x = np.array([[xmin, xmax], [xmin, xmax]]) |
---|
| 1118 | y = np.array([[ymin, ymin], [ymax, ymax]]) |
---|
| 1119 | z = x*0 + offset |
---|
| 1120 | u = np.array([[0., 1], [0, 1]]) |
---|
| 1121 | v = np.array([[0., 0], [1, 1]]) |
---|
| 1122 | ipv.plot_mesh(x, y, z, u=u, v=v, texture=image, wireframe=False) |
---|
| 1123 | def text(self, *args, **kw): |
---|
| 1124 | pass |
---|
| 1125 | def set_xlim(self, limits): |
---|
| 1126 | ipv.xlim(*limits) |
---|
| 1127 | def set_ylim(self, limits): |
---|
| 1128 | ipv.ylim(*limits) |
---|
| 1129 | def set_zlim(self, limits): |
---|
| 1130 | ipv.zlim(*limits) |
---|
| 1131 | def set_axes_on(self): |
---|
| 1132 | ipv.style.axis_on() |
---|
| 1133 | def set_axis_off(self): |
---|
| 1134 | ipv.style.axes_off() |
---|
| 1135 | axes = Plotter() |
---|
| 1136 | |
---|
| 1137 | |
---|
| 1138 | def draw(view, jitter): |
---|
| 1139 | camera = ipv.gcf().camera |
---|
| 1140 | #print(ipv.gcf().__dict__.keys()) |
---|
| 1141 | #print(dir(ipv.gcf())) |
---|
| 1142 | ipv.figure() |
---|
| 1143 | |
---|
| 1144 | # set small jitter as 0 if multiple pd dims |
---|
| 1145 | dims = sum(v > 0 for v in jitter) |
---|
| 1146 | limit = [0, 0.5, 5, 5][dims] |
---|
| 1147 | jitter = [0 if v < limit else v for v in jitter] |
---|
| 1148 | |
---|
| 1149 | ## Visualize as person on globe |
---|
| 1150 | #draw_beam(axes, (0, 0)) |
---|
| 1151 | #draw_sphere(axes) |
---|
| 1152 | #draw_person_on_sphere(axes, view) |
---|
| 1153 | |
---|
| 1154 | ## Move beam instead of shape |
---|
| 1155 | #draw_beam(axes, view=(-view[0], -view[1])) |
---|
| 1156 | #draw_jitter(axes, view=(0,0,0), jitter=(0,0,0)) |
---|
| 1157 | |
---|
| 1158 | ## Move shape and draw scattering |
---|
| 1159 | draw_beam(axes, (0, 0)) |
---|
| 1160 | draw_jitter(axes, view, jitter, dist=dist, size=size, |
---|
| 1161 | draw_shape=draw_shape, projection=projection) |
---|
| 1162 | #draw_mesh(axes, view, jitter, dist=dist, n=mesh, projection=projection) |
---|
| 1163 | #draw_scattering(calculator, axes, view, jitter, dist=dist) |
---|
| 1164 | |
---|
| 1165 | ipv.style.box_off() |
---|
| 1166 | #ipv.style.axes_off() |
---|
| 1167 | ipv.xyzlabel(" ", " ", " ") |
---|
| 1168 | |
---|
| 1169 | ipv.gcf().camera = camera |
---|
| 1170 | ipv.show() |
---|
| 1171 | |
---|
| 1172 | |
---|
| 1173 | trange, prange = (-180., 180., 1.), (-180., 180., 1.) |
---|
| 1174 | dtrange, dprange = (0., 180., 1.), (0., 180., 1.) |
---|
| 1175 | |
---|
| 1176 | ## Super simple interfaca, but uses non-ascii variable namese |
---|
| 1177 | # Ξ Ï Ï ÎΞ ÎÏ ÎÏ |
---|
| 1178 | #def update(**kw): |
---|
| 1179 | # view = kw['Ξ'], kw['Ï'], kw['Ï'] |
---|
| 1180 | # jitter = kw['ÎΞ'], kw['ÎÏ'], kw['ÎÏ'] |
---|
| 1181 | # draw(view, jitter) |
---|
| 1182 | #widgets.interact(update, Ξ=trange, Ï=prange, Ï=prange, ÎΞ=dtrange, ÎÏ=dprange, ÎÏ=dprange) |
---|
| 1183 | |
---|
| 1184 | def update(theta, phi, psi, dtheta, dphi, dpsi): |
---|
| 1185 | draw(view=(theta, phi, psi), jitter=(dtheta, dphi, dpsi)) |
---|
| 1186 | |
---|
| 1187 | def slider(name, slice, init=0.): |
---|
| 1188 | return widgets.FloatSlider( |
---|
| 1189 | value=init, |
---|
| 1190 | min=slice[0], |
---|
| 1191 | max=slice[1], |
---|
| 1192 | step=slice[2], |
---|
| 1193 | description=name, |
---|
| 1194 | disabled=False, |
---|
| 1195 | continuous_update=False, |
---|
| 1196 | orientation='horizontal', |
---|
| 1197 | readout=True, |
---|
| 1198 | readout_format='.1f', |
---|
| 1199 | ) |
---|
| 1200 | theta = slider('Ξ', trange, view[0]) |
---|
| 1201 | phi = slider('Ï', prange, view[1]) |
---|
| 1202 | psi = slider('Ï', prange, view[2]) |
---|
| 1203 | dtheta = slider('ÎΞ', dtrange, jitter[0]) |
---|
| 1204 | dphi = slider('ÎÏ', dprange, jitter[1]) |
---|
| 1205 | dpsi = slider('ÎÏ', dprange, jitter[2]) |
---|
| 1206 | fields = { |
---|
| 1207 | 'theta': theta, 'phi': phi, 'psi': psi, |
---|
| 1208 | 'dtheta': dtheta, 'dphi': dphi, 'dpsi': dpsi, |
---|
| 1209 | } |
---|
| 1210 | ui = widgets.HBox([ |
---|
| 1211 | widgets.VBox([theta, phi, psi]), |
---|
| 1212 | widgets.VBox([dtheta, dphi, dpsi]) |
---|
| 1213 | ]) |
---|
| 1214 | |
---|
| 1215 | out = widgets.interactive_output(update, fields) |
---|
| 1216 | display(ui, out) |
---|
| 1217 | |
---|
| 1218 | |
---|
| 1219 | _ENGINES = { |
---|
| 1220 | "matplotlib": mpl_plot, |
---|
| 1221 | "mpl": mpl_plot, |
---|
| 1222 | #"plotly": plotly_plot, |
---|
| 1223 | "ipvolume": ipv_plot, |
---|
| 1224 | "ipv": ipv_plot, |
---|
| 1225 | } |
---|
| 1226 | PLOT_ENGINE = _ENGINES["matplotlib"] |
---|
| 1227 | def set_plotter(name): |
---|
| 1228 | global PLOT_ENGINE |
---|
| 1229 | PLOT_ENGINE = _ENGINES[name] |
---|
| 1230 | |
---|
[bcb5594] | 1231 | def main(): |
---|
| 1232 | parser = argparse.ArgumentParser( |
---|
| 1233 | description="Display jitter", |
---|
| 1234 | formatter_class=argparse.ArgumentDefaultsHelpFormatter, |
---|
| 1235 | ) |
---|
[d86f0fc] | 1236 | parser.add_argument('-p', '--projection', choices=PROJECTIONS, |
---|
| 1237 | default=PROJECTIONS[0], |
---|
| 1238 | help='coordinate projection') |
---|
| 1239 | parser.add_argument('-s', '--size', type=str, default='10,40,100', |
---|
| 1240 | help='a,b,c lengths') |
---|
[5f12750] | 1241 | parser.add_argument('-v', '--view', type=str, default='0,0,0', |
---|
| 1242 | help='initial view angles') |
---|
| 1243 | parser.add_argument('-j', '--jitter', type=str, default='0,0,0', |
---|
| 1244 | help='initial angular dispersion') |
---|
[d86f0fc] | 1245 | parser.add_argument('-d', '--distribution', choices=DISTRIBUTIONS, |
---|
| 1246 | default=DISTRIBUTIONS[0], |
---|
| 1247 | help='jitter distribution') |
---|
| 1248 | parser.add_argument('-m', '--mesh', type=int, default=30, |
---|
| 1249 | help='#points in theta-phi mesh') |
---|
| 1250 | parser.add_argument('shape', choices=SHAPES, nargs='?', default=SHAPES[0], |
---|
| 1251 | help='oriented shape') |
---|
[bcb5594] | 1252 | opts = parser.parse_args() |
---|
[5f12750] | 1253 | size = tuple(float(v) for v in opts.size.split(',')) |
---|
| 1254 | view = tuple(float(v) for v in opts.view.split(',')) |
---|
| 1255 | jitter = tuple(float(v) for v in opts.jitter.split(',')) |
---|
| 1256 | run(opts.shape, size=size, view=view, jitter=jitter, |
---|
[bcb5594] | 1257 | mesh=opts.mesh, dist=opts.distribution, |
---|
| 1258 | projection=opts.projection) |
---|
| 1259 | |
---|
[782dd1f] | 1260 | if __name__ == "__main__": |
---|
[bcb5594] | 1261 | main() |
---|