[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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[782dd1f] | 7 | """ |
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[aa6989b] | 8 | from __future__ import division, print_function |
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| 9 | |
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[bcb5594] | 10 | import argparse |
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| 11 | |
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[42158d2] | 12 | try: # CRUFT: travis-ci does not support mpl_toolkits.mplot3d |
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| 13 | import mpl_toolkits.mplot3d # Adds projection='3d' option to subplot |
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| 14 | except ImportError: |
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| 15 | pass |
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| 16 | |
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[7d97437] | 17 | import matplotlib as mpl |
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[782dd1f] | 18 | import matplotlib.pyplot as plt |
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[802c412] | 19 | from matplotlib.widgets import Slider |
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[782dd1f] | 20 | import numpy as np |
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| 21 | from numpy import pi, cos, sin, sqrt, exp, degrees, radians |
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| 22 | |
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[802c412] | 23 | def draw_beam(axes, view=(0, 0)): |
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[aa6989b] | 24 | """ |
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| 25 | Draw the beam going from source at (0, 0, 1) to detector at (0, 0, -1) |
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| 26 | """ |
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[802c412] | 27 | #axes.plot([0,0],[0,0],[1,-1]) |
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| 28 | #axes.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=0.8) |
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[782dd1f] | 29 | |
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| 30 | steps = 25 |
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| 31 | u = np.linspace(0, 2 * np.pi, steps) |
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| 32 | v = np.linspace(-1, 1, steps) |
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| 33 | |
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| 34 | r = 0.02 |
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| 35 | x = r*np.outer(np.cos(u), np.ones_like(v)) |
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| 36 | y = r*np.outer(np.sin(u), np.ones_like(v)) |
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[8678a34] | 37 | z = 1.3*np.outer(np.ones_like(u), v) |
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| 38 | |
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| 39 | theta, phi = view |
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| 40 | shape = x.shape |
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| 41 | points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) |
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| 42 | points = Rz(phi)*Ry(theta)*points |
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| 43 | x, y, z = [v.reshape(shape) for v in points] |
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[782dd1f] | 44 | |
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[802c412] | 45 | axes.plot_surface(x, y, z, rstride=4, cstride=4, color='y', alpha=0.5) |
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[85190c2] | 46 | |
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[802c412] | 47 | def draw_ellipsoid(axes, size, view, jitter, steps=25, alpha=1): |
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[aa6989b] | 48 | """Draw an ellipsoid.""" |
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[d86f0fc] | 49 | a, b, c = size |
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[782dd1f] | 50 | u = np.linspace(0, 2 * np.pi, steps) |
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| 51 | v = np.linspace(0, np.pi, steps) |
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| 52 | x = a*np.outer(np.cos(u), np.sin(v)) |
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| 53 | y = b*np.outer(np.sin(u), np.sin(v)) |
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| 54 | z = c*np.outer(np.ones_like(u), np.cos(v)) |
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[8678a34] | 55 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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[782dd1f] | 56 | |
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[802c412] | 57 | axes.plot_surface(x, y, z, rstride=4, cstride=4, color='w', alpha=alpha) |
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[782dd1f] | 58 | |
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[802c412] | 59 | draw_labels(axes, view, jitter, [ |
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[d86f0fc] | 60 | ('c+', [+0, +0, +c], [+1, +0, +0]), |
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| 61 | ('c-', [+0, +0, -c], [+0, +0, -1]), |
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| 62 | ('a+', [+a, +0, +0], [+0, +0, +1]), |
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| 63 | ('a-', [-a, +0, +0], [+0, +0, -1]), |
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| 64 | ('b+', [+0, +b, +0], [-1, +0, +0]), |
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| 65 | ('b-', [+0, -b, +0], [-1, +0, +0]), |
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[8678a34] | 66 | ]) |
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[782dd1f] | 67 | |
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[802c412] | 68 | def draw_sc(axes, size, view, jitter, steps=None, alpha=1): |
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[d86f0fc] | 69 | """Draw points for simple cubic paracrystal""" |
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[58a1be9] | 70 | atoms = _build_sc() |
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[802c412] | 71 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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[58a1be9] | 72 | |
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[802c412] | 73 | def draw_fcc(axes, size, view, jitter, steps=None, alpha=1): |
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[d86f0fc] | 74 | """Draw points for face-centered cubic paracrystal""" |
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[58a1be9] | 75 | # Build the simple cubic crystal |
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| 76 | atoms = _build_sc() |
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| 77 | # Define the centers for each face |
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| 78 | # x planes at -1, 0, 1 have four centers per plane, at +/- 0.5 in y and z |
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| 79 | x, y, z = ( |
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| 80 | [-1]*4 + [0]*4 + [1]*4, |
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| 81 | ([-0.5]*2 + [0.5]*2)*3, |
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| 82 | [-0.5, 0.5]*12, |
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| 83 | ) |
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| 84 | # y and z planes can be generated by substituting x for y and z respectively |
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| 85 | atoms.extend(zip(x+y+z, y+z+x, z+x+y)) |
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[802c412] | 86 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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[58a1be9] | 87 | |
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[802c412] | 88 | def draw_bcc(axes, size, view, jitter, steps=None, alpha=1): |
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[d86f0fc] | 89 | """Draw points for body-centered cubic paracrystal""" |
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[58a1be9] | 90 | # Build the simple cubic crystal |
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| 91 | atoms = _build_sc() |
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| 92 | # Define the centers for each octant |
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| 93 | # x plane at +/- 0.5 have four centers per plane at +/- 0.5 in y and z |
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| 94 | x, y, z = ( |
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| 95 | [-0.5]*4 + [0.5]*4, |
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| 96 | ([-0.5]*2 + [0.5]*2)*2, |
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| 97 | [-0.5, 0.5]*8, |
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| 98 | ) |
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| 99 | atoms.extend(zip(x, y, z)) |
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[802c412] | 100 | _draw_crystal(axes, size, view, jitter, atoms=atoms) |
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[58a1be9] | 101 | |
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[b3703f5] | 102 | def _draw_crystal(axes, size, view, jitter, atoms=None): |
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[58a1be9] | 103 | atoms, size = np.asarray(atoms, 'd').T, np.asarray(size, 'd') |
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| 104 | x, y, z = atoms*size[:, None] |
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| 105 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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[802c412] | 106 | axes.scatter([x[0]], [y[0]], [z[0]], c='yellow', marker='o') |
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| 107 | axes.scatter(x[1:], y[1:], z[1:], c='r', marker='o') |
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[58a1be9] | 108 | |
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| 109 | def _build_sc(): |
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| 110 | # three planes of 9 dots for x at -1, 0 and 1 |
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| 111 | x, y, z = ( |
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| 112 | [-1]*9 + [0]*9 + [1]*9, |
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| 113 | ([-1]*3 + [0]*3 + [1]*3)*3, |
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| 114 | [-1, 0, 1]*9, |
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| 115 | ) |
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| 116 | atoms = list(zip(x, y, z)) |
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| 117 | #print(list(enumerate(atoms))) |
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[199bd07] | 118 | # Pull the dot at (0, 0, 1) to the front of the list |
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[58a1be9] | 119 | # It will be highlighted in the view |
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[199bd07] | 120 | index = 14 |
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[58a1be9] | 121 | highlight = atoms[index] |
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| 122 | del atoms[index] |
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| 123 | atoms.insert(0, highlight) |
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| 124 | return atoms |
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| 125 | |
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[802c412] | 126 | def draw_parallelepiped(axes, size, view, jitter, steps=None, alpha=1): |
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[aa6989b] | 127 | """Draw a parallelepiped.""" |
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[31a02f1] | 128 | a, b, c = size |
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[d86f0fc] | 129 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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| 130 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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| 131 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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[782dd1f] | 132 | tri = np.array([ |
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| 133 | # counter clockwise triangles |
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| 134 | # z: up/down, x: right/left, y: front/back |
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[d86f0fc] | 135 | [0, 1, 2], [3, 2, 1], # top face |
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| 136 | [6, 5, 4], [5, 6, 7], # bottom face |
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| 137 | [0, 2, 6], [6, 4, 0], # right face |
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| 138 | [1, 5, 7], [7, 3, 1], # left face |
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| 139 | [2, 3, 6], [7, 6, 3], # front face |
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| 140 | [4, 1, 0], [5, 1, 4], # back face |
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[782dd1f] | 141 | ]) |
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| 142 | |
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[8678a34] | 143 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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[802c412] | 144 | axes.plot_trisurf(x, y, triangles=tri, Z=z, color='w', alpha=alpha) |
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[782dd1f] | 145 | |
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[31a02f1] | 146 | # Draw pink face on box. |
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| 147 | # Since I can't control face color, instead draw a thin box situated just |
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[58a1be9] | 148 | # in front of the "c+" face. Use the c face so that rotations about psi |
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| 149 | # rotate that face. |
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[31a02f1] | 150 | if 1: |
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[d86f0fc] | 151 | x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) |
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| 152 | y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) |
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| 153 | z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) |
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[58a1be9] | 154 | x, y, z = transform_xyz(view, jitter, x, y, abs(z)+0.001) |
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[802c412] | 155 | axes.plot_trisurf(x, y, triangles=tri, Z=z, color=[1, 0.6, 0.6], alpha=alpha) |
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[31a02f1] | 156 | |
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[802c412] | 157 | draw_labels(axes, view, jitter, [ |
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[d86f0fc] | 158 | ('c+', [+0, +0, +c], [+1, +0, +0]), |
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| 159 | ('c-', [+0, +0, -c], [+0, +0, -1]), |
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| 160 | ('a+', [+a, +0, +0], [+0, +0, +1]), |
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| 161 | ('a-', [-a, +0, +0], [+0, +0, -1]), |
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| 162 | ('b+', [+0, +b, +0], [-1, +0, +0]), |
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| 163 | ('b-', [+0, -b, +0], [-1, +0, +0]), |
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[8678a34] | 164 | ]) |
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[782dd1f] | 165 | |
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[802c412] | 166 | def draw_sphere(axes, radius=10., steps=100): |
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[aa6989b] | 167 | """Draw a sphere""" |
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| 168 | u = np.linspace(0, 2 * np.pi, steps) |
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| 169 | v = np.linspace(0, np.pi, steps) |
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| 170 | |
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| 171 | x = radius * np.outer(np.cos(u), np.sin(v)) |
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| 172 | y = radius * np.outer(np.sin(u), np.sin(v)) |
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| 173 | z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) |
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[802c412] | 174 | axes.plot_surface(x, y, z, rstride=4, cstride=4, color='w') |
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[aa6989b] | 175 | |
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[802c412] | 176 | def draw_jitter(axes, view, jitter, dist='gaussian', size=(0.1, 0.4, 1.0), |
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[58a1be9] | 177 | draw_shape=draw_parallelepiped): |
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| 178 | """ |
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| 179 | Represent jitter as a set of shapes at different orientations. |
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| 180 | """ |
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| 181 | # set max diagonal to 0.95 |
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| 182 | scale = 0.95/sqrt(sum(v**2 for v in size)) |
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| 183 | size = tuple(scale*v for v in size) |
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| 184 | |
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| 185 | #np.random.seed(10) |
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| 186 | #cloud = np.random.randn(10,3) |
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| 187 | cloud = [ |
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| 188 | [-1, -1, -1], |
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[d86f0fc] | 189 | [-1, -1, +0], |
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| 190 | [-1, -1, +1], |
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| 191 | [-1, +0, -1], |
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| 192 | [-1, +0, +0], |
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| 193 | [-1, +0, +1], |
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| 194 | [-1, +1, -1], |
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| 195 | [-1, +1, +0], |
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| 196 | [-1, +1, +1], |
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| 197 | [+0, -1, -1], |
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| 198 | [+0, -1, +0], |
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| 199 | [+0, -1, +1], |
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| 200 | [+0, +0, -1], |
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| 201 | [+0, +0, +0], |
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| 202 | [+0, +0, +1], |
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| 203 | [+0, +1, -1], |
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| 204 | [+0, +1, +0], |
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| 205 | [+0, +1, +1], |
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| 206 | [+1, -1, -1], |
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| 207 | [+1, -1, +0], |
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| 208 | [+1, -1, +1], |
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| 209 | [+1, +0, -1], |
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| 210 | [+1, +0, +0], |
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| 211 | [+1, +0, +1], |
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| 212 | [+1, +1, -1], |
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| 213 | [+1, +1, +0], |
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| 214 | [+1, +1, +1], |
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[58a1be9] | 215 | ] |
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| 216 | dtheta, dphi, dpsi = jitter |
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| 217 | if dtheta == 0: |
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| 218 | cloud = [v for v in cloud if v[0] == 0] |
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| 219 | if dphi == 0: |
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| 220 | cloud = [v for v in cloud if v[1] == 0] |
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| 221 | if dpsi == 0: |
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| 222 | cloud = [v for v in cloud if v[2] == 0] |
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[802c412] | 223 | draw_shape(axes, size, view, [0, 0, 0], steps=100, alpha=0.8) |
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[58a1be9] | 224 | scale = {'gaussian':1, 'rectangle':1/sqrt(3), 'uniform':1/3}[dist] |
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| 225 | for point in cloud: |
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| 226 | delta = [scale*dtheta*point[0], scale*dphi*point[1], scale*dpsi*point[2]] |
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[802c412] | 227 | draw_shape(axes, size, view, delta, alpha=0.8) |
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[58a1be9] | 228 | for v in 'xyz': |
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| 229 | a, b, c = size |
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[d86f0fc] | 230 | lim = np.sqrt(a**2 + b**2 + c**2) |
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[802c412] | 231 | getattr(axes, 'set_'+v+'lim')([-lim, lim]) |
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| 232 | getattr(axes, v+'axis').label.set_text(v) |
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[58a1be9] | 233 | |
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[bcb5594] | 234 | PROJECTIONS = [ |
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[4991048] | 235 | # in order of PROJECTION number; do not change without updating the |
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| 236 | # constants in kernel_iq.c |
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| 237 | 'equirectangular', 'sinusoidal', 'guyou', 'azimuthal_equidistance', |
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[8cfb486] | 238 | 'azimuthal_equal_area', |
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[bcb5594] | 239 | ] |
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[802c412] | 240 | def draw_mesh(axes, view, jitter, radius=1.2, n=11, dist='gaussian', |
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[bcb5594] | 241 | projection='equirectangular'): |
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[aa6989b] | 242 | """ |
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| 243 | Draw the dispersion mesh showing the theta-phi orientations at which |
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| 244 | the model will be evaluated. |
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[bcb5594] | 245 | |
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| 246 | jitter projections |
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| 247 | <https://en.wikipedia.org/wiki/List_of_map_projections> |
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| 248 | |
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| 249 | equirectangular (standard latitude-longitude mesh) |
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| 250 | <https://en.wikipedia.org/wiki/Equirectangular_projection> |
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| 251 | Allows free movement in phi (around the equator), but theta is |
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| 252 | limited to +/- 90, and points are cos-weighted. Jitter in phi is |
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| 253 | uniform in weight along a line of latitude. With small theta and |
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| 254 | phi ranging over +/- 180 this forms a wobbling disk. With small |
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| 255 | phi and theta ranging over +/- 90 this forms a wedge like a slice |
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| 256 | of an orange. |
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| 257 | azimuthal_equidistance (Postel) |
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| 258 | <https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection> |
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| 259 | Preserves distance from center, and so is an excellent map for |
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| 260 | representing a bivariate gaussian on the surface. Theta and phi |
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| 261 | operate identically, cutting wegdes from the antipode of the viewing |
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| 262 | angle. This unfortunately does not allow free movement in either |
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| 263 | theta or phi since the orthogonal wobble decreases to 0 as the body |
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| 264 | rotates through 180 degrees. |
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| 265 | sinusoidal (Sanson-Flamsteed, Mercator equal-area) |
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| 266 | <https://en.wikipedia.org/wiki/Sinusoidal_projection> |
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| 267 | Preserves arc length with latitude, giving bad behaviour at |
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| 268 | theta near +/- 90. Theta and phi operate somewhat differently, |
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| 269 | so a system with a-b-c dtheta-dphi-dpsi will not give the same |
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| 270 | value as one with b-a-c dphi-dtheta-dpsi, as would be the case |
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| 271 | for azimuthal equidistance. Free movement using theta or phi |
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| 272 | uniform over +/- 180 will work, but not as well as equirectangular |
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| 273 | phi, with theta being slightly worse. Computationally it is much |
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| 274 | cheaper for wide theta-phi meshes since it excludes points which |
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| 275 | lie outside the sinusoid near theta +/- 90 rather than packing |
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[d73a5ac] | 276 | them close together as in equirectangle. Note that the poles |
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| 277 | will be slightly overweighted for theta > 90 with the circle |
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| 278 | from theta at 90+dt winding backwards around the pole, overlapping |
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| 279 | the circle from theta at 90-dt. |
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[0f65169] | 280 | Guyou (hemisphere-in-a-square) **not weighted** |
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[bcb5594] | 281 | <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection> |
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[0f65169] | 282 | With tiling, allows rotation in phi or theta through +/- 180, with |
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| 283 | uniform spacing. Both theta and phi allow free rotation, with wobble |
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| 284 | in the orthogonal direction reasonably well behaved (though not as |
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| 285 | good as equirectangular phi). The forward/reverse transformations |
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| 286 | relies on elliptic integrals that are somewhat expensive, so the |
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| 287 | behaviour has to be very good to justify the cost and complexity. |
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| 288 | The weighting function for each point has not yet been computed. |
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| 289 | Note: run the module *guyou.py* directly and it will show the forward |
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| 290 | and reverse mappings. |
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[bcb5594] | 291 | azimuthal_equal_area **incomplete** |
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| 292 | <https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection> |
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| 293 | Preserves the relative density of the surface patches. Not that |
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| 294 | useful and not completely implemented |
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| 295 | Gauss-Kreuger **not implemented** |
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| 296 | <https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Ellipsoidal_transverse_Mercator> |
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| 297 | Should allow free movement in theta, but phi is distorted. |
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[aa6989b] | 298 | """ |
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[802c412] | 299 | # TODO: try Kent distribution instead of a gaussian warped by projection |
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| 300 | |
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[b3703f5] | 301 | dist_x = np.linspace(-1, 1, n) |
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| 302 | weights = np.ones_like(dist_x) |
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[aa6989b] | 303 | if dist == 'gaussian': |
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[b3703f5] | 304 | dist_x *= 3 |
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| 305 | weights = exp(-0.5*dist_x**2) |
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[aa6989b] | 306 | elif dist == 'rectangle': |
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| 307 | # Note: uses sasmodels ridiculous definition of rectangle width |
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[b3703f5] | 308 | dist_x *= sqrt(3) |
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[bcb5594] | 309 | elif dist == 'uniform': |
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| 310 | pass |
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[782dd1f] | 311 | else: |
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[bcb5594] | 312 | raise ValueError("expected dist to be gaussian, rectangle or uniform") |
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[782dd1f] | 313 | |
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[4991048] | 314 | if projection == 'equirectangular': #define PROJECTION 1 |
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[d86f0fc] | 315 | def _rotate(theta_i, phi_j): |
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[87a6591] | 316 | return Rx(phi_j)*Ry(theta_i) |
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[802c412] | 317 | def _weight(theta_i, phi_j, w_i, w_j): |
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| 318 | return w_i*w_j*abs(cos(radians(theta_i))) |
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[4991048] | 319 | elif projection == 'sinusoidal': #define PROJECTION 2 |
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[d86f0fc] | 320 | def _rotate(theta_i, phi_j): |
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[4991048] | 321 | latitude = theta_i |
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| 322 | scale = cos(radians(latitude)) |
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| 323 | longitude = phi_j/scale if abs(phi_j) < abs(scale)*180 else 0 |
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| 324 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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| 325 | return Rx(longitude)*Ry(latitude) |
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[802c412] | 326 | def _weight(theta_i, phi_j, w_i, w_j): |
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[4991048] | 327 | latitude = theta_i |
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| 328 | scale = cos(radians(latitude)) |
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[802c412] | 329 | active = 1 if abs(phi_j) < abs(scale)*180 else 0 |
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| 330 | return active*w_i*w_j |
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[4991048] | 331 | elif projection == 'guyou': #define PROJECTION 3 (eventually?) |
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[d86f0fc] | 332 | def _rotate(theta_i, phi_j): |
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[802c412] | 333 | from .guyou import guyou_invert |
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[4991048] | 334 | #latitude, longitude = guyou_invert([theta_i], [phi_j]) |
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| 335 | longitude, latitude = guyou_invert([phi_j], [theta_i]) |
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| 336 | return Rx(longitude[0])*Ry(latitude[0]) |
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[802c412] | 337 | def _weight(theta_i, phi_j, w_i, w_j): |
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| 338 | return w_i*w_j |
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[4991048] | 339 | elif projection == 'azimuthal_equidistance': # Note: Rz Ry, not Rx Ry |
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[d86f0fc] | 340 | def _rotate(theta_i, phi_j): |
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[87a6591] | 341 | latitude = sqrt(theta_i**2 + phi_j**2) |
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| 342 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
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| 343 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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| 344 | return Rz(longitude)*Ry(latitude) |
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[802c412] | 345 | def _weight(theta_i, phi_j, w_i, w_j): |
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[5b5ea20] | 346 | # Weighting for each point comes from the integral: |
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| 347 | # \int\int I(q, lat, log) sin(lat) dlat dlog |
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| 348 | # We are doing a conformal mapping from disk to sphere, so we need |
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| 349 | # a change of variables g(theta, phi) -> (lat, long): |
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| 350 | # lat, long = sqrt(theta^2 + phi^2), arctan(phi/theta) |
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| 351 | # giving: |
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| 352 | # dtheta dphi = det(J) dlat dlong |
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| 353 | # where J is the jacobian from the partials of g. Using |
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| 354 | # R = sqrt(theta^2 + phi^2), |
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| 355 | # then |
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| 356 | # J = [[x/R, Y/R], -y/R^2, x/R^2]] |
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| 357 | # and |
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| 358 | # det(J) = 1/R |
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| 359 | # with the final integral being: |
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| 360 | # \int\int I(q, theta, phi) sin(R)/R dtheta dphi |
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| 361 | # |
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| 362 | # This does approximately the right thing, decreasing the weight |
---|
| 363 | # of each point as you go farther out on the disk, but it hasn't |
---|
| 364 | # yet been checked against the 1D integral results. Prior |
---|
| 365 | # to declaring this "good enough" and checking that integrals |
---|
| 366 | # work in practice, we will examine alternative mappings. |
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| 367 | # |
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| 368 | # The issue is that the mapping does not support the case of free |
---|
| 369 | # rotation about a single axis correctly, with a small deviation |
---|
| 370 | # in the orthogonal axis independent of the first axis. Like the |
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| 371 | # usual polar coordiates integration, the integrated sections |
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| 372 | # form wedges, though at least in this case the wedge cuts through |
---|
| 373 | # the entire sphere, and treats theta and phi identically. |
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[87a6591] | 374 | latitude = sqrt(theta_i**2 + phi_j**2) |
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[802c412] | 375 | weight = sin(radians(latitude))/latitude if latitude != 0 else 1 |
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| 376 | return weight*w_i*w_j if latitude < 180 else 0 |
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[bcb5594] | 377 | elif projection == 'azimuthal_equal_area': |
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[d86f0fc] | 378 | def _rotate(theta_i, phi_j): |
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[802c412] | 379 | radius = min(1, sqrt(theta_i**2 + phi_j**2)/180) |
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| 380 | latitude = 180-degrees(2*np.arccos(radius)) |
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[87a6591] | 381 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
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| 382 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
---|
| 383 | return Rz(longitude)*Ry(latitude) |
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[802c412] | 384 | def _weight(theta_i, phi_j, w_i, w_j): |
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[5b5ea20] | 385 | latitude = sqrt(theta_i**2 + phi_j**2) |
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[802c412] | 386 | weight = sin(radians(latitude))/latitude if latitude != 0 else 1 |
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| 387 | return weight*w_i*w_j if latitude < 180 else 0 |
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[b9578fc] | 388 | else: |
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[bcb5594] | 389 | raise ValueError("unknown projection %r"%projection) |
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[b9578fc] | 390 | |
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[8678a34] | 391 | # mesh in theta, phi formed by rotating z |
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[d86f0fc] | 392 | dtheta, dphi, dpsi = jitter |
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[8678a34] | 393 | z = np.matrix([[0], [0], [radius]]) |
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[d86f0fc] | 394 | points = np.hstack([_rotate(theta_i, phi_j)*z |
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[b3703f5] | 395 | for theta_i in dtheta*dist_x |
---|
| 396 | for phi_j in dphi*dist_x]) |
---|
| 397 | dist_w = np.array([_weight(theta_i, phi_j, w_i, w_j) |
---|
| 398 | for w_i, theta_i in zip(weights, dtheta*dist_x) |
---|
| 399 | for w_j, phi_j in zip(weights, dphi*dist_x)]) |
---|
| 400 | #print(max(dist_w), min(dist_w), min(dist_w[dist_w > 0])) |
---|
| 401 | points = points[:, dist_w > 0] |
---|
| 402 | dist_w = dist_w[dist_w > 0] |
---|
| 403 | dist_w /= max(dist_w) |
---|
[87a6591] | 404 | |
---|
[8678a34] | 405 | # rotate relative to beam |
---|
| 406 | points = orient_relative_to_beam(view, points) |
---|
[782dd1f] | 407 | |
---|
[8678a34] | 408 | x, y, z = [np.array(v).flatten() for v in points] |
---|
[87a6591] | 409 | #plt.figure(2); plt.clf(); plt.hist(z, bins=np.linspace(-1, 1, 51)) |
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[b3703f5] | 410 | axes.scatter(x, y, z, c=dist_w, marker='o', vmin=0., vmax=1.) |
---|
[782dd1f] | 411 | |
---|
[802c412] | 412 | def draw_labels(axes, view, jitter, text): |
---|
[aa6989b] | 413 | """ |
---|
| 414 | Draw text at a particular location. |
---|
| 415 | """ |
---|
| 416 | labels, locations, orientations = zip(*text) |
---|
| 417 | px, py, pz = zip(*locations) |
---|
| 418 | dx, dy, dz = zip(*orientations) |
---|
| 419 | |
---|
| 420 | px, py, pz = transform_xyz(view, jitter, px, py, pz) |
---|
| 421 | dx, dy, dz = transform_xyz(view, jitter, dx, dy, dz) |
---|
| 422 | |
---|
| 423 | # TODO: zdir for labels is broken, and labels aren't appearing. |
---|
| 424 | for label, p, zdir in zip(labels, zip(px, py, pz), zip(dx, dy, dz)): |
---|
| 425 | zdir = np.asarray(zdir).flatten() |
---|
[802c412] | 426 | axes.text(p[0], p[1], p[2], label, zdir=zdir) |
---|
[aa6989b] | 427 | |
---|
| 428 | # Definition of rotation matrices comes from wikipedia: |
---|
| 429 | # https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations |
---|
[782dd1f] | 430 | def Rx(angle): |
---|
[aa6989b] | 431 | """Construct a matrix to rotate points about *x* by *angle* degrees.""" |
---|
[802c412] | 432 | angle = radians(angle) |
---|
[b3703f5] | 433 | rot = [[1, 0, 0], |
---|
| 434 | [0, +cos(angle), -sin(angle)], |
---|
| 435 | [0, +sin(angle), +cos(angle)]] |
---|
| 436 | return np.matrix(rot) |
---|
[782dd1f] | 437 | |
---|
| 438 | def Ry(angle): |
---|
[aa6989b] | 439 | """Construct a matrix to rotate points about *y* by *angle* degrees.""" |
---|
[802c412] | 440 | angle = radians(angle) |
---|
[b3703f5] | 441 | rot = [[+cos(angle), 0, +sin(angle)], |
---|
| 442 | [0, 1, 0], |
---|
| 443 | [-sin(angle), 0, +cos(angle)]] |
---|
| 444 | return np.matrix(rot) |
---|
[782dd1f] | 445 | |
---|
| 446 | def Rz(angle): |
---|
[aa6989b] | 447 | """Construct a matrix to rotate points about *z* by *angle* degrees.""" |
---|
[802c412] | 448 | angle = radians(angle) |
---|
[b3703f5] | 449 | rot = [[+cos(angle), -sin(angle), 0], |
---|
| 450 | [+sin(angle), +cos(angle), 0], |
---|
| 451 | [0, 0, 1]] |
---|
| 452 | return np.matrix(rot) |
---|
[782dd1f] | 453 | |
---|
[8678a34] | 454 | def transform_xyz(view, jitter, x, y, z): |
---|
[aa6989b] | 455 | """ |
---|
| 456 | Send a set of (x,y,z) points through the jitter and view transforms. |
---|
| 457 | """ |
---|
[8678a34] | 458 | x, y, z = [np.asarray(v) for v in (x, y, z)] |
---|
| 459 | shape = x.shape |
---|
[d86f0fc] | 460 | points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) |
---|
[8678a34] | 461 | points = apply_jitter(jitter, points) |
---|
| 462 | points = orient_relative_to_beam(view, points) |
---|
| 463 | x, y, z = [np.array(v).reshape(shape) for v in points] |
---|
| 464 | return x, y, z |
---|
| 465 | |
---|
| 466 | def apply_jitter(jitter, points): |
---|
[aa6989b] | 467 | """ |
---|
| 468 | Apply the jitter transform to a set of points. |
---|
| 469 | |
---|
| 470 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
| 471 | """ |
---|
[8678a34] | 472 | dtheta, dphi, dpsi = jitter |
---|
[d4c33d6] | 473 | points = Rx(dphi)*Ry(dtheta)*Rz(dpsi)*points |
---|
[8678a34] | 474 | return points |
---|
| 475 | |
---|
| 476 | def orient_relative_to_beam(view, points): |
---|
[aa6989b] | 477 | """ |
---|
| 478 | Apply the view transform to a set of points. |
---|
| 479 | |
---|
| 480 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
---|
| 481 | """ |
---|
[8678a34] | 482 | theta, phi, psi = view |
---|
| 483 | points = Rz(phi)*Ry(theta)*Rz(psi)*points |
---|
| 484 | return points |
---|
| 485 | |
---|
[aa6989b] | 486 | # translate between number of dimension of dispersity and the number of |
---|
| 487 | # points along each dimension. |
---|
| 488 | PD_N_TABLE = { |
---|
| 489 | (0, 0, 0): (0, 0, 0), # 0 |
---|
| 490 | (1, 0, 0): (100, 0, 0), # 100 |
---|
| 491 | (0, 1, 0): (0, 100, 0), |
---|
| 492 | (0, 0, 1): (0, 0, 100), |
---|
| 493 | (1, 1, 0): (30, 30, 0), # 900 |
---|
| 494 | (1, 0, 1): (30, 0, 30), |
---|
| 495 | (0, 1, 1): (0, 30, 30), |
---|
| 496 | (1, 1, 1): (15, 15, 15), # 3375 |
---|
| 497 | } |
---|
| 498 | |
---|
| 499 | def clipped_range(data, portion=1.0, mode='central'): |
---|
| 500 | """ |
---|
| 501 | Determine range from data. |
---|
| 502 | |
---|
| 503 | If *portion* is 1, use full range, otherwise use the center of the range |
---|
| 504 | or the top of the range, depending on whether *mode* is 'central' or 'top'. |
---|
| 505 | """ |
---|
| 506 | if portion == 1.0: |
---|
| 507 | return data.min(), data.max() |
---|
| 508 | elif mode == 'central': |
---|
| 509 | data = np.sort(data.flatten()) |
---|
| 510 | offset = int(portion*len(data)/2 + 0.5) |
---|
| 511 | return data[offset], data[-offset] |
---|
| 512 | elif mode == 'top': |
---|
| 513 | data = np.sort(data.flatten()) |
---|
| 514 | offset = int(portion*len(data) + 0.5) |
---|
| 515 | return data[offset], data[-1] |
---|
| 516 | |
---|
[802c412] | 517 | def draw_scattering(calculator, axes, view, jitter, dist='gaussian'): |
---|
[aa6989b] | 518 | """ |
---|
| 519 | Plot the scattering for the particular view. |
---|
| 520 | |
---|
[802c412] | 521 | *calculator* is returned from :func:`build_model`. *axes* are the 3D axes |
---|
[aa6989b] | 522 | on which the data will be plotted. *view* and *jitter* are the current |
---|
| 523 | orientation and orientation dispersity. *dist* is one of the sasmodels |
---|
| 524 | weight distributions. |
---|
| 525 | """ |
---|
[bcb5594] | 526 | if dist == 'uniform': # uniform is not yet in this branch |
---|
| 527 | dist, scale = 'rectangle', 1/sqrt(3) |
---|
| 528 | else: |
---|
| 529 | scale = 1 |
---|
[aa6989b] | 530 | |
---|
| 531 | # add the orientation parameters to the model parameters |
---|
| 532 | theta, phi, psi = view |
---|
| 533 | theta_pd, phi_pd, psi_pd = [scale*v for v in jitter] |
---|
[d86f0fc] | 534 | theta_pd_n, phi_pd_n, psi_pd_n = PD_N_TABLE[(theta_pd > 0, phi_pd > 0, psi_pd > 0)] |
---|
[aa6989b] | 535 | ## increase pd_n for testing jitter integration rather than simple viz |
---|
| 536 | #theta_pd_n, phi_pd_n, psi_pd_n = [5*v for v in (theta_pd_n, phi_pd_n, psi_pd_n)] |
---|
| 537 | |
---|
| 538 | pars = dict( |
---|
| 539 | theta=theta, theta_pd=theta_pd, theta_pd_type=dist, theta_pd_n=theta_pd_n, |
---|
| 540 | phi=phi, phi_pd=phi_pd, phi_pd_type=dist, phi_pd_n=phi_pd_n, |
---|
| 541 | psi=psi, psi_pd=psi_pd, psi_pd_type=dist, psi_pd_n=psi_pd_n, |
---|
| 542 | ) |
---|
| 543 | pars.update(calculator.pars) |
---|
| 544 | |
---|
| 545 | # compute the pattern |
---|
| 546 | qx, qy = calculator._data.x_bins, calculator._data.y_bins |
---|
| 547 | Iqxy = calculator(**pars).reshape(len(qx), len(qy)) |
---|
| 548 | |
---|
| 549 | # scale it and draw it |
---|
| 550 | Iqxy = np.log(Iqxy) |
---|
| 551 | if calculator.limits: |
---|
| 552 | # use limits from orientation (0,0,0) |
---|
| 553 | vmin, vmax = calculator.limits |
---|
| 554 | else: |
---|
[4991048] | 555 | vmax = Iqxy.max() |
---|
| 556 | vmin = vmax*10**-7 |
---|
| 557 | #vmin, vmax = clipped_range(Iqxy, portion=portion, mode='top') |
---|
[aa6989b] | 558 | #print("range",(vmin,vmax)) |
---|
| 559 | #qx, qy = np.meshgrid(qx, qy) |
---|
| 560 | if 0: |
---|
| 561 | level = np.asarray(255*(Iqxy - vmin)/(vmax - vmin), 'i') |
---|
[d86f0fc] | 562 | level[level < 0] = 0 |
---|
[aa6989b] | 563 | colors = plt.get_cmap()(level) |
---|
[802c412] | 564 | axes.plot_surface(qx, qy, -1.1, rstride=1, cstride=1, facecolors=colors) |
---|
[aa6989b] | 565 | elif 1: |
---|
[802c412] | 566 | axes.contourf(qx/qx.max(), qy/qy.max(), Iqxy, zdir='z', offset=-1.1, |
---|
[b3703f5] | 567 | levels=np.linspace(vmin, vmax, 24)) |
---|
[aa6989b] | 568 | else: |
---|
[802c412] | 569 | axes.pcolormesh(qx, qy, Iqxy) |
---|
[aa6989b] | 570 | |
---|
| 571 | def build_model(model_name, n=150, qmax=0.5, **pars): |
---|
| 572 | """ |
---|
| 573 | Build a calculator for the given shape. |
---|
| 574 | |
---|
| 575 | *model_name* is any sasmodels model. *n* and *qmax* define an n x n mesh |
---|
| 576 | on which to evaluate the model. The remaining parameters are stored in |
---|
| 577 | the returned calculator as *calculator.pars*. They are used by |
---|
| 578 | :func:`draw_scattering` to set the non-orientation parameters in the |
---|
| 579 | calculation. |
---|
| 580 | |
---|
| 581 | Returns a *calculator* function which takes a dictionary or parameters and |
---|
| 582 | produces Iqxy. The Iqxy value needs to be reshaped to an n x n matrix |
---|
| 583 | for plotting. See the :class:`sasmodels.direct_model.DirectModel` class |
---|
| 584 | for details. |
---|
| 585 | """ |
---|
[b3703f5] | 586 | from sasmodels.core import load_model_info, build_model as build_sasmodel |
---|
[aa6989b] | 587 | from sasmodels.data import empty_data2D |
---|
| 588 | from sasmodels.direct_model import DirectModel |
---|
| 589 | |
---|
| 590 | model_info = load_model_info(model_name) |
---|
[b3703f5] | 591 | model = build_sasmodel(model_info) #, dtype='double!') |
---|
[aa6989b] | 592 | q = np.linspace(-qmax, qmax, n) |
---|
| 593 | data = empty_data2D(q, q) |
---|
| 594 | calculator = DirectModel(data, model) |
---|
| 595 | |
---|
| 596 | # stuff the values for non-orientation parameters into the calculator |
---|
| 597 | calculator.pars = pars.copy() |
---|
| 598 | calculator.pars.setdefault('backgound', 1e-3) |
---|
| 599 | |
---|
| 600 | # fix the data limits so that we can see if the pattern fades |
---|
| 601 | # under rotation or angular dispersion |
---|
| 602 | Iqxy = calculator(theta=0, phi=0, psi=0, **calculator.pars) |
---|
| 603 | Iqxy = np.log(Iqxy) |
---|
| 604 | vmin, vmax = clipped_range(Iqxy, 0.95, mode='top') |
---|
| 605 | calculator.limits = vmin, vmax+1 |
---|
| 606 | |
---|
| 607 | return calculator |
---|
| 608 | |
---|
[d86f0fc] | 609 | def select_calculator(model_name, n=150, size=(10, 40, 100)): |
---|
[aa6989b] | 610 | """ |
---|
| 611 | Create a model calculator for the given shape. |
---|
| 612 | |
---|
| 613 | *model_name* is one of sphere, cylinder, ellipsoid, triaxial_ellipsoid, |
---|
| 614 | parallelepiped or bcc_paracrystal. *n* is the number of points to use |
---|
| 615 | in the q range. *qmax* is chosen based on model parameters for the |
---|
| 616 | given model to show something intersting. |
---|
| 617 | |
---|
| 618 | Returns *calculator* and tuple *size* (a,b,c) giving minor and major |
---|
| 619 | equitorial axes and polar axis respectively. See :func:`build_model` |
---|
| 620 | for details on the returned calculator. |
---|
| 621 | """ |
---|
[59e537a] | 622 | a, b, c = size |
---|
[58a1be9] | 623 | d_factor = 0.06 # for paracrystal models |
---|
[aa6989b] | 624 | if model_name == 'sphere': |
---|
| 625 | calculator = build_model('sphere', n=n, radius=c) |
---|
| 626 | a = b = c |
---|
[58a1be9] | 627 | elif model_name == 'sc_paracrystal': |
---|
| 628 | a = b = c |
---|
| 629 | dnn = c |
---|
| 630 | radius = 0.5*c |
---|
| 631 | calculator = build_model('sc_paracrystal', n=n, dnn=dnn, |
---|
[d86f0fc] | 632 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
| 633 | background=0) |
---|
[58a1be9] | 634 | elif model_name == 'fcc_paracrystal': |
---|
| 635 | a = b = c |
---|
| 636 | # nearest neigbour distance dnn should be 2 radius, but I think the |
---|
| 637 | # model uses lattice spacing rather than dnn in its calculations |
---|
| 638 | dnn = 0.5*c |
---|
| 639 | radius = sqrt(2)/4 * c |
---|
| 640 | calculator = build_model('fcc_paracrystal', n=n, dnn=dnn, |
---|
[d86f0fc] | 641 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
| 642 | background=0) |
---|
[aa6989b] | 643 | elif model_name == 'bcc_paracrystal': |
---|
| 644 | a = b = c |
---|
[58a1be9] | 645 | # nearest neigbour distance dnn should be 2 radius, but I think the |
---|
| 646 | # model uses lattice spacing rather than dnn in its calculations |
---|
| 647 | dnn = 0.5*c |
---|
| 648 | radius = sqrt(3)/2 * c |
---|
| 649 | calculator = build_model('bcc_paracrystal', n=n, dnn=dnn, |
---|
[d86f0fc] | 650 | d_factor=d_factor, radius=(1-d_factor)*radius, |
---|
| 651 | background=0) |
---|
[aa6989b] | 652 | elif model_name == 'cylinder': |
---|
| 653 | calculator = build_model('cylinder', n=n, qmax=0.3, radius=b, length=c) |
---|
| 654 | a = b |
---|
| 655 | elif model_name == 'ellipsoid': |
---|
| 656 | calculator = build_model('ellipsoid', n=n, qmax=1.0, |
---|
| 657 | radius_polar=c, radius_equatorial=b) |
---|
| 658 | a = b |
---|
| 659 | elif model_name == 'triaxial_ellipsoid': |
---|
| 660 | calculator = build_model('triaxial_ellipsoid', n=n, qmax=0.5, |
---|
| 661 | radius_equat_minor=a, |
---|
| 662 | radius_equat_major=b, |
---|
| 663 | radius_polar=c) |
---|
| 664 | elif model_name == 'parallelepiped': |
---|
| 665 | calculator = build_model('parallelepiped', n=n, a=a, b=b, c=c) |
---|
| 666 | else: |
---|
| 667 | raise ValueError("unknown model %s"%model_name) |
---|
[8678a34] | 668 | |
---|
[aa6989b] | 669 | return calculator, (a, b, c) |
---|
[8678a34] | 670 | |
---|
[bcb5594] | 671 | SHAPES = [ |
---|
[58a1be9] | 672 | 'parallelepiped', |
---|
| 673 | 'sphere', 'ellipsoid', 'triaxial_ellipsoid', |
---|
| 674 | 'cylinder', |
---|
| 675 | 'fcc_paracrystal', 'bcc_paracrystal', 'sc_paracrystal', |
---|
[d86f0fc] | 676 | ] |
---|
[bcb5594] | 677 | |
---|
[58a1be9] | 678 | DRAW_SHAPES = { |
---|
| 679 | 'fcc_paracrystal': draw_fcc, |
---|
| 680 | 'bcc_paracrystal': draw_bcc, |
---|
| 681 | 'sc_paracrystal': draw_sc, |
---|
| 682 | 'parallelepiped': draw_parallelepiped, |
---|
| 683 | } |
---|
| 684 | |
---|
[bcb5594] | 685 | DISTRIBUTIONS = [ |
---|
| 686 | 'gaussian', 'rectangle', 'uniform', |
---|
| 687 | ] |
---|
| 688 | DIST_LIMITS = { |
---|
| 689 | 'gaussian': 30, |
---|
| 690 | 'rectangle': 90/sqrt(3), |
---|
| 691 | 'uniform': 90, |
---|
| 692 | } |
---|
| 693 | |
---|
| 694 | def run(model_name='parallelepiped', size=(10, 40, 100), |
---|
| 695 | dist='gaussian', mesh=30, |
---|
| 696 | projection='equirectangular'): |
---|
[aa6989b] | 697 | """ |
---|
| 698 | Show an interactive orientation and jitter demo. |
---|
[8678a34] | 699 | |
---|
[58a1be9] | 700 | *model_name* is one of: sphere, ellipsoid, triaxial_ellipsoid, |
---|
| 701 | parallelepiped, cylinder, or sc/fcc/bcc_paracrystal |
---|
[0d5a655] | 702 | |
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| 703 | *size* gives the dimensions (a, b, c) of the shape. |
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| 704 | |
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| 705 | *dist* is the type of dispersition: gaussian, rectangle, or uniform. |
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| 706 | |
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| 707 | *mesh* is the number of points in the dispersion mesh. |
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| 708 | |
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| 709 | *projection* is the map projection to use for the mesh: equirectangular, |
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| 710 | sinusoidal, guyou, azimuthal_equidistance, or azimuthal_equal_area. |
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[aa6989b] | 711 | """ |
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[4991048] | 712 | # projection number according to 1-order position in list, but |
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| 713 | # only 1 and 2 are implemented so far. |
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| 714 | from sasmodels import generate |
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| 715 | generate.PROJECTION = PROJECTIONS.index(projection) + 1 |
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| 716 | if generate.PROJECTION > 2: |
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| 717 | print("*** PROJECTION %s not implemented in scattering function ***"%projection) |
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| 718 | generate.PROJECTION = 2 |
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| 719 | |
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[aa6989b] | 720 | # set up calculator |
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[59e537a] | 721 | calculator, size = select_calculator(model_name, n=150, size=size) |
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[58a1be9] | 722 | draw_shape = DRAW_SHAPES.get(model_name, draw_parallelepiped) |
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[8678a34] | 723 | |
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[aa6989b] | 724 | ## uncomment to set an independent the colour range for every view |
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| 725 | ## If left commented, the colour range is fixed for all views |
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| 726 | calculator.limits = None |
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| 727 | |
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| 728 | ## initial view |
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| 729 | #theta, dtheta = 70., 10. |
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| 730 | #phi, dphi = -45., 3. |
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| 731 | #psi, dpsi = -45., 3. |
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| 732 | theta, phi, psi = 0, 0, 0 |
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| 733 | dtheta, dphi, dpsi = 0, 0, 0 |
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| 734 | |
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| 735 | ## create the plot window |
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[782dd1f] | 736 | #plt.hold(True) |
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[de71632] | 737 | plt.subplots(num=None, figsize=(5.5, 5.5)) |
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[782dd1f] | 738 | plt.set_cmap('gist_earth') |
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| 739 | plt.clf() |
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[de71632] | 740 | plt.gcf().canvas.set_window_title(projection) |
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[782dd1f] | 741 | #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) |
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[802c412] | 742 | #axes = plt.subplot(gs[0], projection='3d') |
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| 743 | axes = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') |
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[36b3154] | 744 | try: # CRUFT: not all versions of matplotlib accept 'square' 3d projection |
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[802c412] | 745 | axes.axis('square') |
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[36b3154] | 746 | except Exception: |
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| 747 | pass |
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[782dd1f] | 748 | |
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[7d97437] | 749 | # CRUFT: use axisbg instead of facecolor for matplotlib<2 |
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| 750 | facecolor_prop = 'facecolor' if mpl.__version__ > '2' else 'axisbg' |
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| 751 | props = {facecolor_prop: 'lightgoldenrodyellow'} |
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[8678a34] | 752 | |
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[aa6989b] | 753 | ## add control widgets to plot |
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[7d97437] | 754 | axes_theta = plt.axes([0.1, 0.15, 0.45, 0.04], **props) |
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| 755 | axes_phi = plt.axes([0.1, 0.1, 0.45, 0.04], **props) |
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| 756 | axes_psi = plt.axes([0.1, 0.05, 0.45, 0.04], **props) |
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[802c412] | 757 | stheta = Slider(axes_theta, 'Theta', -90, 90, valinit=theta) |
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| 758 | sphi = Slider(axes_phi, 'Phi', -180, 180, valinit=phi) |
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| 759 | spsi = Slider(axes_psi, 'Psi', -180, 180, valinit=psi) |
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| 760 | |
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[7d97437] | 761 | axes_dtheta = plt.axes([0.75, 0.15, 0.15, 0.04], **props) |
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| 762 | axes_dphi = plt.axes([0.75, 0.1, 0.15, 0.04], **props) |
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| 763 | axes_dpsi = plt.axes([0.75, 0.05, 0.15, 0.04], **props) |
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[aa6989b] | 764 | # Note: using ridiculous definition of rectangle distribution, whose width |
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| 765 | # in sasmodels is sqrt(3) times the given width. Divide by sqrt(3) to keep |
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| 766 | # the maximum width to 90. |
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[bcb5594] | 767 | dlimit = DIST_LIMITS[dist] |
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[802c412] | 768 | sdtheta = Slider(axes_dtheta, 'dTheta', 0, 2*dlimit, valinit=dtheta) |
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| 769 | sdphi = Slider(axes_dphi, 'dPhi', 0, 2*dlimit, valinit=dphi) |
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| 770 | sdpsi = Slider(axes_dpsi, 'dPsi', 0, 2*dlimit, valinit=dpsi) |
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[aa6989b] | 771 | |
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[58a1be9] | 772 | |
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[aa6989b] | 773 | ## callback to draw the new view |
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[782dd1f] | 774 | def update(val, axis=None): |
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[8678a34] | 775 | view = stheta.val, sphi.val, spsi.val |
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| 776 | jitter = sdtheta.val, sdphi.val, sdpsi.val |
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[aa6989b] | 777 | # set small jitter as 0 if multiple pd dims |
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| 778 | dims = sum(v > 0 for v in jitter) |
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[1198f90] | 779 | limit = [0, 0.5, 5][dims] |
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[aa6989b] | 780 | jitter = [0 if v < limit else v for v in jitter] |
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[802c412] | 781 | axes.cla() |
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| 782 | draw_beam(axes, (0, 0)) |
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| 783 | draw_jitter(axes, view, jitter, dist=dist, size=size, draw_shape=draw_shape) |
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| 784 | #draw_jitter(axes, view, (0,0,0)) |
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| 785 | draw_mesh(axes, view, jitter, dist=dist, n=mesh, projection=projection) |
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| 786 | draw_scattering(calculator, axes, view, jitter, dist=dist) |
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[782dd1f] | 787 | plt.gcf().canvas.draw() |
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| 788 | |
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[aa6989b] | 789 | ## bind control widgets to view updater |
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[d86f0fc] | 790 | stheta.on_changed(lambda v: update(v, 'theta')) |
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[782dd1f] | 791 | sphi.on_changed(lambda v: update(v, 'phi')) |
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| 792 | spsi.on_changed(lambda v: update(v, 'psi')) |
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| 793 | sdtheta.on_changed(lambda v: update(v, 'dtheta')) |
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| 794 | sdphi.on_changed(lambda v: update(v, 'dphi')) |
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| 795 | sdpsi.on_changed(lambda v: update(v, 'dpsi')) |
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| 796 | |
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[aa6989b] | 797 | ## initialize view |
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[782dd1f] | 798 | update(None, 'phi') |
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| 799 | |
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[aa6989b] | 800 | ## go interactive |
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[782dd1f] | 801 | plt.show() |
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| 802 | |
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[bcb5594] | 803 | def main(): |
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| 804 | parser = argparse.ArgumentParser( |
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| 805 | description="Display jitter", |
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| 806 | formatter_class=argparse.ArgumentDefaultsHelpFormatter, |
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| 807 | ) |
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[d86f0fc] | 808 | parser.add_argument('-p', '--projection', choices=PROJECTIONS, |
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| 809 | default=PROJECTIONS[0], |
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| 810 | help='coordinate projection') |
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| 811 | parser.add_argument('-s', '--size', type=str, default='10,40,100', |
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| 812 | help='a,b,c lengths') |
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| 813 | parser.add_argument('-d', '--distribution', choices=DISTRIBUTIONS, |
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| 814 | default=DISTRIBUTIONS[0], |
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| 815 | help='jitter distribution') |
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| 816 | parser.add_argument('-m', '--mesh', type=int, default=30, |
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| 817 | help='#points in theta-phi mesh') |
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| 818 | parser.add_argument('shape', choices=SHAPES, nargs='?', default=SHAPES[0], |
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| 819 | help='oriented shape') |
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[bcb5594] | 820 | opts = parser.parse_args() |
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| 821 | size = tuple(int(v) for v in opts.size.split(',')) |
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| 822 | run(opts.shape, size=size, |
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| 823 | mesh=opts.mesh, dist=opts.distribution, |
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| 824 | projection=opts.projection) |
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| 825 | |
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[782dd1f] | 826 | if __name__ == "__main__": |
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[bcb5594] | 827 | main() |
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