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GeezerVison is showing github.com — ThinkPython2/python_thinking/Frame.py at master · PenseAllen/ThinkPython2 Expand file tree/ Copy pathFrame.pyMore file actions 311 lines (230 loc) · 7.52 KB / Copy pathFrame.pyFile metadata and controls311 lines (230 loc) · 7.52 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 """Exploration of Vectors and Frames. Copyright 2012 Allen B. Downey License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html """ from __future__ import print_function, division import sys import numpy import math def println(s): print(s, '\n') class FrameError(ValueError): """Represents a problem with frame of reference.""" class Vector: def __init__(self, array, frame=None): """A vector is an array of coordinates and a frame of reference. array: frame: Frame object """ self.array = array self.frame = frame def __str__(self): if self.frame == None: return '^{O}%s' % (str(self.array), ) else: return '^{%s}%s' % (str(self.frame), str(self.array)) def __add__(self, other): if self.frame != other.frame: raise FrameError("Vectors must be relative to the same frame.") return Vector(self.array + other.array, self.frame) @staticmethod def from_list(t, frame=None): """Makes a vector from a list. t: list of coordinates frame: reference Frame """ return Vector(numpy.array(t), frame) class Rotation: def __init__(self, array): self.array = array def __str__(self): return 'Rotation\n%s' % str(self.array) def __neg__(self): return Rotation(-self.array) def __mul__(self, other): """Apply the rotation to a Vector.""" return numpy.dot(self.array, other.array) __call__ = __mul__ @staticmethod def from_axis(axis, theta): x, y, z = numpy.ravel(axis.array) c = math.cos(theta) u = 1.0-c s = math.sqrt(1.0-c*c) xu, yu, zu = x*u, y*u, z*u v1 = [x*xu + c, x*yu - z*s, x*zu + y*s] v2 = [x*yu + z*s, y*yu + c, y*zu - x*s] v3 = [x*zu - y*s, y*zu + x*s, z*zu + c] return Rotation(numpy.array([v1, v2, v3])) def to_axis(self): # return the equivalent angle-axis as (khat, theta) pass def transpose(self): return Rotation(numpy.transpose(self.array)) inverse = transpose class Transform: """Represents a transform from one Frame to another.""" def __init__(self, rot, org, source=None): """Instantiates a Transform. rot: Rotation object org: origin Vector source: source Frame """ self.rot = rot self.org = org self.dest = org.frame self.source = source self.source.add_transform(self) def __str__(self): """Returns a string representation of the Transform.""" if self.dest == None: return '%s' % self.source.name return '_{%s}^{O}T' % self.source.name else: return '_{%s}^{%s}T' % (self.source.name, self.dest.name) def __mul__(self, other): """Applies a Transform to a Vector or Transform.""" if isinstance(other, Vector): return self.mul_vector(other) if isinstance(other, Transform): return self.mul_transform(other) __call__ = __mul__ def mul_vector(self, p): """Applies a Transform to a Vector. p: Vector Returns: Vector """ if p.frame != self.source: raise FrameError( "The frame of the vector must be the source of the transform") return Vector(self.rot * p, self.dest) + self.org def mul_transform(self, other): """Applies a Transform to another Transform. other: Transform Returns Transform """ if other.dest != self.source: raise FrameError( "This frames source must be the other frame's destination.") rot = Rotation(self.rot * other.rot) t = Transform(rot, self * other.org, other.source) return t def inverse(self): """Computes the inverse transform. Returns: Transform """ irot = self.rot.inverse() iorg = Vector(-(irot * self.org), self.source) t = Transform(irot, iorg, self.dest) return t class Frame: """Represents a frame of reference.""" # list of Frames roster = [] def __init__(self, name): """Instantiate a Frame. name: string """ self.name = name self.transforms = {} Frame.roster.append(self) def __str__(self): return self.name def add_transform(self, transform): """A frames is defined by a Transform relative to another Frame. transform: Transform object """ if transform.source != self: raise FrameError("Source of the transform must be this Frame.") if transform.dest: self.transforms[transform.dest] = transform def dests(self): """Returns a list of the Frames we know how to Transform to.""" return self.transforms.keys() class Vertex: """Represents a node in a graph.""" def __init__(self, frame): self.frame = frame self.dist = 1000000 self.out = [] def __str__(self): return '%s %d' % (self.frame.name, self.dist) def shortest_path(start, frames): """For a given list of frames and a starting frame, find the shortest path of transforms from the starting frame to all other frames. The 'distance' is the number of inverse transformations that must be calculated. The result is a dictionary of vertices, where each vertex is labeled with the frame it corresponds to, the distance from the starting frame, and the prev frame along the path from start. """ map = dict([(f, Vertex(f)) for f in frames]) length = {} for v in map.values(): for dest in v.frame.transforms: w = map[dest] v.out.append(w) length[(v, w)] = 0 w.out.append(v) length[(w, v)] = 1 s = map[start] s.dist = 0 queue = [s] while queue: v = queue.pop() for w in v.out: d = v.dist + length[(v,w)] if d < w.dist: w.dist = d w.prev = v if w not in queue: queue.append(w) return map def print_shortest_path(map): for source, v in map.items(): try: v.prev print(source, v.dist, v.prev.frame) except: print(source, v.dist) def print_length(length): for v, w in length: print(v.frame.name, w.frame.name, length[(v, w)]) print() def main(name): theta = math.pi/2 #v_o = Vector.from_list([0, 0, 0], None) origin = Frame('O') #o_trans = Transform(None, v_o, origin) xhat = Vector.from_list([1, 0, 0], origin) rx = Rotation.from_axis(xhat, theta) a = Frame('A') t_ao = Transform(rx, xhat, a) yhat = Vector.from_list([0, 1, 0], a) ry = Rotation.from_axis(yhat, theta) b = Frame('B') t_ba = Transform(ry, yhat, b) zhat = Vector.from_list([0, 0, 1], b) rz = Rotation.from_axis(zhat, theta) c = Frame('C') t_cb = Transform(rz, zhat, c) p_c = Vector.from_list([1, 1, 1], c) println(p_c) p_b = t_cb(p_c) println(p_b) p_a = t_ba(p_b) println(p_a) p = t_ao(p_a) println(p) map = shortest_path(origin, Frame.roster) print_shortest_path(map) cbao = t_ao(t_ba(t_cb)) p = cbao(p_c) println(p) inv = cbao.inverse() p_c = inv(p) println(p_c) map = shortest_path(origin, Frame.roster) print_shortest_path(map) if __name__ == '__main__': main(*sys.argv) |
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