Welcome, guest | Sign In | My Account | Store | Cart

This recipe implements vectors in pure Python and does not use "C" for speed enhancements. As a result, much effort has gone towards optimizing the instructions for the class methods. There are a few things that have yet to be improved, but it is being posted as an RFC. Comments on the structure, method names, and coding technique are requested for change. Once this code is standardized, work may commence on writing Vector3, Vector4, and VectorX. Please note that there is a difference between the "direction" and "degrees" properties.

Python, 482 lines
  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
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
from math import *
from functools import wraps

################################################################################

def autocast(method): # Optional method decorator
    @wraps(method)
    def wrapper(self, obj):
        try:
            return method(self, self.__class__(*obj))
        except TypeError:
            return method(self, obj)
    return wrapper

################################################################################

def Polar2(magnitude, degrees):
    x = magnitude * sin(radians(degrees))
    y = magnitude * cos(radians(degrees))
    return Vector2(x, y)

################################################################################
    
class Vector2:

    __slots__ = 'x', 'y'

    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return 'Vector2({!r}, {!r})'.format(self.x, self.y)

    def polar_repr(self):
        x, y = self.x, self.y
        magnitude = hypot(x, y)
        angle = degrees(atan2(x, y)) % 360
        return 'Polar2({!r}, {!r})'.format(magnitude, angle)

    # Rich Comparison Methods

    def __lt__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 < x2 * x2 + y2 * y2
        return hypot(self.x, self.y) < obj

    def __le__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 <= x2 * x2 + y2 * y2
        return hypot(self.x, self.y) <= obj

    def __eq__(self, obj):
        if isinstance(obj, Vector2):
            return self.x == obj.x and self.y == obj.y
        return hypot(self.x, self.y) == obj

    def __ne__(self, obj):
        if isinstance(obj, Vector2):
            return self.x != obj.x or self.y != obj.y
        return hypot(self.x, self.y) != obj

    def __gt__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 > x2 * x2 + y2 * y2
        return hypot(self.x, self.y) > obj

    def __ge__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 >= x2 * x2 + y2 * y2
        return hypot(self.x, self.y) >= obj

    # Boolean Operation

    def __bool__(self):
        return self.x != 0 or self.y != 0

    # Container Methods

    def __len__(self):
        return 2

    def __getitem__(self, index):
        return (self.x, self.y)[index]

    def __setitem__(self, index, value):
        temp = [self.x, self.y]
        temp[index] = value
        self.x, self.y = temp

    def __iter__(self):
        yield self.x
        yield self.y

    def __reversed__(self):
        yield self.y
        yield self.x

    def __contains__(self, obj):
        return obj in (self.x, self.y)

    # Binary Arithmetic Operations

    def __add__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x + obj.x, self.y + obj.y)
        return Vector2(self.x + obj, self.y + obj)

    def __sub__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x - obj.x, self.y - obj.y)
        return Vector2(self.x - obj, self.y - obj)

    def __mul__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x * obj.x, self.y * obj.y)
        return Vector2(self.x * obj, self.y * obj)

    def __truediv__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x / obj.x, self.y / obj.y)
        return Vector2(self.x / obj, self.y / obj)

    def __floordiv__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x // obj.x, self.y // obj.y)
        return Vector2(self.x // obj, self.y // obj)

    def __mod__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x % obj.x, self.y % obj.y)
        return Vector2(self.x % obj, self.y % obj)

    def __divmod__(self, obj):
        if isinstance(obj, Vector2):
            return (Vector2(self.x // obj.x, self.y // obj.y),
                    Vector2(self.x % obj.x, self.y % obj.y))
        return (Vector2(self.x // obj, self.y // obj),
                Vector2(self.x % obj, self.y % obj))

    def __pow__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x ** obj.x, self.y ** obj.y)
        return Vector2(self.x ** obj, self.y ** obj)

    def __lshift__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x << obj.x, self.y << obj.y)
        return Vector2(self.x << obj, self.y << obj)

    def __rshift__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x >> obj.x, self.y >> obj.y)
        return Vector2(self.x >> obj, self.y >> obj)

    def __and__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x & obj.x, self.y & obj.y)
        return Vector2(self.x & obj, self.y & obj)

    def __xor__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x ^ obj.x, self.y ^ obj.y)
        return Vector2(self.x ^ obj, self.y ^ obj)

    def __or__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x | obj.x, self.y | obj.y)
        return Vector2(self.x | obj, self.y | obj)

    # Binary Arithmetic Operations (with reflected operands)

    def __radd__(self, obj):
        return Vector2(obj + self.x, obj + self.y)

    def __rsub__(self, obj):
        return Vector2(obj - self.x, obj - self.y)

    def __rmul__(self, obj):
        return Vector2(obj * self.x, obj * self.y)

    def __rtruediv__(self, obj):
        return Vector2(obj / self.x, obj / self.y)

    def __rfloordiv__(self, obj):
        return Vector2(obj // self.x, obj // self.y)

    def __rmod__(self, obj):
        return Vector2(obj % self.x, obj % self.y)

    def __rdivmod__(self, obj):
        return (Vector2(obj // self.x, obj // self.y),
                Vector2(obj % self.x, obj % self.y))

    def __rpow__(self, obj):
        return Vector2(obj ** self.x, obj ** self.y)

    def __rlshift__(self, obj):
        return Vector2(obj << self.x, obj << self.y)

    def __rrshift__(self, obj):
        return Vector2(obj >> self.x, obj >> self.y)

    def __rand__(self, obj):
        return Vector2(obj & self.x, obj & self.y)

    def __rxor__(self, obj):
        return Vector2(obj ^ self.x, obj ^ self.y)

    def __ror__(self, obj):
        return Vector2(obj | self.x, obj | self.y)

    # Augmented Arithmetic Assignments

    def __iadd__(self, obj):
        if isinstance(obj, Vector2):
            self.x += obj.x
            self.y += obj.y
        else:
            self.x += obj
            self.y += obj
        return self

    def __isub__(self, obj):
        if isinstance(obj, Vector2):
            self.x -= obj.x
            self.y -= obj.y
        else:
            self.x -= obj
            self.y -= obj
        return self

    def __imul__(self, obj):
        if isinstance(obj, Vector2):
            self.x *= obj.x
            self.y *= obj.y
        else:
            self.x *= obj
            self.y *= obj
        return self

    def __itruediv__(self, obj):
        if isinstance(obj, Vector2):
            self.x /= obj.x
            self.y /= obj.y
        else:
            self.x /= obj
            self.y /= obj
        return self

    def __ifloordiv__(self, obj):
        if isinstance(obj, Vector2):
            self.x //= obj.x
            self.y //= obj.y
        else:
            self.x //= obj
            self.y //= obj
        return self

    def __imod__(self, obj):
        if isinstance(obj, Vector2):
            self.x %= obj.x
            self.y %= obj.y
        else:
            self.x %= obj
            self.y %= obj
        return self

    def __ipow__(self, obj):        
        if isinstance(obj, Vector2):
            self.x **= obj.x
            self.y **= obj.y
        else:
            self.x **= obj
            self.y **= obj
        return self

    def __ilshift__(self, obj):
        if isinstance(obj, Vector2):
            self.x <<= obj.x
            self.y <<= obj.y
        else:
            self.x <<= obj
            self.y <<= obj
        return self

    def __irshift__(self, obj):
        if isinstance(obj, Vector2):
            self.x >>= obj.x
            self.y >>= obj.y
        else:
            self.x >>= obj
            self.y >>= obj
        return self

    def __iand__(self, obj):
        if isinstance(obj, Vector2):
            self.x &= obj.x
            self.y &= obj.y
        else:
            self.x &= obj
            self.y &= obj
        return self

    def __ixor__(self, obj):
        if isinstance(obj, Vector2):
            self.x ^= obj.x
            self.y ^= obj.y
        else:
            self.x ^= obj
            self.y ^= obj
        return self

    def __ior__(self, obj):
        if isinstance(obj, Vector2):
            self.x |= obj.x
            self.y |= obj.y
        else:
            self.x |= obj
            self.y |= obj
        return self

    # Unary Arithmetic Operations

    def __pos__(self):
        return Vector2(+self.x, +self.y)

    def __neg__(self):
        return Vector2(-self.x, -self.y)

    def __invert__(self):
        return Vector2(~self.x, ~self.y)

    def __abs__(self):
        return Vector2(abs(self.x), abs(self.y))

    # Virtual "magnitude" Attribute
    
    def __fg_ma(self):
        return hypot(self.x, self.y)

    def __fs_ma(self, value):
        x, y = self.x, self.y
        temp = value / hypot(x, y)
        self.x, self.y = x * temp, y * temp

    magnitude = property(__fg_ma, __fs_ma, doc='Virtual "magnitude" Attribute')

    # Virtual "direction" Attribute
    
    def __fg_di(self):
        return atan2(self.y, self.x)

    def __fs_di(self, value):
        temp = hypot(self.x, self.y)
        self.x, self.y = cos(value) * temp, sin(value) * temp

    direction = property(__fg_di, __fs_di, doc='Virtual "direction" Attribute')

    # Virtual "degrees" Attribute
    
    def __fg_de(self):
        return degrees(atan2(self.x, self.y)) % 360

    def __fs_de(self, value):
        temp = hypot(self.x, self.y)
        self.x, self.y = sin(radians(value)) * temp, cos(radians(value)) * temp

    degrees = property(__fg_de, __fs_de, doc='Virtual "degrees" Attribute')

    # Virtual "xy" Attribute

    def __fg_xy(self):
        return self.x, self.y

    def __fs_xy(self, value):
        self.x, self.y = value

    xy = property(__fg_xy, __fs_xy, doc='Virtual "xy" Attribute')

    # Virtual "yx" Attribute

    def __fg_yx(self):
        return self.y, self.x

    def __fs_yx(self, value):
        self.y, self.x = value

    yx = property(__fg_yx, __fs_yx, doc='Virtual "yx" Attribute')

    # Unit Vector Operations

    def unit_vector(self):
        x, y = self.x, self.y
        temp = hypot(x, y)
        return Vector2(x / temp, y / temp)

    def normalize(self):
        x, y = self.x, self.y
        temp = hypot(x, y)
        self.x, self.y = x / temp, y / temp
        return self

    # Vector Multiplication Operations

    def dot_product(self, vec):
        return self.x * vec.x + self.y * vec.y

    def cross_product(self, vec):
        return self.x * vec.y - self.y * vec.x

    # Geometric And Physical Reflections

    def reflect(self, vec):
        x1, y1, x2, y2 = self.x, self.y, vec.x, vec.y
        temp = 2 * (x1 * x2 + y1 * y2) / (x2 * x2 + y2 * y2)
        return Vector2(x2 * temp - x1, y2 * temp - y1)

    def bounce(self, vec):
        x1, y1, x2, y2 = self.x, self.y, +vec.y, -vec.x
        temp = 2 * (x1 * x2 + y1 * y2) / (x2 * x2 + y2 * y2)
        return Vector2(x2 * temp - x1, y2 * temp - y1)

    # Standard Vector Operations

    def project(self, vec):
        x, y = vec.x, vec.y
        temp = (self.x * x + self.y * y) / (x * x + y * y)
        return Vector2(x * temp, y * temp)

    def rotate(self, vec):
        x1, y1, x2, y2 = self.x, self.y, vec.x, vec.y
        return Vector2(x1 * x2 + y1 * y2, y1 * x2 - x1 * y2)

    def interpolate(self, vec, bias):
        a = 1 - bias
        return Vector2(self.x * a + vec.x * bias, self.y * a + vec.y * bias)

    # Other Useful Methods

    def near(self, vec, dist):
        x, y = self.x, self.y
        return x * x + y * y <= dist * dist

    def perpendicular(self):
        return Vector2(+self.y, -self.x)

    def subset(self, vec1, vec2):
        x1, x2 = vec1.x, vec2.x
        if x1 <= x2:
            if x1 <= self.x <= x2:
                y1, y2 = vec1.y, vec2.y
                if y1 <= y2:
                    return y1 <= self.y <= y2
                return y2 <= self.y <= y1
        else:
            if x2 <= self.x <= x1:
                y1, y2 = vec1.y, vec2.y
                if y1 <= y2:
                    return y1 <= self.y <= y2
                return y2 <= self.y <= y1
        return False

    # Synonymous Definitions

    copy = __pos__

    inverse = __neg__

    unit = unit_vector

    dot = dot_product

    cross = cross_product

    lerp = interpolate

    perp = perpendicular

4 comments

Stephen Chappell (author) 14 years, 7 months ago  # | flag

Would someone mind testing the following code for their respective speeds?

timeit.Timer('test1(1.2, 4.3)', 'def test1(a, b): return (a * a + b * b) ** 0.5').timeit()

timeit.Timer('test2(1.2, 4.3)', 'import math\ndef test2(a, b, h=math.hypot): return h(a, b)').timeit()

Gabriel Genellina pointed out that the second should be faster, but the opposite appears to be true while running on my computer.

Scott Lyons 14 years, 7 months ago  # | flag

Here's what I get for those lines:

>>> import timeit
>>> timeit.Timer('test1(1.2, 4.3)', 'def test1(a, b): return (a * a + b * b) ** 0.5').timeit()
0.41190791130065918
>>> timeit.Timer('test2(1.2, 4.3)', 'import math\ndef test2(a, b, h=math.hypot): return h(a, b)').timeit()
0.3513648509979248

MacBook Pro (Core2Duo 2.6) running 10.6

Stephen Chappell (author) 14 years, 7 months ago  # | flag

Compaq Presario CQ60

Genuine Intel(R) CPU - 585 @ 2.16GHz, 2161 Mhz, 1 Core(s), 1 Logical Processor(s)

Microsoft(R) Windows Vista(TM) Home Basic

Python 3.1.1 (r311:74483, Aug 17 2009, 17:02:12) [MSC v.1500 32 bit (Intel)] on win32

>>> import timeit

>>> timeit.Timer('test1(1.2, 4.3)', 'def test1(a, b): return (a * a + b * b) ** 0.5').timeit()

0.5237614696839962

>>> timeit.Timer('test2(1.2, 4.3)', 'import math\ndef test2(a, b, h=math.hypot): return h(a, b)').timeit()

0.8653614495697077

Can anyone explain the difference in time (or the "correct" syntax for post code block in the comments)?

Those numbers are mostly consistent at a ratio of difference at about 1.6; the second is never faster here.

Are most of you running on Linux kernels? Many people run Python in Linux, and I have heard that Mac uses it now.

Scott Lyons 14 years, 7 months ago  # | flag

OSX 10.5 came with 2.4 and 2.5, 10.6 comes with 2.4, 2.5 and 2.6 (which is what I ran my tests on).

To get the code blocks working, you have to either indent 4 spaces, or replace the ">>>" (just re-type it, copying and pasting doesn't work for some reason).