Skip to content

Geography Module Documentation

This module provides functions for working with geographic coordinates.

Functions:

Name Description
latlon_to_zone_number

Determines the UTM zone number for a given latitude and longitude.
latlon_to_zone_letter

Determines the UTM zone letter for a given latitude.
ll2utm

Converts latitude and longitude to UTM coordinates.
utm2ll

Converts UTM coordinates to latitude and longitude.
deg2m_lat

Converts latitude from degrees to meters.
deg2m_lon

Converts longitude from degrees to meters.
ll2xy

Converts latitude and longitude to xy mercator coordinates from an origin.
xy2ll

Converts xy mercator coordinates to latitude and longitude from an origin.
dms_to_decimal

Converts DMS (degrees, minutes, seconds) to decimal degrees.
local_gravity

Calculates the local gravity at a given latitude and depth.

Converts latitude from degrees to meters.

Parameters:

Name Type Description Default
latitude Union[int, float, ndarray, list]

Latitude in degrees.

 required

Returns:

Name Type Description
latitude Union[float, ndarray]

Latitude in meters.

Examples:

>>> deg2m_lat(1)
1.1057e+05
Source code in navlib/geo/geography.py 
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
def deg2m_lat(
    latitude: Union[int, float, np.ndarray, list],
) -> Union[float, np.ndarray]:
    """
    Converts latitude from degrees to meters.

    Args:
        latitude (Union[int, float, np.ndarray, list]): Latitude in degrees.

    Returns:
        latitude (Union[float, np.ndarray]): Latitude in meters.

    Examples:
        >>> deg2m_lat(1)
        1.1057e+05
    """
    # Convert lists to numpy arrays
    if isinstance(latitude, list):
        latitude = np.array(latitude)

    # Check input type
    if not isinstance(latitude, (float, np.ndarray, int)):
        raise TypeError("Latitude must be an integer, float or a numpy array.")

    # Convert to radians
    latrad = np.deg2rad(latitude)
    dy = (
        111132.09
        - 566.05 * np.cos(2.0 * latrad)
        + 1.20 * np.cos(4.0 * latrad)
        - 0.002 * np.cos(6.0 * latrad)
    )
    return dy

Converts longitude from degrees to meters.

Parameters:

Name Type Description Default
longitude Union[int, float, ndarray, list]

Latitude in degrees.

 required

Returns:

Name Type Description
latitude Union[float, ndarray]

Longitude in meters.

Examples:

>>> deg2m_lon(1)
1.1113e+05
Source code in navlib/geo/geography.py 
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
def deg2m_lon(
    longitude: Union[int, float, np.ndarray, list],
) -> Union[float, np.ndarray]:
    """
    Converts longitude from degrees to meters.

    Args:
        longitude (Union[int, float, np.ndarray, list]): Latitude in degrees.

    Returns:
        latitude (Union[float, np.ndarray]): Longitude in meters.

    Examples:
        >>> deg2m_lon(1)
        1.1113e+05
    """
    # Convert lists to numpy arrays
    if isinstance(longitude, list):
        longitude = np.array(longitude)

    # Check input type
    if not isinstance(longitude, (float, np.ndarray, int)):
        raise TypeError("Longitude must be an integer, float or a numpy array.")

    # Convert to radians
    latrad = np.deg2rad(longitude)
    dx = (
        111415.13 * np.cos(latrad)
        - 94.55 * np.cos(3.0 * latrad)
        + 0.12 * np.cos(5.0 * latrad)
    )
    return dx

Convert DMS (degrees, minutes, seconds) to decimal degrees.

Parameters:

Name Type Description Default
degrees int

Degrees

 required
minutes int

Minutes

 required
seconds float

Seconds

 required
direction str

Direction ('N', 'S', 'E', 'W')

 required

Returns:

Name Type Description
decimal float

Decimal degrees

Raises:

Type Description
ValueError

If the inputs are not of the correct dimensions.

Examples:

>>> dms_to_decimal(37, 46, 29.52, 'N')
37.77486666666667
Source code in navlib/geo/geography.py 
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
def dms_to_decimal(degrees: int, minutes: int, seconds: float, direction: str) -> float:
    """
    Convert DMS (degrees, minutes, seconds) to decimal degrees.

    Args:
        degrees (int): Degrees
        minutes (int): Minutes
        seconds (float): Seconds
        direction (str): Direction ('N', 'S', 'E', 'W')

    Returns:
        decimal (float): Decimal degrees

    Raises:
        ValueError: If the inputs are not of the correct dimensions.

    Examples:
        >>> dms_to_decimal(37, 46, 29.52, 'N')
        37.77486666666667
    """
    # Check data types validity
    if not isinstance(degrees, int):
        raise TypeError("Degrees must be an integer.")
    if not isinstance(minutes, int):
        raise TypeError("Minutes must be an integer.")
    if not isinstance(seconds, (int, float)):
        raise TypeError("Seconds must be a float or an integer.")

    # Check data validity
    if direction in ["N", "S"] and (degrees < 0 or degrees > 90):
        raise ValueError("Degrees must be between 0 and 90 for directions 'N' or 'S'.")
    if direction in ["E", "W"] and (degrees < 0 or degrees > 180):
        raise ValueError("Degrees must be between 0 and 180 for directions 'E' or 'W'.")
    if minutes < 0 or minutes >= 60:
        raise ValueError("Minutes must be between 0 and 59.")
    if seconds < 0 or seconds >= 60:
        raise ValueError("Seconds must be between 0 and 59.")
    if direction not in ["N", "S", "E", "W"]:
        raise ValueError("Direction must be 'N', 'S', 'E', or 'W'.")

    decimal = degrees + minutes / 60 + seconds / 3600
    if direction in ["S", "W"]:
        decimal = -decimal
    return decimal

Calculate the local gravity at a given latitude and depth.

Parameters:

Name Type Description Default
latitude_deg float

Latitude in degrees.

 required
depth_m Union[float, int]

Depth in meters. Default is 0.

 0.0

Returns:

Name Type Description
float float

Local gravity in m/s^2.
Source code in navlib/geo/geography.py 
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
def get_local_gravity(latitude_deg: float, depth_m: Union[float, int] = 0.0) -> float:
    """
    Calculate the local gravity at a given latitude and depth.

    Args:
        latitude_deg (float): Latitude in degrees.
        depth_m (Union[float, int]): Depth in meters. Default is 0.

    Returns:
        float: Local gravity in m/s^2.
    """
    # Check input type
    if not isinstance(latitude_deg, (float, int)):
        raise TypeError("Latitude must be a float or an integer.")
    if not isinstance(depth_m, (float, int)):
        raise TypeError("Depth must be a float or an integer.")

    # Check data validity
    if not (-90 <= latitude_deg <= 90):
        raise ValueError("Latitude must be between -90 and 90 degrees.")

    phi = np.radians(latitude_deg)
    # Gravity constants from the International Gravity Formula:
    EQUATORIAL_GRAVITY = 9.780327  # [m/s^2] Equatorial gravity at sea level
    LATITUDE_CORRECTION = (
        0.0053024  # [unitless] Correction for latitude (centrifugal force)
    )
    ELLIPTICITY_CORRECTION = (
        0.0000058  # [unitless] Correction for latitude (ellipticity of Earth)
    )
    DEPTH_CORRECTION = (
        3.086e-6  # [m/s^2 per meter] Correction for depth below sea level
    )

    g0 = EQUATORIAL_GRAVITY * (
        1
        + LATITUDE_CORRECTION * np.sin(phi) ** 2
        - ELLIPTICITY_CORRECTION * np.sin(2 * phi) ** 2
    )
    return g0 + DEPTH_CORRECTION * np.abs(depth_m)

Determines the UTM zone letter for a given latitude.

Parameters:

Name Type Description Default
latitude float

Latitude in degrees.

 required

Returns:

Name Type Description
utm_zone str

UTM zone letter.

Raises:

Type Description
ValueError

If the latitude is not within the valid range.

Examples:

>>> latlon_to_zone_letter(37.7749)
'T'
Source code in navlib/geo/geography.py 
 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
def latlon_to_zone_letter(latitude: float) -> str:
    """
    Determines the UTM zone letter for a given latitude.

    Args:
        latitude (float): Latitude in degrees.

    Returns:
        utm_zone (str): UTM zone letter.

    Raises:
        ValueError: If the latitude is not within the valid range.

    Examples:
        >>> latlon_to_zone_letter(37.7749)
        'T'
    """
    # Check if the latitude is within the valid range.
    if not (-80.0 <= latitude <= 84.0):
        raise ValueError("Latitude must be within the valid range.")

    if 84 >= latitude >= 72:
        return "X"
    if 72 > latitude >= 64:
        return "W"
    if 64 > latitude >= 56:
        return "V"
    if 56 > latitude >= 48:
        return "U"
    if 48 > latitude >= 40:
        return "T"
    if 40 > latitude >= 32:
        return "S"
    if 32 > latitude >= 24:
        return "R"
    if 24 > latitude >= 16:
        return "Q"
    if 16 > latitude >= 8:
        return "P"
    if 8 > latitude >= 0:
        return "N"
    if 0 > latitude >= -8:
        return "M"
    if -8 > latitude >= -16:
        return "L"
    if -16 > latitude >= -24:
        return "K"
    if -24 > latitude >= -32:
        return "J"
    if -32 > latitude >= -40:
        return "H"
    if -40 > latitude >= -48:
        return "G"
    if -48 > latitude >= -56:
        return "F"
    if -56 > latitude >= -64:
        return "E"
    if -64 > latitude >= -72:
        return "D"
    if -72 > latitude >= -80:
        return "C"
    return "Z"

Determines the UTM zone number for a given latitude and longitude.

Parameters:

Name Type Description Default
latitude float

Latitude in degrees.

 required
longitude float

Longitude in degrees.

 required

Returns:

Name Type Description
utm_zone int

UTM zone number.

Raises:

Type Description
ValueError

If the latitude and longitude are not within the valid range.

Examples:

>>> latlon_to_zone_number(37.7749, -122.4194)
10
Source code in navlib/geo/geography.py 
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
def latlon_to_zone_number(latitude: float, longitude: float) -> int:
    """
    Determines the UTM zone number for a given latitude and longitude.

    Args:
        latitude (float): Latitude in degrees.
        longitude (float): Longitude in degrees.

    Returns:
        utm_zone (int): UTM zone number.

    Raises:
        ValueError: If the latitude and longitude are not within the valid range.

    Examples:
        >>> latlon_to_zone_number(37.7749, -122.4194)
        10
    """
    # Check if the latitude and longitude are within the valid range.
    if not (-80.0 <= latitude <= 84.0) or not (-180.0 <= longitude <= 180.0):
        raise ValueError("Latitude and longitude must be within the valid range.")

    if 56.0 <= latitude < 64.0 and 3.0 <= longitude < 12.0:
        return 32
    if 72.0 <= latitude < 84.0 and 0.0 <= longitude < 42.0:
        return 31
    return int((longitude + 180) / 6) + 1

Converts latitude and longitude to UTM coordinates.

In this case we will use ENU (not following NED): x-axis is pointing EAST y-axis is pointing NORTH and z-axis is pointing UP.

Parameters:

Name Type Description Default
latitude Union[int, float, ndarray, list]

Latitude in degrees.

 required
longitude Union[int, float, ndarray, list]

Longitude in degrees.

 required

Returns:

Name Type Description
easting Union[float, ndarray]

UTM easting in meters.
northing Union[float, ndarray]

UTM northing in meters.
zone_number int

UTM zone number.
hemisphere str

Hemisphere ('north' or 'south').

Raises:

Type Description
ValueError

If the latitude and longitude are not within the valid range.

Examples:

>>> ll2utm(37.7749, -122.4194)
(551730.0, 4163834.0, 10, 'north')
>>> ll2utm([37.7749, 37.7749], [-122.4194, -122.4194])
(array([551730., 551730.]), array([4163834., 4163834.]), 10, 'north')
Source code in navlib/geo/geography.py 
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
def ll2utm(
    latitude: Union[int, float, np.ndarray, list],
    longitude: Union[int, float, np.ndarray, list],
) -> Tuple[Union[float, np.ndarray], int, str]:
    """
    Converts latitude and longitude to UTM coordinates.

    In this case we will use ENU (not following NED): x-axis is pointing EAST
    y-axis is pointing NORTH and z-axis is pointing UP.

    Args:
        latitude (Union[int, float, np.ndarray, list]): Latitude in degrees.
        longitude (Union[int, float, np.ndarray, list]): Longitude in degrees.

    Returns:
        easting (Union[float, np.ndarray]): UTM easting in meters.
        northing (Union[float, np.ndarray]): UTM northing in meters.
        zone_number (int): UTM zone number.
        hemisphere (str): Hemisphere ('north' or 'south').

    Raises:
        ValueError: If the latitude and longitude are not within the valid range.

    Examples:
        >>> ll2utm(37.7749, -122.4194)
        (551730.0, 4163834.0, 10, 'north')
        >>> ll2utm([37.7749, 37.7749], [-122.4194, -122.4194])
        (array([551730., 551730.]), array([4163834., 4163834.]), 10, 'north')
    """
    # Convert to array if its a list
    if isinstance(latitude, list):
        latitude = np.array(latitude)
    if isinstance(longitude, list):
        longitude = np.array(longitude)

    # Check input type
    if not isinstance(latitude, (float, np.ndarray, int)):
        raise TypeError("Latitude must be an integer, a float or a numpy array.")
    if not isinstance(longitude, (float, np.ndarray, int)):
        raise TypeError("Longitude must be an integer, a float or a numpy array.")
    if type(latitude) is not type(longitude):
        raise TypeError("Latitude and Longitude types do not match")

    # Check data validity
    if isinstance(latitude, np.ndarray) and isinstance(longitude, np.ndarray):
        if latitude.shape != longitude.shape:
            raise ValueError("Latitude and longitude must have the same shape.")

    # Check if the latitude and longitude are within the valid range.
    if isinstance(latitude, np.ndarray) and isinstance(longitude, np.ndarray):
        if not (np.all((-80.0 <= latitude) & (latitude <= 84.0))):
            raise ValueError("Latitude must be within the valid range.")
        if not (np.all((-180.0 <= longitude) & (longitude <= 180.0))):
            raise ValueError("Longitude must be within the valid range.")
    else:
        if not (-80.0 <= latitude <= 84.0) or not (-180.0 <= longitude <= 180.0):
            raise ValueError("Latitude and longitude must be within the valid range.")

    if isinstance(latitude, np.ndarray):
        zone_number = latlon_to_zone_number(mean(latitude), mean(longitude))
        hemisphere = "north" if mean(latitude) > 0 else "south"
    else:
        zone_number = latlon_to_zone_number(latitude, longitude)
        hemisphere = "north" if latitude > 0 else "south"

    if hemisphere == "north":
        utm_proj = pyproj.Proj(
            proj="utm", zone=f"{zone_number}", ellps="WGS84", datum="WGS84", units="m"
        )
    else:
        utm_proj = pyproj.Proj(
            proj="utm",
            zone=f"{zone_number}",
            ellps="WGS84",
            datum="WGS84",
            units="m",
            south=True,
        )

    # utm_x and utm_y hold the UTM coordinates corresponding to the given latitude and longitude, i.e., easting and
    # northing, respectively.
    easting, northing = utm_proj(longitude, latitude)

    return easting, northing, zone_number, hemisphere

Converts latitude and longitude to xy mercator coordinates from an origin.

In this case we will use ENU (not following NED): x-axis is pointing EAST y-axis is pointing NORTH and z-axis is pointing UP.

Parameters:

Name Type Description Default
latitude Union[int, float, ndarray, list]

Latitude in degrees.

 required
longitude Union[int, float, ndarray, list]

Longitude in degrees.

 required
origin_latitude float

Origin latitude in degrees.

 0.0
origin_longitude float

Origin longitude in degrees.

 0.0

Returns:

Name Type Description
x Union[float, ndarray]

x coordinate in meters.
y Union[float, ndarray]

y coordinate in meters.

Examples:

>>> ll2xy(37.7749, -122.4194)
(551730.0, 4163834.0)
Source code in navlib/geo/geography.py 
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
def ll2xy(
    latitude: Union[int, float, np.ndarray, list],
    longitude: Union[int, float, np.ndarray, list],
    origin_latitude: float = 0.0,
    origin_longitude: float = 0.0,
) -> Tuple[Union[float, np.ndarray], Union[float, np.ndarray]]:
    """
    Converts latitude and longitude to xy mercator coordinates from an origin.

    In this case we will use ENU (not following NED): x-axis is pointing EAST
    y-axis is pointing NORTH and z-axis is pointing UP.

    Args:
        latitude (Union[int, float, np.ndarray, list]): Latitude in degrees.
        longitude (Union[int, float, np.ndarray, list]): Longitude in degrees.
        origin_latitude (float): Origin latitude in degrees.
        origin_longitude (float): Origin longitude in degrees.

    Returns:
        x (Union[float, np.ndarray]): x coordinate in meters.
        y (Union[float, np.ndarray]): y coordinate in meters.

    Examples:
        >>> ll2xy(37.7749, -122.4194)
        (551730.0, 4163834.0)
    """
    # Convert lists to numpy arrays
    if isinstance(latitude, list):
        latitude = np.array(latitude)
    if isinstance(longitude, list):
        longitude = np.array(longitude)

    # Check input type
    if not isinstance(latitude, (float, np.ndarray, int)):
        raise TypeError("Latitude must be an integer, float or a numpy array.")
    if not isinstance(longitude, (float, np.ndarray, int)):
        raise TypeError("Longitude must be an integer, float or a numpy array.")
    if type(latitude) is not type(longitude):
        raise TypeError("Latitude and Longitude types do not match")
    if not isinstance(origin_latitude, (float, int)):
        raise TypeError("Origin latitude must be an integer or a float.")
    if not isinstance(origin_longitude, (float, int)):
        raise TypeError("Origin longitude must be an integer or a float.")

    # Check data validity
    if isinstance(latitude, np.ndarray):
        if latitude.shape != longitude.shape:
            raise ValueError("Latitude and longitude must have the same shape.")

    x = (longitude - origin_longitude) * deg2m_lon(origin_latitude)
    y = (latitude - origin_latitude) * deg2m_lat(origin_latitude)
    return x, y

Converts the UTMx (easting) and UTMy (northing) and UTM zone coordinates to the latitude and longitude mercator projection.

Parameters:

Name Type Description Default
northing Union[int, float, ndarray, list]

Northing in meters.

 required
easting Union[int, float, ndarray, list]

Easting in meters.

 required
zone_str str

UTM zone. Example: '10N'.

 required

Returns:

Name Type Description
latitude Union[float, ndarray]

Latitude in degrees.
longitude Union[float, ndarray]

Longitude in degrees.

Raises:

Type Description
ValueError

If the UTM zone is not valid.

Examples:

>>> utm2ll(4163834.0, 551730.0, '10N')
(37.7749, -122.4194)
Source code in navlib/geo/geography.py 
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
def utm2ll(
    northing: Union[int, float, np.ndarray, list],
    easting: Union[int, float, np.ndarray, list],
    zone_str: str,
) -> Tuple[Union[float, np.ndarray], Union[float, np.ndarray]]:
    """
    Converts the UTMx (easting) and UTMy (northing) and UTM zone coordinates to
    the latitude and longitude mercator projection.

    Args:
        northing (Union[int, float, np.ndarray, list]): Northing in meters.
        easting (Union[int, float, np.ndarray, list]): Easting in meters.
        zone_str (str): UTM zone. Example: '10N'.

    Returns:
        latitude (Union[float, np.ndarray]): Latitude in degrees.
        longitude (Union[float, np.ndarray]): Longitude in degrees.

    Raises:
        ValueError: If the UTM zone is not valid.

    Examples:
        >>> utm2ll(4163834.0, 551730.0, '10N')
        (37.7749, -122.4194)
    """
    # Convert lists to numpy arrays
    if isinstance(northing, list):
        northing = np.array(northing)
    if isinstance(easting, list):
        easting = np.array(easting)

    # Check input type
    if not isinstance(northing, (float, np.ndarray, int)):
        raise TypeError("Northing must be an integer, float or a numpy array.")
    if not isinstance(easting, (float, np.ndarray, int)):
        raise TypeError("Easting must be an integer, float or a numpy array.")
    if type(northing) is not type(easting):
        raise TypeError("Northing and Easting types do not match")
    if not isinstance(zone_str, str):
        raise TypeError("Zone must be a string.")

    # Check data validity
    if isinstance(northing, np.ndarray):
        if northing.shape != easting.shape:
            raise ValueError("Northing and easting must have the same shape.")

    # Check if the zone is a valid UTM zone.
    if not zone_str[0].isdigit() or not zone_str[-1].isalpha():
        raise ValueError("Invalid UTM zone.")

    zone_number = zone_str[:-1]

    if int(zone_number) > 60 or int(zone_number) < 1:
        raise ValueError("Invalid UTM zone.")

    if zone_str[-1].upper() == "N":
        ll_proj = pyproj.Proj(
            proj="utm",
            zone=zone_number,
            ellps="WGS84",
            datum="WGS84",
            units="m",
            no_defs=True,
        )
    elif zone_str[-1].upper() == "S":
        ll_proj = pyproj.Proj(
            proj="utm",
            zone=zone_number,
            ellps="WGS84",
            datum="WGS84",
            units="m",
            south=True,
            no_defs=True,
        )
    else:
        raise ValueError("Invalid UTM zone.")

    longitude, latitude = ll_proj(easting, northing, inverse=True)

    return latitude, longitude

Converts xy mercator coordinates to latitude and longitude from an origin.

Parameters:

Name Type Description Default
x Union[int, float, ndarray, list]

x coordinate in meters.

 required
y Union[int, float, ndarray, list]

y coordinate in meters.

 required
origin_latitude float

Origin latitude in degrees.

 0.0
origin_longitude float

Origin longitude in degrees.

 0.0

Returns:

Name Type Description
latitude Union[float, ndarray]

Latitude in degrees.
longitude Union[float, ndarray]

Longitude in degrees.

Examples:

>>> xy2ll(551730.0, 4163834.0)
(37.7749, -122.4194)
Source code in navlib/geo/geography.py 
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
def xy2ll(
    x: Union[int, float, np.ndarray, list],
    y: Union[int, float, np.ndarray, list],
    origin_latitude: float = 0.0,
    origin_longitude: float = 0.0,
) -> Tuple[Union[float, np.ndarray], Union[float, np.ndarray]]:
    """
    Converts xy mercator coordinates to latitude and longitude from an origin.

    Args:
        x (Union[int, float, np.ndarray, list]): x coordinate in meters.
        y (Union[int, float, np.ndarray, list]): y coordinate in meters.
        origin_latitude (float): Origin latitude in degrees.
        origin_longitude (float): Origin longitude in degrees.

    Returns:
        latitude (Union[float, np.ndarray]): Latitude in degrees.
        longitude (Union[float, np.ndarray]): Longitude in degrees.

    Examples:
        >>> xy2ll(551730.0, 4163834.0)
        (37.7749, -122.4194)
    """
    # Convert lists to numpy arrays
    if isinstance(x, list):
        x = np.array(x)
    if isinstance(y, list):
        y = np.array(y)

    # Check input type
    if not isinstance(x, (float, np.ndarray, int)):
        raise TypeError("x must be an integer, float or a numpy array.")
    if not isinstance(y, (float, np.ndarray, int)):
        raise TypeError("y must be an integer, float or a numpy array.")
    if type(x) is not type(y):
        raise TypeError("x and y types do not match")
    if not isinstance(origin_latitude, (float, int)):
        raise TypeError("Origin latitude must be an integer or a float.")
    if not isinstance(origin_longitude, (float, int)):
        raise TypeError("Origin longitude must be an integer or a float.")

    # Check data validity
    if isinstance(x, np.ndarray):
        if x.shape != y.shape:
            raise ValueError("x and y must have the same shape.")

    latitude = y / deg2m_lat(origin_latitude) + origin_latitude
    longitude = x / deg2m_lon(origin_longitude) + origin_longitude
    return latitude, longitude