Rotate long/lat coordinates based on True North

I have a file with latitude and longitude coordinates called coordinates.txt

29.66150677   -98.39336541
29.66150677   -98.39337576
29.66150651   -98.39336541
29.66150328   -98.39337576
29.66150677   -98.39336475
29.66150677   -98.39338611
29.66150393   -98.39338611
29.66150677   -98.39339646
29.66150659   -98.39339646
29.66150677   -98.39339693
29.66151576   -98.39334472
29.66151576   -98.39335506
29.66151511   -98.39334472
29.66151058   -98.39335506
29.66151576   -98.39334322
29.66151576   -98.39336541
29.66151576   -98.39337576
29.66151576   -98.39338611
29.66151576   -98.39339646
29.66151576   -98.39340681
29.66151067   -98.39340681
29.66151576   -98.39341515
29.66152475   -98.39332402
29.66152475   -98.39333437
29.66152443   -98.39332402
29.66151973   -98.39333437
29.66152475   -98.39332332
29.66152475   -98.39334472
29.66152475   -98.39335506
29.66152475   -98.39336541
29.66152475   -98.39337576
29.66152475   -98.39338611
29.66152475   -98.39339646
29.66152475   -98.39340681
29.66152475   -98.39341716
29.66151699   -98.39341716
29.66152475   -98.39342722
29.66153375   -98.39331367
29.66153375   -98.39332402
29.6615302    -98.39331367
29.66153375   -98.3933086
29.66153375   -98.39333437
29.66153375   -98.39334472
29.66153375   -98.39335506
29.66153375   -98.39336541
29.66153375   -98.39337576
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29.66153375   -98.39340681
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29.66153375   -98.39342751
29.66152507   -98.39342751
29.66153375   -98.39343443
29.66154274   -98.39330332
29.66154274   -98.39331367
29.66153745   -98.39330332
29.66154274   -98.39329625
29.66154274   -98.39332402
29.66154274   -98.39333437
29.66154274   -98.39334472
29.66154274   -98.39335506
29.66154274   -98.39336541
29.66154274   -98.39337576
29.66154274   -98.39338611
29.66154274   -98.39339646
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29.66154274   -98.39342751
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29.66155173   -98.39332402
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29.66155173   -98.39335506
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29.66155173   -98.39344106
29.66156073   -98.39328262
29.66156073   -98.39329297
29.66155555   -98.39328262
29.66156073   -98.39327744
29.66156073   -98.39330332
29.66156073   -98.39331367
29.66156073   -98.39332402
29.66156073   -98.39333437
29.66156073   -98.39334472
29.66156073   -98.39335506
29.66156073   -98.39336541
29.66156073   -98.39337576
29.66156073   -98.39338611
29.66156073   -98.39339646
29.66156073   -98.39340681
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29.66156073   -98.39342751
29.66156073   -98.39343786
29.66156073   -98.39344196
29.66156972   -98.39327227
29.66156972   -98.39328262
29.66156651   -98.39327227
29.66156972   -98.39326964
29.66156972   -98.39329297
29.66156972   -98.39330332
29.66156972   -98.39331367
29.66156972   -98.39332402
29.66156972   -98.39333437
29.66156972   -98.39334472
29.66156972   -98.39335506
29.66156972   -98.39336541
29.66156972   -98.39337576
29.66156972   -98.39338611
29.66156972   -98.39339646
29.66156972   -98.39340681
29.66156972   -98.39341716
29.66156972   -98.39342751
29.66156972   -98.39343786
29.66156972   -98.393442
29.66157871   -98.39327227
29.66157871   -98.39328262
29.66157871   -98.39326327
29.66157871   -98.39329297
29.66157871   -98.39330332
29.66157871   -98.39331367
29.66157871   -98.39332402
29.66157871   -98.39333437
29.66157871   -98.39334472
29.66157871   -98.39335506
29.66157871   -98.39336541
29.66157871   -98.39337576
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29.66157871   -98.39339646
29.66157871   -98.39340681
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29.66158771   -98.39335506
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29.66158771   -98.39337576
29.66158771   -98.39338611
29.66158771   -98.39339646
29.66158771   -98.39340681
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29.66158771   -98.39343786
29.66158771   -98.39343926
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29.6615967    -98.39328262
29.6615967    -98.39329297
29.6615967    -98.39330332
29.6615967    -98.39331367
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29.6615967    -98.39333437
29.6615967    -98.39334472
29.6615967    -98.39335506
29.6615967    -98.39336541
29.6615967    -98.39337576
29.6615967    -98.39338611
29.6615967    -98.39339646
29.6615967    -98.39340681
29.6615967    -98.39341716
29.6615967    -98.39342751
29.6615967    -98.39343623
29.66160569   -98.39325157
29.66160569   -98.39326192
29.66160564   -98.39325157
29.66160569   -98.39325156
29.66160569   -98.39327227
29.66160569   -98.39328262
29.66160569   -98.39329297
29.66160569   -98.39330332
29.66160569   -98.39331367
29.66160569   -98.39332402
29.66160569   -98.39333437
29.66160569   -98.39334472
29.66160569   -98.39335506
29.66160569   -98.39336541
29.66160569   -98.39337576
29.66160569   -98.39338611
29.66160569   -98.39339646
29.66160569   -98.39340681
29.66160569   -98.39341716
29.66160569   -98.39342751
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29.66161468   -98.39325157
29.66161468   -98.39326192
29.66161468   -98.39324921
29.66161468   -98.39327227
29.66161468   -98.39328262
29.66161468   -98.39329297
29.66161468   -98.39330332
29.66161468   -98.39331367
29.66161468   -98.39332402
29.66161468   -98.39333437
29.66161468   -98.39334472
29.66161468   -98.39335506
29.66161468   -98.39336541
29.66161468   -98.39337576
29.66161468   -98.39338611
29.66161468   -98.39339646
29.66161468   -98.39340681
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29.66161592   -98.39342751
29.66162368   -98.39325157
29.66162368   -98.39326192
29.66162368   -98.39324697
29.66162368   -98.39327227
29.66162368   -98.39328262
29.66162368   -98.39329297
29.66162368   -98.39330332
29.66162368   -98.39331367
29.66162368   -98.39332402
29.66162368   -98.39333437
29.66162368   -98.39334472
29.66162368   -98.39335506
29.66162368   -98.39336541
29.66162368   -98.39337576
29.66162368   -98.39338611
29.66162368   -98.39339646
29.66162368   -98.39340681
29.66162368   -98.39341716
29.66162368   -98.39342302
29.66163267   -98.39325157
29.66163267   -98.39326192
29.66163267   -98.39324642
29.66163267   -98.39327227
29.66163267   -98.39328262
29.66163267   -98.39329297
29.66163267   -98.39330332
29.66163267   -98.39331367
29.66163267   -98.39332402
29.66163267   -98.39333437
29.66163267   -98.39334472
29.66163267   -98.39335506
29.66163267   -98.39336541
29.66163267   -98.39337576
29.66163267   -98.39338611
29.66163267   -98.39339646
29.66163267   -98.39340681
29.66163267   -98.39341716
29.66163267   -98.39341722
29.66163275   -98.39341716
29.66164166   -98.39325157
29.66164166   -98.39326192
29.66164166   -98.39324588
29.66164166   -98.39327227
29.66164166   -98.39328262
29.66164166   -98.39329297
29.66164166   -98.39330332
29.66164166   -98.39331367
29.66164166   -98.39332402
29.66164166   -98.39333437
29.66164166   -98.39334472
29.66164166   -98.39335506
29.66164166   -98.39336541
29.66164166   -98.39337576
29.66164166   -98.39338611
29.66164166   -98.39339646
29.66164166   -98.39340681
29.66164166   -98.39341103
29.66164749   -98.39340681
29.66165066   -98.39325157
29.66165066   -98.39326192
29.66165066   -98.39324533
29.66165066   -98.39327227
29.66165066   -98.39328262
29.66165066   -98.39329297
29.66165066   -98.39330332
29.66165066   -98.39331367
29.66165066   -98.39332402
29.66165066   -98.39333437
29.66165066   -98.39334472
29.66165066   -98.39335506
29.66165066   -98.39336541
29.66165066   -98.39337576
29.66165066   -98.39338611
29.66165066   -98.39339646
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29.66165965   -98.39325157
29.66165965   -98.39326192
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29.66165965   -98.39327227
29.66165965   -98.39328262
29.66165965   -98.39329297
29.66165965   -98.39330332
29.66165965   -98.39331367
29.66165965   -98.39332402
29.66165965   -98.39333437
29.66165965   -98.39334472
29.66165965   -98.39335506
29.66165965   -98.39336541
29.66165965   -98.39337576
29.66165965   -98.39338611
29.66165965   -98.39339646
29.66165965   -98.39339783
29.6616615    -98.39339646
29.66166864   -98.39325157
29.66166864   -98.39326192
29.66166864   -98.39324424
29.66166864   -98.39327227
29.66166864   -98.39328262
29.66166864   -98.39329297
29.66166864   -98.39330332
29.66166864   -98.39331367
29.66166864   -98.39332402
29.66166864   -98.39333437
29.66166864   -98.39334472
29.66166864   -98.39335506
29.66166864   -98.39336541
29.66166864   -98.39337576
29.66166864   -98.39338611
29.66166864   -98.39339119
29.66167552   -98.39338611
29.66167764   -98.39325157
29.66167764   -98.39326192
29.66167764   -98.3932437
29.66167764   -98.39327227
29.66167764   -98.39328262
29.66167764   -98.39329297
29.66167764   -98.39330332
29.66167764   -98.39331367
29.66167764   -98.39332402
29.66167764   -98.39333437
29.66167764   -98.39334472
29.66167764   -98.39335506
29.66167764   -98.39336541
29.66167764   -98.39337576
29.66167764   -98.39338455
29.66168663   -98.39325157
29.66168663   -98.39326192
29.66168663   -98.39324315
29.66168663   -98.39327227
29.66168663   -98.39328262
29.66168663   -98.39329297
29.66168663   -98.39330332
29.66168663   -98.39331367
29.66168663   -98.39332402
29.66168663   -98.39333437
29.66168663   -98.39334472
29.66168663   -98.39335506
29.66168663   -98.39336541
29.66168663   -98.39337576
29.66168663   -98.39337791
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29.66169562   -98.39325157
29.66169562   -98.39326192
29.66169562   -98.39324277
29.66169562   -98.39327227
29.66169562   -98.39328262
29.66169562   -98.39329297
29.66169562   -98.39330332
29.66169562   -98.39331367
29.66169562   -98.39332402
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29.66169562   -98.39334472
29.66169562   -98.39335506
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29.66170462   -98.39325157
29.66170462   -98.39326192
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29.66170462   -98.39327227
29.66170462   -98.39328262
29.66170462   -98.39329297
29.66170462   -98.39330332
29.66170462   -98.39331367
29.66170462   -98.39332402
29.66170462   -98.39333437
29.66170462   -98.39334472
29.66170462   -98.39335506
29.66170462   -98.39336463
29.66171361   -98.39325157
29.66171361   -98.39326192
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29.66171361   -98.39327227
29.66171361   -98.39328262
29.66171361   -98.39329297
29.66171361   -98.39330332
29.66171361   -98.39331367
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29.66171361   -98.39334472
29.66171361   -98.39335506
29.66171361   -98.39335799
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29.6617226    -98.39327227
29.6617226    -98.39328262
29.6617226    -98.39329297
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29.6617226    -98.39331367
29.6617226    -98.39332402
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29.6617226    -98.39334472
29.6617226    -98.39335135
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29.6617316    -98.39327227
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29.6617316    -98.39329297
29.6617316    -98.39330332
29.6617316    -98.39331367
29.6617316    -98.39332402
29.6617316    -98.39333437
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29.66174059   -98.39325157
29.66174059   -98.39326192
29.66174059   -98.393242
29.66174059   -98.39327227
29.66174059   -98.39328262
29.66174059   -98.39329297
29.66174059   -98.39330332
29.66174059   -98.39331367
29.66174059   -98.39332402
29.66174059   -98.39333437
29.66174059   -98.39333807
29.66174561   -98.39333437
29.66174958   -98.39325157
29.66174958   -98.39326192
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29.66174958   -98.39327227
29.66174958   -98.39328262
29.66174958   -98.39329297
29.66174958   -98.39330332
29.66174958   -98.39331367
29.66174958   -98.39332402
29.66174958   -98.39333143
29.66175858   -98.39325157
29.66175858   -98.39326192
29.66176663   -98.39325157
29.66176757   -98.39326192
29.66175858   -98.39324585
29.66175858   -98.39327227
29.66175858   -98.39328262
29.66175858   -98.39329297
29.66175858   -98.39330332
29.66175858   -98.39331367
29.66175858   -98.39332402
29.66175858   -98.39332427
29.6617589    -98.39332402
29.66176757   -98.39327227
29.66177412   -98.39326192
29.66177656   -98.39327227
29.66176757   -98.3932525
29.66176757   -98.39328262
29.66176757   -98.39329297
29.66176757   -98.39330332
29.66176757   -98.39331367
29.66177543   -98.39330332
29.66176974   -98.39331367
29.66176757   -98.3933162
29.66177656   -98.39328262
29.66177775   -98.39327227
29.66177872   -98.39328262
29.66177656   -98.39326599
29.66177656   -98.39329297
29.66177855   -98.39329297
29.66177656   -98.39330028

In addition, I have a reference point, anchor

anchor = [29.66165674, -98.39334562]

I want to rescale the latitude and longitude coordinates to a cartesian plane where anchor is the origin / (0,0)

import numpy as np
import utm

latlongs = np.loadtxt('coordinates.txt')

center = utm.from_latlon(center[0], center[1])
latlongs = utm.from_latlon(latlongs[:, 0], latlongs[:, 1])

center_x, center_y = center[0], center[1]
x, y = latlongs[0], latlongs[1]

x -= center_x
y -= center_y

plt.axis('equal')
plt.scatter(x, y, marker='o', color='black')

plt.show()

The output looks as follows:

Now, I want to rotate the contour. I am not sure how this is done. But I have two data sources. I know that

trueNorth = 166    # I don't know the definition, only the value

and a compass:

How do I calculate the rotation angle or how do I update the long-, latitudes coordinates?

trueNorth appears to be the angle of rotation of north with respect to the ascending vertical in the trigonometric direction. To apply the rotation you can use a Rotation matrix. Be careful to convert degrees in radians.

Here is the complete code to do this:

import matplotlib.pyplot as plt
import numpy as np
import utm

latlongs = np.loadtxt("coordinates.txt")

anchor = [29.66165674, -98.39334562]
center = utm.from_latlon(anchor[0], anchor[1])
latlongs = utm.from_latlon(latlongs[:, 0], latlongs[:, 1])

center_x, center_y = center[0], center[1]
x, y = latlongs[0], latlongs[1]

x -= center_x
y -= center_y

# Rotation
# ========
trueNorth = 166 * np.pi / 180
rot_x = x * np.cos(trueNorth) - y * np.sin(trueNorth)
rot_y = x * np.sin(trueNorth) + y * np.cos(trueNorth)

plt.axis('equal')
plt.scatter(rot_x, rot_y, marker='o', color='black')

plt.show()

The output looks as follows: