根据真北旋转长/纬度坐标

Question

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
29.66153375   -98.39338611
29.66153375   -98.39339646
29.66153375   -98.39340681
29.66153375   -98.39341716
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
29.66154274   -98.39340681
29.66154274   -98.39341716
29.66154274   -98.39342751
29.66154274   -98.39343786
29.66153992   -98.39343786
29.66154274   -98.3934387
29.66155173   -98.39329297
29.66155173   -98.39330332
29.6615457    -98.39329297
29.66155173   -98.39328644
29.66155173   -98.39331367
29.66155173   -98.39332402
29.66155173   -98.39333437
29.66155173   -98.39334472
29.66155173   -98.39335506
29.66155173   -98.39336541
29.66155173   -98.39337576
29.66155173   -98.39338611
29.66155173   -98.39339646
29.66155173   -98.39340681
29.66155173   -98.39341716
29.66155173   -98.39342751
29.66155173   -98.39343786
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
29.66156073   -98.39341716
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
29.66157871   -98.39338611
29.66157871   -98.39339646
29.66157871   -98.39340681
29.66157871   -98.39341716
29.66157871   -98.39342751
29.66157871   -98.39343786
29.66157871   -98.39344084
29.66158771   -98.39326192
29.66158771   -98.39327227
29.66158097   -98.39326192
29.66158771   -98.39325788
29.66158771   -98.39328262
29.66158771   -98.39329297
29.66158771   -98.39330332
29.66158771   -98.39331367
29.66158771   -98.39332402
29.66158771   -98.39333437
29.66158771   -98.39334472
29.66158771   -98.39335506
29.66158771   -98.39336541
29.66158771   -98.39337576
29.66158771   -98.39338611
29.66158771   -98.39339646
29.66158771   -98.39340681
29.66158771   -98.39341716
29.66158771   -98.39342751
29.66158771   -98.39343786
29.66158771   -98.39343926
29.66159226   -98.39343786
29.6615967    -98.39326192
29.6615967    -98.39327227
29.6615967    -98.39325426
29.6615967    -98.39328262
29.6615967    -98.39329297
29.6615967    -98.39330332
29.6615967    -98.39331367
29.6615967    -98.39332402
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
29.66160569   -98.39343291
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
29.66161468   -98.39341716
29.66161468   -98.39342751
29.66161468   -98.39342823
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
29.66165066   -98.39340447
29.66165965   -98.39325157
29.66165965   -98.39326192
29.66165965   -98.39324479
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
29.66168954   -98.39337576
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
29.66169562   -98.39333437
29.66169562   -98.39334472
29.66169562   -98.39335506
29.66169562   -98.39336541
29.66169562   -98.39337127
29.66170356   -98.39336541
29.66170462   -98.39325157
29.66170462   -98.39326192
29.66170462   -98.39324245
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
29.66171361   -98.39324213
29.66171361   -98.39327227
29.66171361   -98.39328262
29.66171361   -98.39329297
29.66171361   -98.39330332
29.66171361   -98.39331367
29.66171361   -98.39332402
29.66171361   -98.39333437
29.66171361   -98.39334472
29.66171361   -98.39335506
29.66171361   -98.39335799
29.66171758   -98.39335506
29.6617226    -98.39325157
29.6617226    -98.39326192
29.6617226    -98.393242
29.6617226    -98.39327227
29.6617226    -98.39328262
29.6617226    -98.39329297
29.6617226    -98.39330332
29.6617226    -98.39331367
29.6617226    -98.39332402
29.6617226    -98.39333437
29.6617226    -98.39334472
29.6617226    -98.39335135
29.66173159   -98.39334472
29.6617316    -98.39325157
29.6617316    -98.39326192
29.6617316    -98.393242
29.6617316    -98.39327227
29.6617316    -98.39328262
29.6617316    -98.39329297
29.6617316    -98.39330332
29.6617316    -98.39331367
29.6617316    -98.39332402
29.6617316    -98.39333437
29.6617316    -98.39334471
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
29.66174958   -98.39324293
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?

Answer 1

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:

Answer 2

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

Judging from that and your compass image you are required to rotate 166 degrees counter-clockwise from normal position. Rotation matrix provides way to rotate point (x,y) around original point (double zero) counter-clockwise from which following observation could be derived

After rotating counter-clockwise point (x,y) by angle a it becomes point with cordinates x * cos(a) - y * sin(a), x * sin(a) + y * cos(a)

you should be able to implement above using sin and cos functions, either from math (built-in module) or numpy , but be watchful to not mistake x and y, especially if you use numpy convention (y,x) and that mentioned function accept values in radians, not degrees (see radians function for possible means of conversion).