File:Auxiliary Latitudes Difference.svg

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Original file(SVG file, nominally 540 × 360 pixels, file size: 47 KB)

Captions

Captions

Graph of the difference between geodetic latitude and five auxiliary latitudes

Summary

[edit]
Description
English: Graph of the difference between geodetic latitude and five auxiliary latitudes on the WGS 84 ellipsoid. Conformal and Geocentric are indistinguishable at this resolution.
Date
Source Own work
Author Apocheir
SVG development
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The source code of this SVG is invalid due to an error.
 
This W3C-invalid plot was created with Matplotlib.
Source code
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Python code

mport numpy as np
from scipy.special import ellipeinc
import matplotlib.pyplot as plt

f = 1/298.257223563
esq = f*(2-f)
e = np.sqrt(esq)

def gd(x):
    return 2*np.arctan(np.tanh(x/2))

def gdinv(x):
    return 2*np.arctanh(np.tan(x/2))

npts = 181
geodetic = np.linspace(0,np.pi/2,npts)
geocentric = np.arctan((1-f)**2 * np.tan(geodetic))
parametric = np.arctan((1-f) * np.tan(geodetic))
m = (ellipeinc(geodetic, esq) -
     esq * np.sin(geodetic) * np.cos(geodetic) / 
     np.sqrt(1 - esq * np.sin(geodetic)**2))
rectifying = np.pi/2*m/m.max()
qp = 1 + (1-esq)/e*np.arctanh(e)
q = ((1 - esq)*np.sin(geodetic)/(1 - esq*np.sin(geodetic)**2) + 
     (1 - esq)/e*np.arctanh(e*np.sin(geodetic)))
authalic = np.arcsin(q/qp)
conformal = gd(gdinv(geodetic) - e * np.arctanh(e*np.sin(geodetic)))

gddegrees = np.linspace(0,90,npts)
gdmindiff = np.zeros(gddegrees.shape)
parmindiff = 10800/np.pi*(parametric - geodetic)
autmindiff = 10800/np.pi*(authalic - geodetic)
recmindiff = 10800/np.pi*(rectifying - geodetic)
conmindiff = 10800/np.pi*(conformal - geodetic)
gcmindiff = 10800/np.pi*(geocentric - geodetic)

fig = plt.figure()
ax = plt.axes()
#in this order so conformal and geocentric get contrasting colors
ax.plot(gddegrees, conmindiff, label='conformal', dashes=[4, 4])
ax.plot(gddegrees, gcmindiff, label='geocentric', dashes=[0, 4, 4, 0])
ax.plot(gddegrees, gdmindiff, label='geodetic')
ax.plot(gddegrees, parmindiff, label='parametric')
ax.plot(gddegrees, autmindiff, label='authalic')
ax.plot(gddegrees, recmindiff, label='rectifying')
bbox = dict(color='white', alpha=0)
ax.text(45, -0.1, 'Geodetic', bbox=bbox,
        horizontalalignment='center', verticalalignment='top')
ax.text(45, min(parmindiff) + 0.2, 'Parametric', bbox=bbox, 
        horizontalalignment='center', verticalalignment='bottom')
ax.text(45, min(autmindiff) + 0.15, 'Authalic', bbox=bbox, 
        horizontalalignment='center', verticalalignment='bottom')
ax.text(45, min(recmindiff) + 0.25, 'Rectifying', bbox=bbox, 
        horizontalalignment='center', verticalalignment='bottom')
ax.text(45, min(gcmindiff) + 0.35, 'Conformal/\nGeocentric', bbox=bbox,
        horizontalalignment='center', verticalalignment='bottom')
ax.set(xlim=(0, 90),
       xlabel='Geodetic latitude (degrees)', 
       ylabel='Difference from geodetic latitude (minutes)',
       title='Auxiliary latitudes');
ax.xaxis.set_major_locator(plt.MaxNLocator(7))
plt.savefig("Auxiliary Latitudes Difference.svg")

Licensing

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

File history

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Date/TimeThumbnailDimensionsUserComment
current23:24, 5 September 2019Thumbnail for version as of 23:24, 5 September 2019540 × 360 (47 KB)Apocheir (talk | contribs)User created page with UploadWizard

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