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Kartenprojektionen - azimutale Karten

Die Abbildung der gekrümmten Erdoberfläche in ebene Karten ist auf ganz verschiedene Weise möglich - jede hat Vor- und Nachteile. Ich habe in drei Aufsätzen die Herangehensweise der Kartographen erläutert. Alle Programme enthalten eine Koordinatenliste der Erdoberfläche. Leider sind die Punkte in der Nähe der Polgebeite es was dünn bzw. fehlen, obwohl hier durchaus "Land" ist und dies in einigen der Projektionen auch wiedergegeben werden könnte.

Auf Anfrage eines Sternfreundes habe ich die  transversale stereographische Projektion programmiert. Sie ist in den Heften nicht enthalten.


# Programm azimutaleKarten


from turtle import *; from math import *

def plotN(x,y):
  penup()
  goto(x,y)
  pendown()
  dot(3)
  hideturtle()

def plot(x,y):
  penup()
  goto(x,y)
  pendown()
  dot(2)
  hideturtle()

k=[[-2.63519, -1.39622],
[-2.65841, -1.38947],
[-2.70211, -1.37488],
[-2.73642, -1.36111],
[-2.75368, -1.35147],
[-2.73049, -1.34912],
[-2.69291, -1.35147],
[-2.69291, -1.34147],
[-2.73049, -1.33922],
[-2.75368, -1.33264],
[-2.75981, -1.32433],
[-2.76595, -1.31638],
[-2.73642, -1.31247],
[-2.68485, -1.31638],
[-2.66664, -1.32639],
[-2.62293, -1.33264],
[-2.57942, -1.32851],
[-2.54491, -1.31837],
[-2.54491, -1.30676],
[-2.55104, -1.2977],
[-2.55622, -1.28906],
[-2.5106, -1.28735],
[-2.47514, -1.28233],
[-2.45173, -1.28568],
[-2.44061, -1.27915],
[-2.41129, -1.27641],
[-2.38196, -1.27171],
[-2.36164, -1.26704],
[-2.31811, -1.26704],
[-2.30087, -1.27171],
[-2.28054, -1.27915],
[-2.26022, -1.28568],
[-2.23088, -1.29079],
[-2.21364, -1.29079],
[-2.21057, -1.284],
[-2.20252, -1.2748],
[-2.18737, -1.26597],
[-2.17011, -1.25997],
[-2.1498, -1.25161],
[-2.15594, -1.24257],
[-2.13255, -1.24257],
[-2.11549, -1.2507],
[-2.0921, -1.25456],
[-2.0921, -1.24779],
[-2.06276, -1.24923],
[-2.03325, -1.24923],
[-2.05164, -1.25752],
[-2.05164, -1.26597],
[-2.02826, -1.2748],
[-1.98168, -1.27641],
[-1.95829, -1.27171],
[-1.96136, -1.26301],
[-1.96441, -1.25456],
[-1.95234, -1.24923],
[-1.9441, -1.25456],
[-1.93509, -1.26301],
[-1.92282, -1.27171],
[-1.89445, -1.2748],
[-1.89157, -1.26597],
[-1.90864, -1.26301],
[-1.90864, -1.25456],
[-1.88851, -1.25456],
[-1.88237, -1.25997],
[-1.89157, -1.26597],
[-1.87432, -1.2732],
[-1.84787, -1.2732],
[-1.8216, -1.27014],
[-1.8216, -1.26452],
[-1.79017, -1.26452],
[-1.76695, -1.26704],
[-1.74357, -1.27171],
[-1.76695, -1.25997],
[-1.75468, -1.25456],
[-1.76887, -1.2507],
[-1.74357, -1.24779],
[-1.72536, -1.24545],
[-1.74357, -1.24018],
[-1.76695, -1.24257],
[-1.78709, -1.23505],
[-1.76695, -1.23374],
[-1.76887, -1.23883],
[-1.73744, -1.23742],
[-1.7173, -1.244],
[-1.70006, -1.24545],
[-1.70006, -1.2507],
[-1.67974, -1.2507],
[-1.6736, -1.24545],
[-1.6736, -1.24018],
[-1.70006, -1.23742],
[-1.7173, -1.23093],
[-1.73744, -1.22632],
[-1.76083, -1.22269],
[-1.74051, -1.21993],
[-1.71425, -1.22354],
[-1.69086, -1.22131],
[-1.66767, -1.22494],
[-1.66767, -1.22997],
[-1.63814, -1.23232],
[-1.60785, -1.23505],
[-1.57736, -1.23742],
[-1.54707, -1.23742],
[-1.51679, -1.23742],
[-1.49033, -1.24018],
[-1.4702, -1.23742],
[-1.44682, -1.23602],
[-1.41633, -1.23742],
[-1.38605, -1.23883],
[-1.36879, -1.24257],
[-1.37186, -1.23602],
[-1.35959, -1.22997],
[-1.33332, -1.23232],
[-1.30802, -1.23602],
[-1.2898, -1.23883],
[-1.29882, -1.24634],
[-1.27255, -1.24545],
[-1.24629, -1.244],
[-1.22079, -1.24115],
[-1.19452, -1.24018],
[-1.17728, -1.23602],
[-1.16825, -1.22859],
[-1.16825, -1.22131],
[-1.17728, -1.2163],
[-1.17728, -1.20805],
[-1.18532, -1.20082],
[-1.19452, -1.19487],
[-1.19452, -1.18705],
[-1.17421, -1.18705],
[-1.16213, -1.1825],
[-1.17421, -1.17869],
[-1.1652, -1.16836],
[-1.17728, -1.16356],
[-1.19452, -1.16356],
[-1.20775, -1.16356],
[-1.20871, -1.1578],
[-1.19759, -1.15187],
[-1.18244, -1.14794],
[-1.17939, -1.15382],
[-1.16825, -1.1529],
[-1.15694, -1.1578],
[-1.15694, -1.15038],
[-1.14181, -1.147],
[-1.13375, -1.13738],
[-1.11555, -1.13127],
[-1.11555, -1.12495],
[-1.09829, -1.12654],
[-1.09216, -1.12028],
[-1.0749, -1.11918],
[-1.07202, -1.11279],
[-1.04059, -1.10682],
[-1.0264, -1.10288],
[-1.01106, -1.09909],
[-0.996868, -1.09794],
[-1.01413, -1.10682],
[-0.99802, -1.10682],
[-0.999939, -1.11542],
[-1.01413, -1.1138],
[-1.02832, -1.11654],
[-1.04059, -1.1138],
[-1.05478, -1.11918],
[-1.06993, -1.12398],
[-1.08104, -1.13019],
[-1.08717, -1.13996],
[-1.09216, -1.1455],
[-1.10748, -1.14197],
[-1.11036, -1.15187],
[-1.12762, -1.15187],
[-1.13874, -1.1578],
[-1.14181, -1.16455],
[-1.13068, -1.16836],
[-1.13068, -1.17782],
[-1.11036, -1.17782],
[-1.09216, -1.1825],
[-1.08717, -1.19026],
[-1.08104, -1.19763],
[-1.07202, -1.20358],
[-1.0749, -1.20805],
[-1.06378, -1.21175],
[-1.06071, -1.21759],
[-1.0749, -1.22354],
[-1.06071, -1.22859],
[-1.06378, -1.23374],
[-1.04366, -1.23883],
[-1.04863, -1.244],
[-1.07202, -1.24545],
[-1.06378, -1.2507],
[-1.05783, -1.25997],
[-1.0749, -1.26597],
[-1.0749, -1.2732],
[-1.09829, -1.2748],
[-1.09829, -1.284],
[-1.11036, -1.29241],
[-1.14181, -1.30131],
[-1.17421, -1.31247],
[-1.13375, -1.31638],
[-1.09024, -1.31442],
[-1.04652, -1.31442],
[-1.00512, -1.31837],
[-0.976745, -1.32639],
[-0.936097, -1.33481],
[-0.900633, -1.34374],
[-0.860195, -1.35147],
[-0.830857, -1.35861],
[-0.767015, -1.36111],
[-0.71525, -1.36111],
[-0.67174, -1.35861],
[-0.634164, -1.34678],
[-0.610969, -1.33264],
[-0.581631, -1.32433],
[-0.552119, -1.31638],
[-0.52374, -1.30864],
[-0.49442, -1.30131],
[-0.471225, -1.29241],
[-0.453964, -1.284],
[-0.4185, -1.27803],
[-0.413317, -1.26704],
[-0.390122, -1.26147],
[-0.360609, -1.25604],
[-0.337397, -1.2507],
[-0.308076, -1.24545],
[-0.28469, -1.24018],
[-0.256311, -1.23742],
[-0.235996, -1.23602],
[-0.215856, -1.23232],
[-0.197653, -1.22728],
[-0.195541, -1.22269],
[-0.20973, -1.21897],
[-0.212802, -1.21398],
[-0.200532, -1.2126],
[-0.192469, -1.21759],
[-0.183464, -1.2126],
[-0.170234, -1.20943],
[-0.157005, -1.21175],
[-0.148959, -1.22131],
[-0.128627, -1.21897],
[-0.128627, -1.21037],
[-0.119621, -1.20581],
[-0.102378, -1.20581],
[-0.105432, -1.21398],
[-0.0789913, -1.21398],
[-0.0527248, -1.2126],
[-0.0527248, -1.20445],
[-0.0446617, -1.19859],
[-0.0293381, -1.20082],
[-0.0182207, -1.20445],
[-0.0262664, -1.20943],
[-0.0120773, -1.2126],
[0, -1.2163],
[0.0220429, -1.2126],
[0.0454296, -1.20805],
[0.0605786, -1.20358],
[0.0808936, -1.19988],
[0.109272, -1.19988],
[0.127493, -1.19625],
[0.150687, -1.19625],
[0.174074, -1.19763],
[0.196309, -1.19625],
[0.219696, -1.19625],
[0.249034, -1.19763],
[0.27242, -1.19763],
[0.295615, -1.19763],
[0.319002, -1.19763],
[0.348323, -1.19988],
[0.373629, -1.20082],
[0.400087, -1.20358],
[0.429426, -1.20082],
[0.440543, -1.19763],
[0.469881, -1.19763],
[0.493268, -1.194],
[0.522589, -1.19262],
[0.544823, -1.18939],
[0.557093, -1.18801],
[0.583359, -1.18801],
[0.580305, -1.18108],
[0.583359, -1.1764],
[0.597548, -1.17543],
[0.609818, -1.1801],
[0.626886, -1.18565],
[0.64413, -1.18801],
[0.667516, -1.18939],
[0.67366, -1.19625],
[0.684777, -1.19026],
[0.693783, -1.18337],
[0.696855, -1.17869],
[0.720241, -1.174],
[0.731359, -1.16934],
[0.754553, -1.16455],
[0.774886, -1.16356],
[0.801135, -1.16356],
[0.818396, -1.16119],
[0.838711, -1.16211],
[0.859043, -1.15872],
[0.868049, -1.16455],
[0.879166, -1.16119],
[0.873232, -1.1529],
[0.879166, -1.1455],
[0.896427, -1.14197],
[0.908696, -1.13738],
[0.934945, -1.13583],
[0.960252, -1.13738],
[0.975401, -1.14197],
[0.995733, -1.14445],
[0.981544, -1.14944],
[0.992662, -1.15187],
[1.0099, -1.1529],
[1.02717, -1.1553],
[1.0565, -1.1578],
[1.07375, -1.16119],
[1.09101, -1.16211],
[1.10921, -1.15972],
[1.1326, -1.16119],
[1.15579, -1.16356],
[1.17805, -1.16455],
[1.19644, -1.16455],
[1.21063, -1.16211],
[1.21063, -1.16934],
[1.21964, -1.17543],
[1.2277, -1.18108],
[1.21063, -1.18337],
[1.21656, -1.18939],
[1.21656, -1.19625],
[1.23075, -1.2022],
[1.24801, -1.20082],
[1.2369, -1.19625],
[1.26028, -1.19166],
[1.28041, -1.18939],
[1.29767, -1.19026],
[1.31491, -1.19262],
[1.32699, -1.18801],
[1.34425, -1.18337],
[1.35844, -1.1825],
[1.36456, -1.174],
[1.3757, -1.17078],
[1.40195, -1.16691],
[1.42228, -1.16455],
[1.43741, -1.1578],
[1.45774, -1.1553],
[1.48113, -1.1529],
[1.50432, -1.15038],
[1.52771, -1.14794],
[1.5419, -1.14944],
[1.56202, -1.14944],
[1.58541, -1.14794],
[1.60248, -1.1455],
[1.61974, -1.147],
[1.63698, -1.147],
[1.6552, -1.1455],
[1.67245, -1.14794],
[1.68971, -1.1455],
[1.70179, -1.14794],
[1.71597, -1.1455],
[1.73015, -1.147],
[1.74243, -1.14445],
[1.75355, -1.14445],
[1.76772, -1.13996],
[1.78901, -1.13583],
[1.81221, -1.13738],
[1.82945, -1.13996],
[1.84671, -1.14197],
[1.86397, -1.1455],
[1.88122, -1.147],
[1.89944, -1.15038],
[1.92167, -1.14794],
[1.9278, -1.13996],
[1.94506, -1.13738],
[1.96326, -1.13583],
[1.98052, -1.13487],
[1.99471, -1.13843],
[2.01196, -1.1434],
[2.03018, -1.1455],
[2.0503, -1.14944],
[2.07369, -1.15038],
[2.09594, -1.15038],
[2.11721, -1.14794],
[2.13446, -1.14445],
[2.14865, -1.14944],
[2.16591, -1.14944],
[2.19217, -1.147],
[2.20444, -1.14197],
[2.22457, -1.1455],
[2.23568, -1.15187],
[2.24795, -1.1529],
[2.26521, -1.15187],
[2.26521, -1.1434],
[2.2794, -1.13996],
[2.29953, -1.14092],
[2.32291, -1.13996],
[2.34017, -1.14092],
[2.35742, -1.13996],
[2.37564, -1.1434],
[2.39288, -1.1434],
[2.41014, -1.1455],
[2.42719, -1.147],
[2.44753, -1.14794],
[2.47379, -1.14944],
[2.49718, -1.15038],
[2.51442, -1.1529],
[2.51442, -1.15972],
[2.5265, -1.16119],
[2.54376, -1.15972],
[2.55795, -1.16455],
[2.561, -1.17078],
[2.58441, -1.17311],
[2.59648, -1.17078],
[2.61987, -1.174],
[2.63099, -1.17167],
[2.66031, -1.17543],
[2.68869, -1.17543],
[2.70077, -1.1825],
[2.71803, -1.18565],
[2.72722, -1.18108],
[2.74447, -1.1825],
[2.76461, -1.18476],
[2.78799, -1.18801],
[2.80525, -1.19026],
[2.80525, -1.19625],
[2.80831, -1.2022],
[2.81637, -1.20669],
[2.82845, -1.19763],
[2.84569, -1.19625],
[2.84262, -1.20358],
[2.86908, -1.20358],
[2.89227, -1.2022],
[2.91566, -1.20669],
[2.93887, -1.21175],
[2.96226, -1.2163],
[2.96531, -1.21175],
[2.9795, -1.21993],
[2.96531, -1.22354],
[2.97031, -1.23093],
[2.95612, -1.23602],
[2.9358, -1.24115],
[2.90954, -1.24257],
[2.90954, -1.24923],
[2.90339, -1.25604],
[2.88116, -1.25752],
[2.88116, -1.26301],
[2.86295, -1.26859],
[2.83957, -1.2748],
[2.83458, -1.284],
[2.83458, -1.29241],
[2.83957, -1.30131],
[2.84569, -1.31055],
[2.85184, -1.32025],
[2.85184, -1.3305],
[2.86908, -1.337],
[2.89227, -1.34912],
[2.85777, -1.35147],
[2.81426, -1.35861],
[2.78799, -1.37221],
[2.78799, -1.38947],
[2.78799, -1.39622],
[2.89842, -1.3269],
[2.92985, -1.32851],
[2.95612, -1.32227],
[2.92985, -1.32025],
[2.90339, -1.31442],
[2.89842, -1.32639],
[-2.85911, -1.3591],
[-2.84091, -1.36957],
[-2.85299, -1.37842],
[-2.85299, -1.39622],
[-2.85203, -1.39622],
[-2.79431, -1.3967],
[-2.78915, -1.38378],
[-2.80026, -1.36957],
[-2.81752, -1.35861],
[-2.85911, -1.35861],
[-2.61795, -1.3036],
[-2.58861, -1.30676],
[-2.56523, -1.2995],
[-2.58249, -1.29416],
[-2.61795, -1.30315],
[-1.32833, -1.2109],
[-1.32528, -1.21897],
[-1.30802, -1.22131],
[-1.29594, -1.22632],
[-1.27868, -1.22728],
[-1.27255, -1.23232],
[-1.24629, -1.23374],
[-1.22079, -1.23232],
[-1.20066, -1.22859],
[-1.19452, -1.22269],
[-1.19147, -1.2163],
[-1.19452, -1.20943],
[-1.20066, -1.2022],
[-1.20871, -1.19487],
[-1.21485, -1.18705],
[-1.22597, -1.17869],
[-1.24112, -1.1801],
[-1.24629, -1.18939],
[-1.23805, -1.19625],
[-1.2321, -1.20358],
[-1.25224, -1.20805],
[-1.27255, -1.20943],
[-1.30187, -1.21037],
[-1.32833, -1.21037],
[-1.32833, -1.2041],
[-1.30802, -1.20358],
[-1.2898, -1.2022],
[-1.28463, -1.194],
[-1.29882, -1.19166],
[-1.32125, -1.19487],
[-1.32833, -1.20358],
[-1.12148, -1.1197],
[-1.10748, -1.12127],
[-1.08104, -1.1138],
[-1.09829, -1.11755],
[-1.12148, -1.11918],
[-0.98479, -1.0984],
[-0.959501, -1.10014],
[-0.973673, -1.09401],
[-0.98479, -1.09794],
[1.61571, -1.1343],
[1.80722, -1.1318],
[2.82845, -1.1449],
[2.86908, -1.1583],
[-1.57948, -1.1792],
[-1.06378, -1.0894],
[-1.0517, -1.09005],
[-1.03444, -1.08377],
[-1.02333, -1.08256],
[-1.00512, -1.07849],
[-1.0264, -1.07849],
[-1.0517, -1.08659],
[-1.06378, -1.08886],
[-0.967547, -1.0636],
[-0.944352, -1.0636],
[-0.80843, -1.0576],
[-0.785235, -1.05834],
[-0.802479, -1.05277],
[-0.80843, -1.05706],
[-0.776038, -1.0594],
[-1.3962, -1.57075],
[-1.40329, -0.0153235],
[-1.40828, -0.0293032],
[-1.41039, -0.0415725],
[-1.39812, -0.052655],
[-1.40924, -0.0668092],
[-1.41844, -0.0819059],
[-1.40924, -0.0990794],
[-1.40924, -0.109185],
[-1.39505, -0.119272],
[-1.38605, -0.137336],
[-1.37186, -0.151403],
[-1.36571, -0.168472],
[-1.3546, -0.189467],
[-1.3454, -0.206466],
[-1.33639, -0.218334],
[-1.32833, -0.238283],
[-1.3222, -0.256102],
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[2.09803, -0.0618352],
[2.10206, -0.0465466],
[2.10706, -0.0597409],
[2.11933, -0.0719753],
[2.11817, -0.0819059],
[2.1314, -0.0799861],
[2.1314, -0.0929709],
[2.14557, -0.0929709],
[2.14557, -0.0830403],
[2.13446, -0.0668092],
[2.13236, -0.0557267],
[2.1243, -0.042515],
[2.12737, -0.0293032],
[2.14156, -0.0162834],
[2.15172, -0.0162834],
[2.13542, -0.0132292],
[2.11817, -0.0162834],
[2.10206, -0.0233693],
[2.09191, -0.0122693],
[2.09191, -0.00211179],
[2.10206, 0.00804573],
[2.11529, 0.00804573],
[2.12526, 0.00804573],
[2.14252, 0.00804573],
[2.16072, 0.00689385],
[2.17088, 0.00996554],
[2.182, 0.0253065],
[2.16783, 0.0201231],
[2.14865, 0.015149],
[2.13446, 0.0170688],
[2.11529, 0.0201231],
[2.10206, 0.0120773],
[2.09095, 0.0120773],
[2.08788, -0.00211179],
[2.08175, -0.0162834],
[2.07868, -0.0335268],
[2.07063, -0.0496008],
[2.21861, 0.0180113],
[2.22457, 0.00383961],
[2.22879, -0.0113094],
[2.22879, 0],
[2.23876, 0.00804573],
[2.24183, 0.0180113],
[2.23165, 0.0222348],
[2.22975, 0.0373838],
[2.22169, 0.0253065],
[2.21861, 0.0180113],
[2.19523, -0.0572],
[2.20942, -0.0668092],
[2.21249, -0.0557267],
[2.19523, -0.0566692],
[2.22879, -0.0562],
[2.23876, -0.0597409],
[2.25506, -0.0597409],
[2.26923, -0.0627951],
[2.2723, -0.052655],
[2.256, -0.0486409],
[2.24584, -0.0496008],
[2.23472, -0.0496008],
[2.22879, -0.0557267],
[2.16898, -0.0319],
[2.182, -0.031415],
[2.21861, -0.0298],
[2.2328, -0.0293032],
[2.22265, -0.0233693],
[2.21861, -0.0293032],
[2.26827, -0.0329],
[2.27019, -0.0036],
[2.28649, -0.00516602],
[2.27019, -0.00307169],
[2.35742, -0.0128],
[2.37353, -0.0193551],
[2.35742, -0.0122693],
[2.2794, -0.0239],
[2.28956, -0.026441],
[2.30375, -0.0394607],
[2.32195, -0.0385008],
[2.33211, -0.0354466],
[2.31888, -0.0446268],
[2.3026, -0.0465466],
[2.31179, -0.0566692],
[2.31371, -0.0698635],
[2.32904, -0.0618352],
[2.34515, -0.0719753],
[2.36241, -0.0778917],
[2.37257, -0.0799861],
[2.38272, -0.0849601],
[2.39288, -0.0880144],
[2.40707, -0.0981195],
[2.41206, -0.108225],
[2.41417, -0.118312],
[2.40899, -0.128208],
[2.39883, -0.145329],
[2.40899, -0.145329],
[2.41915, -0.141333],
[2.4293, -0.141333],
[2.43946, -0.13943],
[2.44964, -0.151403],
[2.46573, -0.158419],
[2.48395, -0.161456],
[2.49411, -0.157476],
[2.49411, -0.145329],
[2.50638, -0.138296],
[2.52057, -0.131262],
[2.53666, -0.138296],
[2.54779, -0.148366],
[2.561, -0.163533],
[2.57118, -0.174528],
[2.59034, -0.177373],
[2.6005, -0.178507],
[2.61373, -0.186448],
[2.62389, -0.184563],
[2.60856, -0.173393],
[2.59744, -0.164492],
[2.58326, -0.150443],
[2.58134, -0.13943],
[2.56407, -0.126306],
[2.57615, -0.116218],
[2.56811, -0.102134],
[2.55795, -0.103076],
[2.54779, -0.0981195],
[2.53973, -0.0860946],
[2.5265, -0.0750295],
[2.50926, -0.0648894],
[2.49103, -0.058781],
[2.48088, -0.0547668],
[2.46573, -0.0486409],
[2.44657, -0.0415725],
[2.43026, -0.0385008],
[2.41206, -0.0293032],
[2.39077, -0.0293032],
[2.37869, -0.0385008],
[2.36642, -0.0517126],
[2.3553, -0.058781],
[2.34515, -0.0446268],
[2.33499, -0.0323749],
[2.33307, -0.0122693],
[2.32195, -0.0122693],
[2.3026, -0.00612592],
[2.28649, -0.0153235],
[2.2794, -0.0233693],
[2.08788, 0.282962],
[2.08884, 0.273188],
[2.09191, 0.257167],
[2.10206, 0.257167],
[2.10206, 0.247149],
[2.11222, 0.237131],
[2.12833, 0.238265],
[2.13753, 0.22823],
[2.13542, 0.241093],
[2.15076, 0.226136],
[2.16284, 0.225193],
[2.15268, 0.238265],
[2.14156, 0.247149],
[2.12948, 0.242245],
[2.11933, 0.254147],
[2.11529, 0.266033],
[2.12526, 0.282019],
[2.13446, 0.297971],
[2.12833, 0.312754],
[2.1314, 0.32265],
[2.11721, 0.319665],
[2.10206, 0.32265],
[2.09594, 0.306767],
[2.09594, 0.288966],
[2.08788, 0.282962],
[2.04225, 0.14676],
[2.05433, 0.151717],
[2.06564, 0.163934],
[2.07561, 0.175959],
[2.08175, 0.196134],
[2.07561, 0.18301],
[2.06257, 0.167948],
[2.04725, 0.154771],
[2.04225, 0.14676],
[2.09095, 0.0889568],
[2.10915, 0.102169],
[2.09803, 0.234094],
[2.10706, 0.218177],
[2.11817, 0.218177],
[2.11222, 0.232209],
[2.09803, 0.234094],
[2.16591, 0.218177],
[2.17798, 0.20507],
[2.16783, 0.199189],
[2.16783, 0.189101],
[2.17299, 0.176901],
[2.17798, 0.193098],
[2.1891, 0.193098],
[2.18622, 0.202976],
[2.182, 0.218177],
[2.16591, 0.218177],
[2.1243, 0.18301],
[2.13446, 0.183952],
[2.13945, 0.173847],
[2.13753, 0.1628],
[2.14865, 0.16088],
[2.15575, 0.172905],
[2.16898, 0.167948],
[2.16072, 0.183952],
[2.15076, 0.180915],
[2.14557, 0.200131],
[2.13542, 0.200131],
[2.1243, 0.20603],
[2.12526, 0.190043],
[2.1243, 0.18301],
[2.12526, 0.124578],
[2.13945, 0.134526],
[2.15268, 0.134526],
[2.16495, 0.12744],
[2.16072, 0.111366],
[2.17299, 0.102169],
[2.18507, 0.0971945],
[2.18814, 0.111366],
[2.18622, 0.121506],
[2.1983, 0.110214],
[2.2054, 0.125538],
[2.20137, 0.143689],
[2.20137, 0.153829],
[2.18507, 0.16985],
[2.18622, 0.157825],
[2.17491, 0.156691],
[2.16495, 0.14676],
[2.15172, 0.150757],
[2.13945, 0.141594],
[2.12737, 0.134526],
[2.12526, 0.124578],
[2.58326, -0.0965],
[2.59341, -0.102134],
[2.6076, -0.109185],
[2.62485, -0.109185],
[2.64095, -0.0981195],
[2.65015, -0.0880144],
[2.65226, -0.0729177],
[2.63999, -0.0729177],
[2.64211, -0.0860946],
[2.62792, -0.0960252],
[2.61373, -0.0960252],
[2.60357, -0.0981195],
[2.59341, -0.0981195],
[2.58326, -0.0960252],
[2.55488, -0.0371],
[2.56407, -0.036581],
[2.62792, -0.0461],
[2.63807, -0.052655],
[2.64804, -0.0597409],
[2.66031, -0.0729177],
[2.66434, -0.0849601],
[2.6653, -0.0689036],
[2.65418, -0.0618352],
[2.63807, -0.052655],
[2.69483, -0.0956],
[2.69769, -0.10517],
[2.709, -0.119272],
[2.71092, -0.108225],
[2.70192, -0.0960252],
[2.69483, -0.0950653],
[2.72415, -0.1158],
[2.73431, -0.122327],
[2.74141, -0.126306],
[2.72914, -0.136],
[2.74026, -0.1399],
[2.75042, -0.148366],
[2.76154, -0.1318],
[2.77572, -0.141333],
[2.78185, -0.145329],
[2.79911, -0.1458],
[2.8062, -0.160513],
[2.81426, -0.168472],
[2.7788, -0.162],
[2.78185, -0.171491],
[2.79604, -0.173393],
[2.79203, -0.163533],
[2.7788, -0.161456],
[2.80927, -0.1779],
[2.82845, -0.18739],
[2.80927, -0.177373],
[2.89131, -0.1879],
[2.9055, -0.2575],
[2.90646, -0.272944],
[2.91261, -0.261163],
[2.90646, -0.266015],
[2.91566, -0.2783],
[2.91873, -0.287674],
[2.91566, -0.277796],
[2.93484, -0.3088],
[2.86199, -0.3538],
[2.86793, -0.36307],
[2.88212, -0.374659],
[2.89535, -0.383455],
[2.91261, -0.389319],
[2.90149, -0.377591],
[2.88615, -0.368952],
[2.871, -0.357189],
[2.86199, -0.353314],
[2.91566, -0.3665],
[2.9268, -0.3752],
[2.9268, -0.5072],
[2.77169, -0.552],
[-3.08188, -0.7687],
[-3.07076, -0.768969],
[-3.08188, -0.768167],
[2.89535, -0.8902],
[3.11523, -0.8732],
[2.94596, -0.9237],
[2.76864, -0.9588],
[2.5336, 0.343296],
[2.53762, 0.327501],
[2.54069, 0.306767],
[2.53762, 0.285964],
[2.53973, 0.264148],
[2.53762, 0.261128],
[2.52861, 0.246206],
[2.52152, 0.232209],
[2.28534, 0.051573],
[2.30565, 0.0749597],
[2.30375, 0.0920285],
[2.3371, 0.119412],
[2.33921, 0.121506],
[2.34515, 0.130512],
[2.40707, 0.164894],
[2.43334, 0.173847],
[2.64614, 0.12744],
[2.75654, 0.121506],
[2.83957, 0.0920285],
[2.68256, 0.424888],
[2.90339, 0.336437],
[2.82845, 0.198037],
[2.88423, 0.202033],
[2.92276, 0.151717],
[2.96627, 0.164894],
[2.98353, 0.123426],
[2.95612, 0.102169],
[3.0098, 0.051573],
[3.01382, 0.0231947],
[3.0493, -0.0269],
[2.90858, -0.0097],
[2.95516, -0.0158],
[3.06961, -0.0996],
[3.12234, -0.1489],
[3.08993, -0.3137],
[3.10412, -0.31614],
[3.11312, -0.306488],
[3.09703, -0.302387],
[3.08993, -0.313173],
[3.1112, -0.2891],
[3.12424, -0.290659],
[3.13441, -0.290659],
[3.12234, -0.285824],
[3.1112, -0.288617],
[-3.079, 0.0130372],
[-3.07593, 0.00287971],
[-2.98162, -0.0553],
[-2.99273, -0.0501],
[-3.0353, -0.0633],
[-3.04239, -0.0824],
[-3.00193, -0.0794],
[-2.97568, -0.0654],
[-3.00692, -0.15],
[-2.99696, -0.161],
[-2.98469, -0.164],
[-3.01401, -0.2348],
[-3.00097, -0.239225],
[-2.9868, -0.244287],
[-3.00097, -0.239225],
[-3.01401, -0.234338],
[-2.97453, -0.2497],
[-2.96149, -0.3324],
[-3.03242, -0.3255],
[-3.05254, -0.3674],
[-3.0535, -0.3685],
[-3.10124, -0.5118],
[-2.78511, -0.3294],
[-2.78511, -0.3704],
[-2.75272, -0.383],
[-2.95535, 0.291968],
[-2.82557, 0.102169],
[-2.79623, 0.081871],
[-2.77803, 0.0676819],
[-2.74466, 0.0343122],
[-2.78915, -0.0076],
[-2.70211, -0.0713],
[-2.71726, -0.0986],
[-2.75464, -0.158],
[-2.8085, -0.176],
[-2.80735, -0.182],
[-2.65649, -0.1769],
[-2.64633, -0.2],
[-2.61891, -0.175],
[-2.60779, -0.3049],
[-2.64537, -0.2882],
[-2.60472, -0.4081],
[-2.51557, -0.4817],
[-2.5846, -0.2764],
[-2.53781, -0.2804],
[-2.53072, -0.2566],
[-2.49027, -0.2932],
[-2.35244, -0.4033],
[-2.26733, -0.4379],
[-2.23703, -0.4254],
[-2.44157, -0.1568],
[-2.42337, -0.172],
[-3.09204, 0.493163],
[-3.03242, 0.455448],
[-2.99388, 0.450578],
[-2.92793, 0.43721],
[-2.89765, 0.415236],
[-2.87119, 0.412322],
[-2.82269, 0.402653],
[-2.79316, 0.381378],
[-2.79126, 0.38431],
[-2.78607, 0.385235],
[-2.75885, 0.377504],
[-2.74869, 0.371605],
[-2.75885, 0.377504],
[-2.74045, 0.368655],
[-2.73335, 0.368655],
[-2.73546, 0.363856],
[-2.73145, 0.365706],
[-2.71918, 0.361831],
[-2.73145, 0.365706],
[-2.73049, 0.358864],
[-2.71726, 0.354065],
[-2.71726, 0.337362],
[-2.7071, 0.336437],
[-2.70403, 0.348131],
[-2.71726, 0.354065]]

# Hauptprogramm
z=len(k)
tracer(0,0) # Bildschirmaktualisierung aus
for i in range(z):
  l= k[i][0]
  f= k[i][1]

  ## Orthographisch
  r=cos(f)
  x=r*cos(l)
  y=r*sin(l)
  if f>0: plotN(350*x,350*y) # dickere Punkte
  if f<0: plot(350*x,350*y)

  ## mittelabstandstreue Azimutalprojektion
  #f=pi/2-f
  #x=f*cos(l)
  #y=f*sin(l)

  ##Stereographisch, winkeltreu
  ##f=pi/2-f # Südpol
  #f=f-pi/2 # Nordpol
  #r=tan(f/2)
  #x=r*cos(l)
  #y=r*sin(l)


  ## Lambert, azimutal 
  ##f=pi/2-f # Südpol
  #f=f-pi/2 # Nordpol
  #r=atan(f/2)
  #x=r*cos(l)
  #y=r*sin(l)

  #plot(150*x,150*y) # Auskommentieren für orthographisch
update() # Bildschirm anzeigen 
done()

Transversale stereographische Projektion

Auf Anfrage eines Sternfreunde habe ich die stereographische Projektion zusätzlich so modifiziert, dass sie äquatorständig ist. Alte Landkarten sind oft so gezeichnet. Das Beispiel hier hat den Zentralmeridian bei -110° und 70°:


# Grafik ca. von -300, bis 300
from turtle import *
from math import *


def plot(x,y):
    penup()
    goto(x,y)
    pendown()
    dot(3)
    hideturtle()
        
k=[[-2.63519, -1.39622],
[-2.65841, -1.38947],
[-2.70211, -1.37488],
[-2.73642, -1.36111],
[-2.75368, -1.35147],
[-2.73049, -1.34912],
[-2.69291, -1.35147],
[-2.69291, -1.34147],
[-2.73049, -1.33922],
[-2.75368, -1.33264],
[-2.75981, -1.32433],
[-2.76595, -1.31638],
[-2.73642, -1.31247],
[-2.68485, -1.31638],
[-2.66664, -1.32639],
[-2.62293, -1.33264],
[-2.57942, -1.32851],
[-2.54491, -1.31837],
[-2.54491, -1.30676],
[-2.55104, -1.2977],
[-2.55622, -1.28906],
[-2.5106, -1.28735],
[-2.47514, -1.28233],
[-2.45173, -1.28568],
[-2.44061, -1.27915],
[-2.41129, -1.27641],
[-2.38196, -1.27171],
[-2.36164, -1.26704],
[-2.31811, -1.26704],
[-2.30087, -1.27171],
[-2.28054, -1.27915],
[-2.26022, -1.28568],
[-2.23088, -1.29079],
[-2.21364, -1.29079],
[-2.21057, -1.284],
[-2.20252, -1.2748],
[-2.18737, -1.26597],
[-2.17011, -1.25997],
[-2.1498, -1.25161],
[-2.15594, -1.24257],
[-2.13255, -1.24257],
[-2.11549, -1.2507],
[-2.0921, -1.25456],
[-2.0921, -1.24779],
[-2.06276, -1.24923],
[-2.03325, -1.24923],
[-2.05164, -1.25752],
[-2.05164, -1.26597],
[-2.02826, -1.2748],
[-1.98168, -1.27641],
[-1.95829, -1.27171],
[-1.96136, -1.26301],
[-1.96441, -1.25456],
[-1.95234, -1.24923],
[-1.9441, -1.25456],
[-1.93509, -1.26301],
[-1.92282, -1.27171],
[-1.89445, -1.2748],
[-1.89157, -1.26597],
[-1.90864, -1.26301],
[-1.90864, -1.25456],
[-1.88851, -1.25456],
[-1.88237, -1.25997],
[-1.89157, -1.26597],
[-1.87432, -1.2732],
[-1.84787, -1.2732],
[-1.8216, -1.27014],
[-1.8216, -1.26452],
[-1.79017, -1.26452],
[-1.76695, -1.26704],
[-1.74357, -1.27171],
[-1.76695, -1.25997],
[-1.75468, -1.25456],
[-1.76887, -1.2507],
[-1.74357, -1.24779],
[-1.72536, -1.24545],
[-1.74357, -1.24018],
[-1.76695, -1.24257],
[-1.78709, -1.23505],
[-1.76695, -1.23374],
[-1.76887, -1.23883],
[-1.73744, -1.23742],
[-1.7173, -1.244],
[-1.70006, -1.24545],
[-1.70006, -1.2507],
[-1.67974, -1.2507],
[-1.6736, -1.24545],
[-1.6736, -1.24018],
[-1.70006, -1.23742],
[-1.7173, -1.23093],
[-1.73744, -1.22632],
[-1.76083, -1.22269],
[-1.74051, -1.21993],
[-1.71425, -1.22354],
[-1.69086, -1.22131],
[-1.66767, -1.22494],
[-1.66767, -1.22997],
[-1.63814, -1.23232],
[-1.60785, -1.23505],
[-1.57736, -1.23742],
[-1.54707, -1.23742],
[-1.51679, -1.23742],
[-1.49033, -1.24018],
[-1.4702, -1.23742],
[-1.44682, -1.23602],
[-1.41633, -1.23742],
[-1.38605, -1.23883],
[-1.36879, -1.24257],
[-1.37186, -1.23602],
[-1.35959, -1.22997],
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[2.39077, -0.0293032],
[2.37869, -0.0385008],
[2.36642, -0.0517126],
[2.3553, -0.058781],
[2.34515, -0.0446268],
[2.33499, -0.0323749],
[2.33307, -0.0122693],
[2.32195, -0.0122693],
[2.3026, -0.00612592],
[2.28649, -0.0153235],
[2.2794, -0.0233693],
[2.08788, 0.282962],
[2.08884, 0.273188],
[2.09191, 0.257167],
[2.10206, 0.257167],
[2.10206, 0.247149],
[2.11222, 0.237131],
[2.12833, 0.238265],
[2.13753, 0.22823],
[2.13542, 0.241093],
[2.15076, 0.226136],
[2.16284, 0.225193],
[2.15268, 0.238265],
[2.14156, 0.247149],
[2.12948, 0.242245],
[2.11933, 0.254147],
[2.11529, 0.266033],
[2.12526, 0.282019],
[2.13446, 0.297971],
[2.12833, 0.312754],
[2.1314, 0.32265],
[2.11721, 0.319665],
[2.10206, 0.32265],
[2.09594, 0.306767],
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[2.04225, 0.14676],
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[2.06564, 0.163934],
[2.07561, 0.175959],
[2.08175, 0.196134],
[2.07561, 0.18301],
[2.06257, 0.167948],
[2.04725, 0.154771],
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[2.09095, 0.0889568],
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[2.09803, 0.234094],
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[2.17798, 0.20507],
[2.16783, 0.199189],
[2.16783, 0.189101],
[2.17299, 0.176901],
[2.17798, 0.193098],
[2.1891, 0.193098],
[2.18622, 0.202976],
[2.182, 0.218177],
[2.16591, 0.218177],
[2.1243, 0.18301],
[2.13446, 0.183952],
[2.13945, 0.173847],
[2.13753, 0.1628],
[2.14865, 0.16088],
[2.15575, 0.172905],
[2.16898, 0.167948],
[2.16072, 0.183952],
[2.15076, 0.180915],
[2.14557, 0.200131],
[2.13542, 0.200131],
[2.1243, 0.20603],
[2.12526, 0.190043],
[2.1243, 0.18301],
[2.12526, 0.124578],
[2.13945, 0.134526],
[2.15268, 0.134526],
[2.16495, 0.12744],
[2.16072, 0.111366],
[2.17299, 0.102169],
[2.18507, 0.0971945],
[2.18814, 0.111366],
[2.18622, 0.121506],
[2.1983, 0.110214],
[2.2054, 0.125538],
[2.20137, 0.143689],
[2.20137, 0.153829],
[2.18507, 0.16985],
[2.18622, 0.157825],
[2.17491, 0.156691],
[2.16495, 0.14676],
[2.15172, 0.150757],
[2.13945, 0.141594],
[2.12737, 0.134526],
[2.12526, 0.124578],
[2.58326, -0.0965],
[2.59341, -0.102134],
[2.6076, -0.109185],
[2.62485, -0.109185],
[2.64095, -0.0981195],
[2.65015, -0.0880144],
[2.65226, -0.0729177],
[2.63999, -0.0729177],
[2.64211, -0.0860946],
[2.62792, -0.0960252],
[2.61373, -0.0960252],
[2.60357, -0.0981195],
[2.59341, -0.0981195],
[2.58326, -0.0960252],
[2.55488, -0.0371],
[2.56407, -0.036581],
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[2.63807, -0.052655],
[2.64804, -0.0597409],
[2.66031, -0.0729177],
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[2.6653, -0.0689036],
[2.65418, -0.0618352],
[2.63807, -0.052655],
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[2.7788, -0.161456],
[2.80927, -0.1779],
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[2.89131, -0.1879],
[2.9055, -0.2575],
[2.90646, -0.272944],
[2.91261, -0.261163],
[2.90646, -0.266015],
[2.91566, -0.2783],
[2.91873, -0.287674],
[2.91566, -0.277796],
[2.93484, -0.3088],
[2.86199, -0.3538],
[2.86793, -0.36307],
[2.88212, -0.374659],
[2.89535, -0.383455],
[2.91261, -0.389319],
[2.90149, -0.377591],
[2.88615, -0.368952],
[2.871, -0.357189],
[2.86199, -0.353314],
[2.91566, -0.3665],
[2.9268, -0.3752],
[2.9268, -0.5072],
[2.77169, -0.552],
[-3.08188, -0.7687],
[-3.07076, -0.768969],
[-3.08188, -0.768167],
[2.89535, -0.8902],
[3.11523, -0.8732],
[2.94596, -0.9237],
[2.76864, -0.9588],
[2.5336, 0.343296],
[2.53762, 0.327501],
[2.54069, 0.306767],
[2.53762, 0.285964],
[2.53973, 0.264148],
[2.53762, 0.261128],
[2.52861, 0.246206],
[2.52152, 0.232209],
[2.28534, 0.051573],
[2.30565, 0.0749597],
[2.30375, 0.0920285],
[2.3371, 0.119412],
[2.33921, 0.121506],
[2.34515, 0.130512],
[2.40707, 0.164894],
[2.43334, 0.173847],
[2.64614, 0.12744],
[2.75654, 0.121506],
[2.83957, 0.0920285],
[2.68256, 0.424888],
[2.90339, 0.336437],
[2.82845, 0.198037],
[2.88423, 0.202033],
[2.92276, 0.151717],
[2.96627, 0.164894],
[2.98353, 0.123426],
[2.95612, 0.102169],
[3.0098, 0.051573],
[3.01382, 0.0231947],
[3.0493, -0.0269],
[2.90858, -0.0097],
[2.95516, -0.0158],
[3.06961, -0.0996],
[3.12234, -0.1489],
[3.08993, -0.3137],
[3.10412, -0.31614],
[3.11312, -0.306488],
[3.09703, -0.302387],
[3.08993, -0.313173],
[3.1112, -0.2891],
[3.12424, -0.290659],
[3.13441, -0.290659],
[3.12234, -0.285824],
[3.1112, -0.288617],
[-3.079, 0.0130372],
[-3.07593, 0.00287971],
[-2.98162, -0.0553],
[-2.99273, -0.0501],
[-3.0353, -0.0633],
[-3.04239, -0.0824],
[-3.00193, -0.0794],
[-2.97568, -0.0654],
[-3.00692, -0.15],
[-2.99696, -0.161],
[-2.98469, -0.164],
[-3.01401, -0.2348],
[-3.00097, -0.239225],
[-2.9868, -0.244287],
[-3.00097, -0.239225],
[-3.01401, -0.234338],
[-2.97453, -0.2497],
[-2.96149, -0.3324],
[-3.03242, -0.3255],
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[-3.0535, -0.3685],
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[-2.78511, -0.3294],
[-2.78511, -0.3704],
[-2.75272, -0.383],
[-2.95535, 0.291968],
[-2.82557, 0.102169],
[-2.79623, 0.081871],
[-2.77803, 0.0676819],
[-2.74466, 0.0343122],
[-2.78915, -0.0076],
[-2.70211, -0.0713],
[-2.71726, -0.0986],
[-2.75464, -0.158],
[-2.8085, -0.176],
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[-2.73145, 0.365706],
[-2.71918, 0.361831],
[-2.73145, 0.365706],
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[-2.71726, 0.354065],
[-2.71726, 0.337362],
[-2.7071, 0.336437],
[-2.70403, 0.348131],
[-2.71726, 0.354065]]

# Hauptprogramm
z=len(k)
tracer(0,0) # Bildschirmaktualisierung aus
# Zentralmeridian einstellen (in Grad)
L0=-110
L0=L0*pi/180
for i in range(z):
    l= k[-i][0]-L0
    f= k[-i][1]
    # lambda wieder normalisieren
    if (l>pi): l=l-2*pi
    if (l<-pi): l=l+2*pi
    # transversale stereographische Projektion
    delta=acos(cos(f)*cos(l))
    alpha=acos(sin(f)/sin(delta))
    r=tan(delta/2)
    y=r*cos(alpha)
    x=r*sin(alpha)
    if (l<0): x=-x
    if abs(delta)<pi/2:
        plot(400*x,400*y)
# noch einen Kreis drumrum
for j in range(1000):
    plot(400*sin(j*2*pi/1000),400*cos(j*2*pi/1000))
update() # Bildschirm anzeigen  
done()
name = input("Fertig?")