Processing math: 100%

1. 楕円体から球面への等角写像

斜軸法を適用するために、なんらかの等角写像で回転楕円体上の経緯度を球面に投影する必要がある。国土地理院「300万分の1日本とその周辺」では等角写像として簡単な「正角緯度」(政春(2011)§8.3.3)ではなく、なぜか Gauss (1844) が用いられた。

回転楕円体上の緯度 φ, 経度 λ から球面上の緯度 ˆφ, 経度 ˆλ は次のように与えられる:

ˆλ=c(λλE)+λE

ˆφ=2tan1[tanπ2+φ2(1esinφ1+esinφ)e2]cπ2

c=1+e2cos4(φE)1e2

パラメタとして政春(2011)に従い次を用いると、 回転楕円体上の経緯度グリッド点が投影される球面上の点の経緯度は次表で与えられる。

回転につづく

Projection from spheroid to aposphere
lat/lon122E123E124E125E126E127E128E129E130E131E132E133E134E135E136E137E138E139E140E141E142E143E144E145E146E147E148E
46N(45.98, 121.93)(45.98, 122.93)(45.98, 123.94)(45.98, 124.94)(45.98, 125.95)(45.98, 126.95)(45.98, 127.96)(45.98, 128.96)(45.98, 129.97)(45.98, 130.97)(45.98, 131.98)(45.98, 132.98)(45.98, 133.99)(45.98, 134.99)(45.98, 136.00)(45.98, 137.00)(45.98, 138.00)(45.98, 139.01)(45.98, 140.01)(45.98, 141.02)(45.98, 142.02)(45.98, 143.03)(45.98, 144.03)(45.98, 145.04)(45.98, 146.04)(45.98, 147.05)(45.98, 148.05)
45N(44.98, 121.93)(44.98, 122.93)(44.98, 123.94)(44.98, 124.94)(44.98, 125.95)(44.98, 126.95)(44.98, 127.96)(44.98, 128.96)(44.98, 129.97)(44.98, 130.97)(44.98, 131.98)(44.98, 132.98)(44.98, 133.99)(44.98, 134.99)(44.98, 136.00)(44.98, 137.00)(44.98, 138.00)(44.98, 139.01)(44.98, 140.01)(44.98, 141.02)(44.98, 142.02)(44.98, 143.03)(44.98, 144.03)(44.98, 145.04)(44.98, 146.04)(44.98, 147.05)(44.98, 148.05)
44N(43.97, 121.93)(43.97, 122.93)(43.97, 123.94)(43.97, 124.94)(43.97, 125.95)(43.97, 126.95)(43.97, 127.96)(43.97, 128.96)(43.97, 129.97)(43.97, 130.97)(43.97, 131.98)(43.97, 132.98)(43.97, 133.99)(43.97, 134.99)(43.97, 136.00)(43.97, 137.00)(43.97, 138.00)(43.97, 139.01)(43.97, 140.01)(43.97, 141.02)(43.97, 142.02)(43.97, 143.03)(43.97, 144.03)(43.97, 145.04)(43.97, 146.04)(43.97, 147.05)(43.97, 148.05)
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42N(41.97, 121.93)(41.97, 122.93)(41.97, 123.94)(41.97, 124.94)(41.97, 125.95)(41.97, 126.95)(41.97, 127.96)(41.97, 128.96)(41.97, 129.97)(41.97, 130.97)(41.97, 131.98)(41.97, 132.98)(41.97, 133.99)(41.97, 134.99)(41.97, 136.00)(41.97, 137.00)(41.97, 138.00)(41.97, 139.01)(41.97, 140.01)(41.97, 141.02)(41.97, 142.02)(41.97, 143.03)(41.97, 144.03)(41.97, 145.04)(41.97, 146.04)(41.97, 147.05)(41.97, 148.05)
41N(40.97, 121.93)(40.97, 122.93)(40.97, 123.94)(40.97, 124.94)(40.97, 125.95)(40.97, 126.95)(40.97, 127.96)(40.97, 128.96)(40.97, 129.97)(40.97, 130.97)(40.97, 131.98)(40.97, 132.98)(40.97, 133.99)(40.97, 134.99)(40.97, 136.00)(40.97, 137.00)(40.97, 138.00)(40.97, 139.01)(40.97, 140.01)(40.97, 141.02)(40.97, 142.02)(40.97, 143.03)(40.97, 144.03)(40.97, 145.04)(40.97, 146.04)(40.97, 147.05)(40.97, 148.05)
40N(39.97, 121.93)(39.97, 122.93)(39.97, 123.94)(39.97, 124.94)(39.97, 125.95)(39.97, 126.95)(39.97, 127.96)(39.97, 128.96)(39.97, 129.97)(39.97, 130.97)(39.97, 131.98)(39.97, 132.98)(39.97, 133.99)(39.97, 134.99)(39.97, 136.00)(39.97, 137.00)(39.97, 138.00)(39.97, 139.01)(39.97, 140.01)(39.97, 141.02)(39.97, 142.02)(39.97, 143.03)(39.97, 144.03)(39.97, 145.04)(39.97, 146.04)(39.97, 147.05)(39.97, 148.05)
39N(38.97, 121.93)(38.97, 122.93)(38.97, 123.94)(38.97, 124.94)(38.97, 125.95)(38.97, 126.95)(38.97, 127.96)(38.97, 128.96)(38.97, 129.97)(38.97, 130.97)(38.97, 131.98)(38.97, 132.98)(38.97, 133.99)(38.97, 134.99)(38.97, 136.00)(38.97, 137.00)(38.97, 138.00)(38.97, 139.01)(38.97, 140.01)(38.97, 141.02)(38.97, 142.02)(38.97, 143.03)(38.97, 144.03)(38.97, 145.04)(38.97, 146.04)(38.97, 147.05)(38.97, 148.05)
38N(37.97, 121.93)(37.97, 122.93)(37.97, 123.94)(37.97, 124.94)(37.97, 125.95)(37.97, 126.95)(37.97, 127.96)(37.97, 128.96)(37.97, 129.97)(37.97, 130.97)(37.97, 131.98)(37.97, 132.98)(37.97, 133.99)(37.97, 134.99)(37.97, 136.00)(37.97, 137.00)(37.97, 138.00)(37.97, 139.01)(37.97, 140.01)(37.97, 141.02)(37.97, 142.02)(37.97, 143.03)(37.97, 144.03)(37.97, 145.04)(37.97, 146.04)(37.97, 147.05)(37.97, 148.05)
37N(36.97, 121.93)(36.97, 122.93)(36.97, 123.94)(36.97, 124.94)(36.97, 125.95)(36.97, 126.95)(36.97, 127.96)(36.97, 128.96)(36.97, 129.97)(36.97, 130.97)(36.97, 131.98)(36.97, 132.98)(36.97, 133.99)(36.97, 134.99)(36.97, 136.00)(36.97, 137.00)(36.97, 138.00)(36.97, 139.01)(36.97, 140.01)(36.97, 141.02)(36.97, 142.02)(36.97, 143.03)(36.97, 144.03)(36.97, 145.04)(36.97, 146.04)(36.97, 147.05)(36.97, 148.05)
36N(35.96, 121.93)(35.96, 122.93)(35.96, 123.94)(35.96, 124.94)(35.96, 125.95)(35.96, 126.95)(35.96, 127.96)(35.96, 128.96)(35.96, 129.97)(35.96, 130.97)(35.96, 131.98)(35.96, 132.98)(35.96, 133.99)(35.96, 134.99)(35.96, 136.00)(35.96, 137.00)(35.96, 138.00)(35.96, 139.01)(35.96, 140.01)(35.96, 141.02)(35.96, 142.02)(35.96, 143.03)(35.96, 144.03)(35.96, 145.04)(35.96, 146.04)(35.96, 147.05)(35.96, 148.05)
35N(34.96, 121.93)(34.96, 122.93)(34.96, 123.94)(34.96, 124.94)(34.96, 125.95)(34.96, 126.95)(34.96, 127.96)(34.96, 128.96)(34.96, 129.97)(34.96, 130.97)(34.96, 131.98)(34.96, 132.98)(34.96, 133.99)(34.96, 134.99)(34.96, 136.00)(34.96, 137.00)(34.96, 138.00)(34.96, 139.01)(34.96, 140.01)(34.96, 141.02)(34.96, 142.02)(34.96, 143.03)(34.96, 144.03)(34.96, 145.04)(34.96, 146.04)(34.96, 147.05)(34.96, 148.05)
34N(33.96, 121.93)(33.96, 122.93)(33.96, 123.94)(33.96, 124.94)(33.96, 125.95)(33.96, 126.95)(33.96, 127.96)(33.96, 128.96)(33.96, 129.97)(33.96, 130.97)(33.96, 131.98)(33.96, 132.98)(33.96, 133.99)(33.96, 134.99)(33.96, 136.00)(33.96, 137.00)(33.96, 138.00)(33.96, 139.01)(33.96, 140.01)(33.96, 141.02)(33.96, 142.02)(33.96, 143.03)(33.96, 144.03)(33.96, 145.04)(33.96, 146.04)(33.96, 147.05)(33.96, 148.05)
33N(32.96, 121.93)(32.96, 122.93)(32.96, 123.94)(32.96, 124.94)(32.96, 125.95)(32.96, 126.95)(32.96, 127.96)(32.96, 128.96)(32.96, 129.97)(32.96, 130.97)(32.96, 131.98)(32.96, 132.98)(32.96, 133.99)(32.96, 134.99)(32.96, 136.00)(32.96, 137.00)(32.96, 138.00)(32.96, 139.01)(32.96, 140.01)(32.96, 141.02)(32.96, 142.02)(32.96, 143.03)(32.96, 144.03)(32.96, 145.04)(32.96, 146.04)(32.96, 147.05)(32.96, 148.05)
32N(31.96, 121.93)(31.96, 122.93)(31.96, 123.94)(31.96, 124.94)(31.96, 125.95)(31.96, 126.95)(31.96, 127.96)(31.96, 128.96)(31.96, 129.97)(31.96, 130.97)(31.96, 131.98)(31.96, 132.98)(31.96, 133.99)(31.96, 134.99)(31.96, 136.00)(31.96, 137.00)(31.96, 138.00)(31.96, 139.01)(31.96, 140.01)(31.96, 141.02)(31.96, 142.02)(31.96, 143.03)(31.96, 144.03)(31.96, 145.04)(31.96, 146.04)(31.96, 147.05)(31.96, 148.05)
31N(30.96, 121.93)(30.96, 122.93)(30.96, 123.94)(30.96, 124.94)(30.96, 125.95)(30.96, 126.95)(30.96, 127.96)(30.96, 128.96)(30.96, 129.97)(30.96, 130.97)(30.96, 131.98)(30.96, 132.98)(30.96, 133.99)(30.96, 134.99)(30.96, 136.00)(30.96, 137.00)(30.96, 138.00)(30.96, 139.01)(30.96, 140.01)(30.96, 141.02)(30.96, 142.02)(30.96, 143.03)(30.96, 144.03)(30.96, 145.04)(30.96, 146.04)(30.96, 147.05)(30.96, 148.05)
30N(29.96, 121.93)(29.96, 122.93)(29.96, 123.94)(29.96, 124.94)(29.96, 125.95)(29.96, 126.95)(29.96, 127.96)(29.96, 128.96)(29.96, 129.97)(29.96, 130.97)(29.96, 131.98)(29.96, 132.98)(29.96, 133.99)(29.96, 134.99)(29.96, 136.00)(29.96, 137.00)(29.96, 138.00)(29.96, 139.01)(29.96, 140.01)(29.96, 141.02)(29.96, 142.02)(29.96, 143.03)(29.96, 144.03)(29.96, 145.04)(29.96, 146.04)(29.96, 147.05)(29.96, 148.05)
29N(28.96, 121.93)(28.96, 122.93)(28.96, 123.94)(28.96, 124.94)(28.96, 125.95)(28.96, 126.95)(28.96, 127.96)(28.96, 128.96)(28.96, 129.97)(28.96, 130.97)(28.96, 131.98)(28.96, 132.98)(28.96, 133.99)(28.96, 134.99)(28.96, 136.00)(28.96, 137.00)(28.96, 138.00)(28.96, 139.01)(28.96, 140.01)(28.96, 141.02)(28.96, 142.02)(28.96, 143.03)(28.96, 144.03)(28.96, 145.04)(28.96, 146.04)(28.96, 147.05)(28.96, 148.05)
28N(27.96, 121.93)(27.96, 122.93)(27.96, 123.94)(27.96, 124.94)(27.96, 125.95)(27.96, 126.95)(27.96, 127.96)(27.96, 128.96)(27.96, 129.97)(27.96, 130.97)(27.96, 131.98)(27.96, 132.98)(27.96, 133.99)(27.96, 134.99)(27.96, 136.00)(27.96, 137.00)(27.96, 138.00)(27.96, 139.01)(27.96, 140.01)(27.96, 141.02)(27.96, 142.02)(27.96, 143.03)(27.96, 144.03)(27.96, 145.04)(27.96, 146.04)(27.96, 147.05)(27.96, 148.05)
27N(26.96, 121.93)(26.96, 122.93)(26.96, 123.94)(26.96, 124.94)(26.96, 125.95)(26.96, 126.95)(26.96, 127.96)(26.96, 128.96)(26.96, 129.97)(26.96, 130.97)(26.96, 131.98)(26.96, 132.98)(26.96, 133.99)(26.96, 134.99)(26.96, 136.00)(26.96, 137.00)(26.96, 138.00)(26.96, 139.01)(26.96, 140.01)(26.96, 141.02)(26.96, 142.02)(26.96, 143.03)(26.96, 144.03)(26.96, 145.04)(26.96, 146.04)(26.96, 147.05)(26.96, 148.05)
26N(25.96, 121.93)(25.96, 122.93)(25.96, 123.94)(25.96, 124.94)(25.96, 125.95)(25.96, 126.95)(25.96, 127.96)(25.96, 128.96)(25.96, 129.97)(25.96, 130.97)(25.96, 131.98)(25.96, 132.98)(25.96, 133.99)(25.96, 134.99)(25.96, 136.00)(25.96, 137.00)(25.96, 138.00)(25.96, 139.01)(25.96, 140.01)(25.96, 141.02)(25.96, 142.02)(25.96, 143.03)(25.96, 144.03)(25.96, 145.04)(25.96, 146.04)(25.96, 147.05)(25.96, 148.05)
25N(24.96, 121.93)(24.96, 122.93)(24.96, 123.94)(24.96, 124.94)(24.96, 125.95)(24.96, 126.95)(24.96, 127.96)(24.96, 128.96)(24.96, 129.97)(24.96, 130.97)(24.96, 131.98)(24.96, 132.98)(24.96, 133.99)(24.96, 134.99)(24.96, 136.00)(24.96, 137.00)(24.96, 138.00)(24.96, 139.01)(24.96, 140.01)(24.96, 141.02)(24.96, 142.02)(24.96, 143.03)(24.96, 144.03)(24.96, 145.04)(24.96, 146.04)(24.96, 147.05)(24.96, 148.05)
24N(23.96, 121.93)(23.96, 122.93)(23.96, 123.94)(23.96, 124.94)(23.96, 125.95)(23.96, 126.95)(23.96, 127.96)(23.96, 128.96)(23.96, 129.97)(23.96, 130.97)(23.96, 131.98)(23.96, 132.98)(23.96, 133.99)(23.96, 134.99)(23.96, 136.00)(23.96, 137.00)(23.96, 138.00)(23.96, 139.01)(23.96, 140.01)(23.96, 141.02)(23.96, 142.02)(23.96, 143.03)(23.96, 144.03)(23.96, 145.04)(23.96, 146.04)(23.96, 147.05)(23.96, 148.05)
23N(22.96, 121.93)(22.96, 122.93)(22.96, 123.94)(22.96, 124.94)(22.96, 125.95)(22.96, 126.95)(22.96, 127.96)(22.96, 128.96)(22.96, 129.97)(22.96, 130.97)(22.96, 131.98)(22.96, 132.98)(22.96, 133.99)(22.96, 134.99)(22.96, 136.00)(22.96, 137.00)(22.96, 138.00)(22.96, 139.01)(22.96, 140.01)(22.96, 141.02)(22.96, 142.02)(22.96, 143.03)(22.96, 144.03)(22.96, 145.04)(22.96, 146.04)(22.96, 147.05)(22.96, 148.05)
22N(21.97, 121.93)(21.97, 122.93)(21.97, 123.94)(21.97, 124.94)(21.97, 125.95)(21.97, 126.95)(21.97, 127.96)(21.97, 128.96)(21.97, 129.97)(21.97, 130.97)(21.97, 131.98)(21.97, 132.98)(21.97, 133.99)(21.97, 134.99)(21.97, 136.00)(21.97, 137.00)(21.97, 138.00)(21.97, 139.01)(21.97, 140.01)(21.97, 141.02)(21.97, 142.02)(21.97, 143.03)(21.97, 144.03)(21.97, 145.04)(21.97, 146.04)(21.97, 147.05)(21.97, 148.05)

c = 1.004729

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