3D Earth globe with Natural Earth coastline
Author: Codex
Date: 2026-05-31

地球儀半徑；其他物件由此半徑推導

線條繪製半徑，略大於球面半徑以避免被球面遮住

地球球心，所有球面物件的共同中心

半透明海藍色球面，代表地球表面

緯線間距角度

經線間距角度

最高緯線角度，避免與極點重疊

緯線經緯度座標列表；每條緯線是一個子列表

經線經緯度座標列表；每條經線是一個子列表

本初子午線參考線

180 度子午線參考線

北極點

南極點

球面上的第一個自由點；可沿球面拖曳

球面上的第二個自由點；可沿球面拖曳

P 外推到線條繪製半徑的位置，用來讓大圓弧顯示在球面外側

Q 外推到線條繪製半徑的位置，用來讓大圓弧顯示在球面外側

P、O、Q 形成的球心角，使用 GeoGebra 原生 Angle 指令

P、Q 之間沿球面的最短路徑長度

向北極方向延伸的地軸參考線

向南極方向延伸的地軸參考線

Natural Earth 50m 所有海岸線經緯度資料；list of list，共 152 條線

由 coastCoords 一次生成的全部球面海岸線 polyline list

P、Q 之間的球面最短路徑，使用 CircularArc(O, P, Q)

赤道，地球儀主要參考線

每 15 度一條的緯線組；以 Polyline 繪製避免 3D Curve list 不渲染

每 15 度一條的經線組；以 Polyline 繪製避免 3D Curve list 不渲染

地球平均半徑約 6371 km

r: 3.5
lift = 1.01 (slider from 0.5 to 1.5, step 0.01)
drawR: (r * lift)
O: (0, 0, 0)
globe = Sphere(O, r)
Step_{lat}: 15
Step_{lon}: 15
latMax: 75
Coords_{latitude} = Sequence(Sequence[(lambda, phi), lambda, -180, 180, 10], phi, (-latMax), latMax, Step_{lat})
Coords_{longitude} = Sequence(Sequence[(lambda, phi), phi, -90, 90, 10], lambda, -180, 165, Step_{lon})
primeMeridian = PolyLine(Zip[GeoPoint[C, drawR], C, Sequence[(0, phi), phi, -90, 90, 5]])
dateMeridian = PolyLine(Zip[GeoPoint[C, drawR], C, Sequence[(180, phi), phi, -90, 90, 5]])
northPole: (0, 0, r)
southPole: (0, 0, (-r))
P = PointIn(globe)
Q = PointIn(globe)
Pdraw: (drawR / r * P)
Qdraw: (drawR / r * Q)
theta = Angle(P, O, Q)
d_{PQ}: (r * theta)
routeLabel = Text("球面最短路徑長度  d_{PQ} = " + d_{PQ}, ((-(r + 1.2)), (-(r + 1.1)), r + 0.2))
northAxis = Segment(O, (0, 0, r + 0.8))
southAxis = Segment(O, (0, 0, (-r) - 0.8))
Coords_{coast}: {{(180, 68.9834), (170.161, 69.6266), (170.538, 68.8254), (166.82, 69.4996), (161.566, 68.9052), (160.911, 69.6063), (159.912, 70.5061), (152.509, 70.8345), (150.668, 71.4552), (150.017, 71.8957), (145.189, 71.6958), (145.759, 72.2259), (146.832, 72.2954), (144.169, 72.2588), (141.079, 72.5869), (139.359, 71.9514), (137.918, 71.3841), (137.94, 71.1334), (132.654, 71.926), (128.843, 71.6635), (129.21, 71.9169), (129.284, 72.092), (129.25, 72.7052), (124.541, 73.7513), (123.622, 73.1933), (118.43, 73.2465), (114.061, 73.5847), (113.886, 73.3458), (113.128, 72.8307), (112.147, 73.7089), (110.261, 74.0174), (110.868, 73.7307), (112.925, 75.015), (113.486, 75.564), (106.414, 76.5123), (104.202, 77.1018), (100.906, 76.9007), (98.8057, 76.4807), (99.5407, 75.7986), (96.4971, 75.8912), (94.1563, 75.9592), (85.791, 74.6451), (86.0014, 74.316), (86.6771, 73.1068), (80.5832, 73.5685), (80.8416, 72.9492), (83.1513, 71.1036), (82.6823, 70.2177), (82.2212, 70.3957), (82.3229, 71.26), 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-68.4977), (-62.9333, -68.4426), (-63.7734, -68.6318), (-61.9611, 
(the line above was cut: it had 78111 characters; the first 20000 are kept)
Lines_{coast} = Zip(PolyLine[Zip[GeoPoint[C, drawR], C, coords]], coords, Coords_{coast})
greatCirclePath = CircleArc(O, P, Q)
equator = PolyLine(Zip[GeoPoint[C, r], C, Sequence[(lambda, 0), lambda, -180, 180, 5]])
Lines_{latitude} = Zip(PolyLine[Zip[GeoPoint[C, r], C, coords]], coords, Coords_{latitude})
Lines_{longitude} = Zip(PolyLine[Zip[GeoPoint[C, r], C, coords]], coords, Coords_{longitude})
R_{earth}: 6371
distance_{PQ}: (R_{earth} * theta)
text2: "\text{PQ 最短距離} = " + (LaTeX[distance_{PQ} / rad]) + "  \; \text{km}"

Tool: GeoPoint
GeoPoint(<LongitudeLatitudePoint>,<Radius>)
Input: C, drawR
Output: G

輸入點；x 為經度、y 為緯度

輸入半徑

輸出的球面 3D 點

C: (120, 23)
drawR: 3.5
G: (((drawR * cos((y(C) * pi / 180))) * cos((x(C) * pi / 180))), ((drawR * cos((y(C) * pi / 180))) * sin((x(C) * pi / 180))), (drawR * sin((y(C) * pi / 180))))