r = 3.5 drawR = r * 1.04 O = (0, 0, 0) globe = Sphere(O, r) latStep = 15 lonStep = 15 latMax = 75 latitudeCoords = Sequence(Sequence((lambda, phi), lambda, -180, 180, 10), phi, -latMax, latMax, latStep) longitudeCoords = Sequence(Sequence((lambda, phi), phi, -90, 90, 10), lambda, -180, 165, lonStep) latitudeLines = Zip(Polyline(Zip(GeoPoint(C, drawR), C, coords)), coords, latitudeCoords) longitudeLines = Zip(Polyline(Zip(GeoPoint(C, drawR), C, coords)), coords, longitudeCoords) equator = Polyline(Zip(GeoPoint(C, drawR), C, Sequence((lambda, 0), lambda, -180, 180, 5))) 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 = Point(globe) Q = Point(globe) Pdraw = (drawR / r) * P Qdraw = (drawR / r) * Q theta = Angle(P, O, Q) greatCirclePath = CircularArc(O, Pdraw, Qdraw) 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)) coastCoords = {{(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), (78.4826, 72.395), (76.0324, 71.9104), (75.7336, 71.2659), (75.5032, 71.6546), (75.6035, 72.5811), (73.0862, 71.4449), (73.5781, 69.803), (77.6507, 68.903), (77.5883, 67.7519), (77.2385, 68.4696), (75.1246, 68.8617), (72.0676, 66.2533), (71.5396, 66.6831), (73.0668, 67.7669), (72.7045, 70.9632), (72.8121, 72.6914), (68.2692, 71.6828), (66.7022, 70.8185), (67.6241, 69.5844), (68.5042, 68.3484), (60.1706, 69.5909), (59.896, 68.7063), (59.3705, 68.7384), (55.4181, 68.5678), (53.2605, 68.2675), (54.4912, 68.9923), (52.7227, 68.484), (48.7543, 67.8959), (47.8747, 67.5842), (44.9021, 67.4131), (43.3332, 68.6734), (43.7824, 67.2545), (42.2105, 66.5197), (39.758, 64.5771), (38.0622, 64.091), (35.0354, 64.4402), (31.8953, 67.1614), (41.3588, 67.2097), (33.6844, 69.3103), (33.4543, 69.4282), (33.0078, 69.7221), (29.6946, 69.7446), (30.9606, 70.3438), (28.2718, 70.668), (28.1417, 71.043), (26.5851, 70.41), (26.5069, 70.9128), (24.658, 71.001), (21.3558, 70.2334), (20.6221, 69.9139), (20.3242, 69.9453), (19.1973, 69.7479), (18.2598, 69.4706), (16.5144, 68.5326), (16.3123, 67.8814), (15.6915, 67.5214), (14.4417, 67.2714), (13.6516, 66.9071), (13.1188, 66.2307), (13.0331, 65.9562), (12.9155, 65.3393), (11.6329, 64.8139), (11.4576, 64.003), (8.3607, 63.4989), (8.158, 63.1615), (6.735, 62.7207), (6.1361, 62.4075), (5.1432, 62.1599), (5.3387, 61.4855), (7.1735, 61.166), (7.0387, 60.9529), (5.1158, 60.636), (5.6886, 60.1232), (6.1533, 60.3462), (5.7305, 59.8631), (5.1732, 59.1625), (6.3633, 59.0009), (6.7314, 58.0683), (9.5572, 59.1127), (10.8345, 59.1839), (11.2482, 58.3691), (12.4712, 56.2905), (12.8858, 55.4114), (15.8267, 56.125), (16.9238, 58.4926), (18.2854, 59.1094), (18.9705, 59.7572), (17.1308, 61.5757), (20.7627, 63.8678), (21.1382, 64.8087), (22.401, 65.8621), (25.3727, 65.0095), (22.3197, 63.3104), (21.606, 61.5916), (22.4627, 60.0292), (23.0213, 59.816), (26.5347, 60.4129), (30.1568, 59.9043), (25.5093, 59.639), (24.5291, 58.3542), (23.6478, 56.971), (21.0314, 56.6366), (21.1148, 55.6165), (18.0856, 54.8358), (14.5835, 53.6394), (10.8546, 54.0098), (10.0222, 54.6739), (9.5911, 55.4932), (10.61, 57.7369), (9.1104, 57.0437), (8.164, 56.6069), (8.9572, 54.5383), (8.6189, 53.875), (7.2064, 53.6545), (5.532, 53.2687), (4.2741, 51.4716), (1.7677, 50.9357), (0.4169, 49.4484), (-1.2586, 49.6802), (-2.6923, 48.5368), (-4.2414, 48.3037), (-4.3121, 47.8229), (-2.0925, 46.865), (-0.5485, 45.0006), (-1.9913, 43.3451), (-9.1781, 43.174), (-9.4797, 38.7988), (-8.6683, 38.4243), (-8.9978, 37.0323), (-6.3841, 36.637), (-2.1115, 36.7767), (-0.5208, 38.3173), (-0.327, 39.5199), (3.248, 41.9442), (4.0526, 43.5931), (10.1881, 43.9475), (11.1412, 42.3899), (15.6458, 38.0342), (17.1746, 38.9981), (16.5219, 39.7476), (18.3438, 39.8214), (16.1646, 41.8962), (12.3963, 44.2239), (12.5234, 44.968), (13.7833, 45.6272), (14.5505, 45.2977), (15.1858, 44.1721), (17.7236, 42.8507), (19.3223, 40.4071), (20.7686, 38.8744), (22.4217, 38.4385), (21.8247, 38.3281), (21.7381, 36.8632), (22.4895, 36.4469), (22.7254, 37.5421), (24.0623, 37.7745), (23.0667, 39.0379), (23.3277, 39.1749), (22.9223, 40.5909), (23.9471, 39.9656), (23.7628, 40.7478), (26.7921, 40.6266), (28.9563, 41.0082), (27.4848, 42.4681), (28.5618, 43.5013), (29.6284, 45.7225), (31.8729, 46.6498), (32.578, 46.6156), (32.0085, 46.43), (32.508, 45.4038), (33.91, 44.3876), (36.3934, 45.0654), (35.0229, 45.701), (35.0146, 46.106), (39.2707, 47.0441), (37.7665, 46.6361), (37.6472, 45.3772), (41.4194, 42.7376), (38.3811, 40.9245), (35.0064, 42.0633), (29.1481, 41.221), (28.7879, 40.534), (26.7381, 40.4002), (26.8992, 39.5497), (26.7637, 38.7096), (26.4413, 38.6412), (27.2324, 37.9787), (27.263, 36.9766), (28.9696, 36.7153), (30.4461, 36.2699), (32.7948, 36.0359), (35.3932, 36.5752), (35.9779, 34.5474), (33.6665, 31.1304), (32.136, 31.3411), (29.0721, 30.8303), (24.8785, 31.9843), (23.0906, 32.6187), (20.0132, 30.8007), (15.706, 31.4264), (13.2835, 32.9146), (10.0648, 34.2116), (11.1267, 36.8741), (10.1964, 37.2059), (7.9104, 36.8563), (3.779, 36.8962), (-2.8399, 35.1278), (-4.6283, 35.2064), (-6.901, 33.969), (-9.8087, 31.4246), (-11.5527, 28.3101), (-13.5758, 26.7351), (-15.8993, 23.8444), (-16.8761, 21.0861), (-16.085, 18.5212), (-16.5708, 15.7344), (-16.4405, 13.3532), (-16.768, 12.6284), (-16.7849, 12.4725), (-15.5002, 11.7784), (-15.3931, 11.2172), (-13.0595, 8.8812), (-12.8941, 8.6298), (-12.4856, 7.3863), (-5.0618, 5.1307), (-3.3476, 5.1307), (-3.2464, 5.1141), (3.717, 6.5979), (5.4566, 5.6117), (5.5497, 5.4742), (6.8604, 4.3733), (7.0766, 4.7162), (8.2527, 4.924), (9.6889, 4.0564), (9.618, 0.5765), (9.3549, 0.3436), (8.7031, -0.591), (9.6246, -2.3671), (13.0682, -5.8648), (12.9985, -9.048), (13.6855, -12.1238), (11.7759, -18.0018), (15.2876, -27.275), (18.2108, -31.7425), (18.433, -33.7173), (18.8313, -34.3641), (25.5742, -34.0354), (29.9712, -31.3221), (32.9549, -26.0836), (32.7922, -25.6443), (35.4381, -24.1712), (35.3157, -22.3969), (36.4037, -18.7697), (40.559, -15.4734), (40.4368, -12.9831), (39.304, -8.4438), (39.2281, -4.6655), (43.7176, 0.8579), (47.9753, 4.497), (51.3902, 10.4226), (50.7923, 11.9837), (47.405, 11.174), (43.1617, 11.566), (43.3535, 12.367), (39.7855, 15.1249), (38.574, 18.0729), (36.8704, 22.0158), (35.7839, 23.9378), (33.5471, 27.8981), (33.2478, 28.5677), (34.625, 28.0645), (38.4642, 23.7119), (39.2761, 20.974), (42.2939, 17.435), (43.2319, 13.2671), (48.6684, 14.0501), (52.2175, 15.6555), (55.4791, 17.8433), (57.8116, 19.0171), (58.1694, 20.5895), (58.773, 23.5172), (56.4131, 26.3512), (51.3099, 24.3404), (51.2623, 26.1533), (50.0811, 25.9614), (48.0515, 29.3554), (48.1435, 29.5725), (49.002, 30.5065), (51.5891, 27.8642), (57.3346, 25.7916), (61.4122, 25.1021), (66.4286, 25.5753), (68.235, 23.597), (68.8171, 23.0537), (70.4893, 23.0895), (70.4851, 20.8402), (72.1828, 22.2697), (72.5431, 21.6966), (72.8937, 20.6728), (72.803, 19.0793), (76.5534, 8.9028), (78.0602, 8.3846), (78.9399, 9.5658), (79.6932, 11.3125), (80.0621, 13.6062), (80.2935, 15.7107), (82.2588, 16.5599), (85.4416, 19.6266), (86.2162, 19.8958), (87.9484, 21.8254), (88.1221, 21.6358), (88.745, 21.5844), (89.0515, 22.0932), (89.5686, 21.7674), (90.6161, 22.3622), (90.2691, 23.4559), (91.4801, 22.8848), (92.8283, 20.1776), (93.707, 19.9122), (93.4931, 19.3695), (94.589, 17.5693), (94.6615, 15.9044), (95.177, 15.8257), (96.3243, 16.4444), (96.7654, 16.7104), (97.726, 16.5686), (98.576, 13.1619), (98.4649, 10.6758), (98.3055, 8.2262), (100.119, 6.442), (103.48, 1.3295), (103.439, 2.9331), (100.424, 7.1878), (99.2539, 9.2652), (100.017, 13.3532), (101.724, 12.6894), (103.532, 11.1467), (104.262, 10.5413), (105.114, 8.6292), (106.573, 9.6411), (106.596, 9.8599), (107.007, 10.6605), (109.219, 12.6458), (106.371, 17.7469), (105.622, 18.9663), (108.594, 21.901), (109.931, 21.4806), (109.939, 20.2951), (110.154, 20.9446), (113.52, 23.1021), (116.471, 22.9459), (117.368, 23.5886), (118.657, 24.6214), (119.623, 25.3912), (119.881, 26.3342), (120.087, 26.6716), (121.448, 29.1313), (121.506, 29.4846), (121.258, 30.3041), (120.716, 31.9837), (121.856, 31.8165), (119.165, 34.8488), (120.183, 36.2024), (122.341, 36.8322), (119.287, 37.1383), (118.94, 38.0428), (118.977, 39.1826), (122.264, 40.5002), (121.164, 38.7316), (124.638, 39.6151), (125.555, 38.6862), (124.989, 37.9314), (126.634, 37.7818), (126.16, 36.7719), (126.291, 35.1542), (127.325, 34.4633), (129.214, 35.1818), (128.329, 38.6809), (129.709, 40.8573), (132.31, 43.3135), (133.16, 42.697), (140.625, 50.0824), (140.84, 53.0879), (139.796, 54.2564), (138.25, 53.524), (137.835, 53.9467), (136.719, 53.8041), (135.852, 54.5839), (145.555, 59.4135), (148.727, 59.2579), (149.643, 59.7704), (151.121, 59.0825), (154.15, 59.5285), (160.309, 61.8944), (160.379, 61.0255), (163.085, 61.5706), (164.207, 62.2922), (158.275, 58.009), (156.849, 57.2902), (156.748, 50.9693), (158.472, 53.0324), (159.844, 53.7836), (161.724, 55.4961), (163.038, 56.5219), (163.335, 56.2325), (163.226, 57.7904), (161.96, 58.0769), (164.44, 60.0727), (166.273, 59.8563), (168.463, 60.5922), (170.608, 60.4349), (177.024, 62.7772), (179.571, 62.7735), (178.23, 64.3644), (176.141, 64.5858), (174.549, 64.6839), (176.341, 65.0473), (180, 65.0672)}, {(-136.444, 68.8951), (-151.769, 70.5602), (-152.3, 70.8468), (-155.974, 70.842), (-157.909, 70.8601), (-159.387, 70.5245), (-160.117, 70.5912), (-163.536, 69.1701), (-166.786, 68.3596), (-163.532, 67.1026), (-160.232, 66.4203), (-162.607, 66.8944), (-164.034, 66.2155), (-164.46, 66.5884), (-166.928, 65.1571), (-163.204, 64.652), (-161.759, 64.8163), (-160.988, 64.2513), (-163.288, 63.0464), (-164.758, 62.4967), (-166.168, 61.6508), (-165.115, 60.9328), (-163.421, 60.7574), (-164.805, 60.892), (-162.571, 59.9897), (-162.421, 60.284), (-161.644, 59.1097), (-160.363, 59.0512), (-158.081, 58.9774), (-156.809, 59.1343), (-157.194, 58.1942), (-160.302, 56.3141), (-161.697, 55.9072), (-162.63, 55.2467), (-161.517, 55.6184), (-158.414, 56.4358), (-153.438, 58.7548), (-152.66, 59.9972), (-149.329, 61.4974), (-150.441, 61.0236), (-151.047, 59.7718), (-150.935, 59.2491), (-147.964, 60.4849), (-148.556, 60.827), (-147.991, 60.9483), (-146.571, 60.7291), (-144.691, 60.6691), (-141.409, 60.1177), (-139.431, 60.0123), (-139.512, 59.9536), (-136.061, 58.4527), (-136.226, 58.7655), (-136.043, 58.8216), (-135.364, 59.4194), (-133.877, 58.5182), (-133.194, 57.8777), (-133.649, 57.6423), (-132.119, 55.5698), (-130.748, 55.318), (-130.037, 55.2979), (-129.795, 55.5596), (-129.626, 54.2303), (-129.564, 53.2515), (-128.675, 53.5546), (-129.172, 53.5336), (-128.053, 52.9107), (-128.358, 52.1589), (-127.194, 52.4577), (-127.795, 52.191), (-127.669, 51.4776), (-127.708, 51.1512), (-126.514, 50.6794), (-126.448, 50.5877), (-124.86, 50.8724), (-124.142, 49.7927), (-123.582, 49.6812), (-123.948, 49.5347), (-123.277, 49.3439), (-122.545, 48.7623), (-122.242, 48.0107), (-122.578, 47.2932), (-122.657, 47.8812), (-124.139, 46.9547), (-124.112, 46.8627), (-123.221, 46.1536), (-124.54, 42.8129), (-124.356, 40.3711), (-122.999, 37.9886), (-122.07, 37.4783), (-121.807, 36.8512), (-120.659, 35.1224), (-117.467, 33.2955), (-114.266, 27.9345), (-114.993, 27.736), (-112.377, 26.2139), (-110.006, 22.894), (-110.367, 24.1005), (-111.57, 26.7076), (-114.55, 30.0223), (-113.058, 30.651), (-109.276, 26.5339), (-109.029, 25.4805), (-107.951, 24.6149), (-105.792, 22.6275), (-105.511, 20.8087), (-105.482, 19.9761), (-100.848, 17.2005), (-94.7994, 16.2097), (-94.3742, 16.2848), (-87.4891, 13.3529), (-85.7452, 11.0886), (-85.0771, 9.602), (-83.7369, 9.1503), (-83.2858, 8.6644), (-82.6795, 8.322), (-81.0639, 7.8998), (-80.459, 8.2139), (-78.1419, 8.3861), (-77.3688, 6.5756), (-77.2863, 4.7217), (-77.8136, 2.7164), (-78.5769, 1.7738), (-80.0883, 0.7848), (-80.2824, -0.6205), (-80.2847, -2.7067), (-79.9256, -2.5485), (-81.3366, 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73.6473), (-106.95, 73.5104), (-105.339, 72.9149), (-104.583, 73.3539), (-104.835, 73.6473)}, {(-180, 71.5377), (-178.439, 71.5412), (-177.499, 71.2191), (-180, 70.993)}, {(106.366, -2.4648), (105.91, -1.505), (105.138, -1.9727), (105.786, -2.1813), (105.999, -2.8249), (106.667, -3.0718), (106.819, -2.5733), (106.366, -2.4648)}, {(123.511, 10.923), (122.983, 10.8866), (122.856, 10.0869), (122.4, 9.823), (122.995, 9.0588), (123.32, 9.2729), (123.162, 9.8643), (123.511, 10.923)}, {(-102.58, 75.7802), (-102.008, 75.9394), (-102.728, 76.307), (-104.406, 76.1085), (-102.58, 75.7802)}, {(-134.1, 57.3001), (-133.937, 57.5816), (-134.307, 58.0344), (-133.827, 57.6176), (-133.965, 57.8738), (-134.923, 58.3546), (-134.487, 57.482), (-134.591, 57.092), (-134.1, 57.3001)}, {(-30.9851, -79.8185), (-32.0003, -79.7324), (-29.6145, -79.9096), (-30.9851, -79.8185)}, {(-66.7852, -79.608), (-67.8087, -79.5459), (-66.3195, -80.0751), (-65.5044, -79.9543), (-66.7852, -79.608)}, {(-35.8953, -54.5548), 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55.8068), (-79.1821, 56.2122), (-79.1755, 55.8851), (-78.9632, 56.4217), (-79.2724, 56.6004), (-79.5363, 56.1801), (-79.4589, 56.5397), (-80.0008, 55.9321), (-79.4947, 56.115), (-79.7647, 55.8068)}, {(-68.9014, -67.7442), (-67.9885, -67.4744), (-68.2351, -67.372), (-67.6878, -67.1474), (-67.9684, -67.0322), (-67.7111, -66.633), (-69.0824, -67.4031), (-68.9014, -67.7442)}, {(148.812, 45.51), (147.924, 45.3833), (146.898, 44.4043), (148.812, 45.51)}, {(-74.1144, -43.3579), (-73.4363, -42.9365), (-73.7893, -42.5857), (-73.4708, -42.4663), (-73.5278, -41.8963), (-74.063, -41.8228), (-74.3874, -43.2316), (-74.1144, -43.3579)}, {(12.073, 54.9768), (12.5787, 56.0641), (10.9789, 55.7215), (11.8623, 54.7726), (12.073, 54.9768)}, {(49.2252, 69.5112), (48.4139, 69.3457), (48.3159, 68.9424), (48.9104, 68.7431), (50.283, 69.0889), (49.2252, 69.5112)}, {(60.3926, 69.9624), (59.048, 70.4605), (58.473, 70.2668), (59.7246, 69.7062), (60.4402, 69.7259), (60.3926, 69.9624)}, {(-57.7918, -51.6361), (-58.9175, -51.2721), (-59.6487, -52.1344), (-59.3957, -52.308), (-57.7918, -51.6361)}, {(-162.798, -82.8648), (-163.796, -82.8427), (-161.635, -83.027), (-162.798, -82.8648)}, {(-72.1019, 41.015), (-74.032, 40.6387), (-71.9032, 41.0607), (-72.1019, 41.015)}, {(-82.7064, 62.9445), (-83.3764, 62.9049), (-83.9031, 62.4025), (-83.0158, 62.2099), (-81.9486, 62.884), (-82.7064, 62.9445)}, {(123.103, 11.5415), (121.916, 11.8543), (121.954, 10.4444), (122.77, 10.8238), (123.103, 11.5415)}, {(180, -16.1529), (178.498, -16.7879), (179.928, -16.7444), (179.93, -16.5194), (179.564, -16.6369), (179.999, -16.1686)}, {(31.4819, 80.1079), (33.6293, 80.2174), (31.4819, 80.1079)}, {(120.7, -9.9031), (119.942, -9.3015), (118.959, -9.5193), (120.439, -10.294), (120.804, -10.1085), (120.7, -9.9031)}, {(93.016, 13.3362), (93.0623, 13.5455), (92.5339, 11.8734), (92.7008, 11.5125), (93.016, 13.3362)}, {(-131.116, 52.2191), (-131.972, 52.8798), (-131.635, 52.9222), (-131.754, 53.1956), (-132.547, 53.1375), (-131.116, 52.2191)}, {(124.052, 11.0288), (124.039, 11.2735), (123.332, 9.4229), (124.005, 10.4001), (124.052, 11.0288)}, {(-134.885, 57.2417), (-135.449, 57.5344), (-135.812, 57.0095), (-135.455, 57.2494), (-134.682, 56.2162), (-134.885, 57.2417)}, {(-72.4705, -54.0277), (-72.2054, -53.8074), (-72.4823, -53.5881), (-73.8455, -53.5458), (-73.2106, -53.9858), (-72.7638, -53.8648), (-72.9073, -54.1146), (-72.4705, -54.0277)}, {(-20.6003, -74.1969), (-20.5802, -73.6192), (-22.0354, -74.1065), (-20.489, -74.4927), (-20.6003, -74.1969)}} coastlines = Zip(Polyline(Zip(GeoPoint(C, drawR), C, coords)), coords, coastCoords)