Index 713
right metric tensor, 7
rotation matrix, 8
rotationally symmetric figure, 307
Sanson–Flamsteed projection, 295, 569
scale difference
– canonical form, 31
scale ratio, 11
simultaneous diagonalization, 11
– of two symmetric matrices, 2
singular value decomposition, 8, 9
sinusoidal pseudo-cylindrical mapping, 293, 295
Soldner coordinates, 416, 417, 433, 437–440, 445, 451
Soldner map, 416, 437
special Kepler equation, 296
spherical isometric latitude, 55, 264
spherical side cosine lemma, 129
spherical sine lemma, 129
Stab–Werner mapping, 395, 398, 399, 402
standard series inversion, 416
star orientation, 248
– antipolar, 248
stereographic projection, 70, 543, 552
stretch, 1, 8, 11, 80, 88, 90
– principal, 14, 15, 43, 74, 76, 80, 82, 92
strip transformation, 346, 354
tangent plane, 70
tangent space, 4, 6, 18, 24, 31, 37
tangent vector, 80, 82, 87, 88
Taylor expansion, 426, 427, 429
Taylor series, see Taylor expansion
Tissot circle, 18
Tissot ellipse, 13, 18, 19, 403
Tissot indicatrix, 395, 403, 584, 616
Tissot portrait, 11
torus, 92, 309, 310
torus mapping, 301
transverse frame of reference, 136, 138
transverse Lambert cylindrical equal area projection,
286
transverse Lambert projection, 213, 285, 287
transverse Mercator projection, 285–287, 313, 325,
333, 334, 344
transverse Plate Carr´ ee projection, 285, 286
transverse Postel projection, 210
transverse stereographic projection, 211
triad, 248
triaxial ellipsoid, 655
Tychonov regularization, 453
Universal Lambert Projection, 543, 553
Universal Mercator Projection (UMP), 53, 55, 313,
317, 325, 361, 490, 623
Universal Polar Stereographic Projection (UPS), 53,
62, 161, 168, 318, 360, 361, 551
– sphere, 62
Universal Polycylindric Projection (UPC), 623, 630
Universal Transverse Mercator Projection (UTM),
113, 285, 330, 331, 333, 341, 346, 553, 557, 623
UTM conformal mapping, 325
UTM coordinates, 342, 469
UTM reference frame, 315
UTM strip, 415
variance–covariance matrix, 453, 467
vertical coordinate mean, 574, 575
weight coefficients, 574, 576
Weitzenb¨ ock space, 469
Wiechel polar pseudo-azimuthal projection, 205
World Geodetic Datum 2000, 222, 485, 489
World Geodetic System (WGS 84), 469, 490
Zund equations, 53, 528
– three-dimensional conformal mapping, 102, 103
– two-dimensional conformal diffeomorphism, 104
zweite geod¨ atische Hauptaufgabe, 565
right metric tensor, 7
rotation matrix, 8
rotationally symmetric figure, 307
Sanson–Flamsteed projection, 295, 569
scale difference
– canonical form, 31
scale ratio, 11
simultaneous diagonalization, 11
– of two symmetric matrices, 2
singular value decomposition, 8, 9
sinusoidal pseudo-cylindrical mapping, 293, 295
Soldner coordinates, 416, 417, 433, 437–440, 445, 451
Soldner map, 416, 437
special Kepler equation, 296
spherical isometric latitude, 55, 264
spherical side cosine lemma, 129
spherical sine lemma, 129
Stab–Werner mapping, 395, 398, 399, 402
standard series inversion, 416
star orientation, 248
– antipolar, 248
stereographic projection, 70, 543, 552
stretch, 1, 8, 11, 80, 88, 90
– principal, 14, 15, 43, 74, 76, 80, 82, 92
strip transformation, 346, 354
tangent plane, 70
tangent space, 4, 6, 18, 24, 31, 37
tangent vector, 80, 82, 87, 88
Taylor expansion, 426, 427, 429
Taylor series, see Taylor expansion
Tissot circle, 18
Tissot ellipse, 13, 18, 19, 403
Tissot indicatrix, 395, 403, 584, 616
Tissot portrait, 11
torus, 92, 309, 310
torus mapping, 301
transverse frame of reference, 136, 138
transverse Lambert cylindrical equal area projection,
286
transverse Lambert projection, 213, 285, 287
transverse Mercator projection, 285–287, 313, 325,
333, 334, 344
transverse Plate Carr´ ee projection, 285, 286
transverse Postel projection, 210
transverse stereographic projection, 211
triad, 248
triaxial ellipsoid, 655
Tychonov regularization, 453
Universal Lambert Projection, 543, 553
Universal Mercator Projection (UMP), 53, 55, 313,
317, 325, 361, 490, 623
Universal Polar Stereographic Projection (UPS), 53,
62, 161, 168, 318, 360, 361, 551
– sphere, 62
Universal Polycylindric Projection (UPC), 623, 630
Universal Transverse Mercator Projection (UTM),
113, 285, 330, 331, 333, 341, 346, 553, 557, 623
UTM conformal mapping, 325
UTM coordinates, 342, 469
UTM reference frame, 315
UTM strip, 415
variance–covariance matrix, 453, 467
vertical coordinate mean, 574, 575
weight coefficients, 574, 576
Weitzenb¨ ock space, 469
Wiechel polar pseudo-azimuthal projection, 205
World Geodetic Datum 2000, 222, 485, 489
World Geodetic System (WGS 84), 469, 490
Zund equations, 53, 528
– three-dimensional conformal mapping, 102, 103
– two-dimensional conformal diffeomorphism, 104
zweite geod¨ atische Hauptaufgabe, 565
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