712 Index
Mercator projection, 276, 277, 313, 315, 335, 357,
359, 360, 362, 369
– optimal, 623, 624
meridian convergence, 433
meta-azimuthal projection, 209, 215
meta-colatitude, 128
meta-cylindrical projection, 285, 289
meta-equator, 369–371, 373, 374
meta-equatorial (oblique) frame of reference, 130
meta-equatorial North Pole, 126
meta-equatorial plane, 121
meta-equatorial reference frame, see reference frame,
oblique
meta-latitude, 128, 132, 136, 290
meta-longitude, 121, 128, 132, 136, 290
meta-North Pole, 121, 126–128, 141
meta-South Pole, 121
meta-spherical latitude, 286
meta-spherical longitude, 286
metric, 1
– canonical form, 18
– conformally flat, 64
– Euclidean, 6
Mimas, 637, 655
minimal atlas, 184
minimal distance mapping, 637, 638
minimal total areal distortion, 333
minimal total distance distortion, 333
mixed cylindric map projection, 569
Mollweide gauge, 595
Mollweide projection, 97, 106–109, 296
– generalized, 109, 110, 589
– spherical, 595
Moon, 637, 655
National data files, 113
Nell–Hammer projection, 586
Newton portrait, 546, 550
normal field, 644
normal perspective, 161
normal perspective mapping, 182, 186
Northing, 485, 486
oblique Mercator projection, 291
oblique conformal projection, 289
oblique equal area projection, 289
oblique equatorial plane, 97
oblique equidistant projection, 289
oblique Lambert projection, 218, 291
Oblique Mercator Projection (UOM), 357, 359–361,
369
oblique plane, 93, 126
oblique Plate Carr´ ee projection, 290
oblique Postel projection, 216
oblique quasi-spherical latitude, 144
oblique quasi-spherical longitude, 144
oblique radius, 144
oblique stereographic projection, 217
optimal cylinder projection, 279
optimal map projections, 80, 85
optimal Mercator projection, 623
optimal polycylindric projection, 623
optimal transversal Mercator projection, 331
optimal universal transverse Mercator projection,
537
order diagram, see Hasse diagram
orthogonal projection, 23, 25, 27, 28, 33–35, 190
orthographic projection, 161, 190
parabolic pseudo-cylindrical mapping, 293
parallel projection, 190
parallel transport, 126
perspective mapping, 240
perspective ratio, 174
Phobos, 637
photogrammetric surveying, 638
Plate Carr´ ee projection, 273, 276
polar aspect, 161
polar azimuthal projection, 201
polar coordinate, 248
polar decomposition, 5, 8–10
polynomial
– bivariate homogeneous, 505, 509, 512, 514
– inversion of a bivariate homogeneous, 509, 512
– inversion of a multivariate homogeneous, 516
– inversion of an univariate homogeneous, 505, 508
– multivariate homogeneous, 505, 519
– univariate homogeneous, 505, 507, 508
– vector-valued bivariate homogeneous, 512
Postel map, 161
power set, 500, 501
principal distortion, 417, 440, 443, 445
projection, see mapping
projection plane, 24, 64, 70, 72
pseudo-azimuthal projection, 202
pseudo-conic projection, 395
pseudo-cylindrical mapping equations, 570
pseudo-cylindrical projection, 19, 293
pseudo-observations, 453, 460, 463, 467
Ptolemy mapping, 379, 382–384
pullback, 4, 5, 29, 440
pushforward, 4, 29
quadrant rule, 249
Rechtswert, 485
rectified skew orthomorphic projections, 359, 377
rectilinear pseudo-cylindrical mapping, 293, 299
reference ellipsoid, 469
reference frame
– Cartan, 87, 88
– Darboux, 87, 88, 416, 417, 419, 424, 425
– meta-equatorial, 124, 126, 128
– oblique, 124, 126, 128, 129, 131, 138, 139, 141, 143,
360, 364–366
– – of the sphere, 126–128, 132
– oblique equatorial, 126
– orthogonal, 24
– transformations between oblique frames, 139
relative angular shear, 40
relative eccentricity, 361, 366, 376
remote sensing, 589
rhumb line, 273
Riemann coordinates, 415–417, 426
Riemann manifold, 1–3, 32, 43, 47, 49, 53, 74, 80, 82,
92, 95
Mercator projection, 276, 277, 313, 315, 335, 357,
359, 360, 362, 369
– optimal, 623, 624
meridian convergence, 433
meta-azimuthal projection, 209, 215
meta-colatitude, 128
meta-cylindrical projection, 285, 289
meta-equator, 369–371, 373, 374
meta-equatorial (oblique) frame of reference, 130
meta-equatorial North Pole, 126
meta-equatorial plane, 121
meta-equatorial reference frame, see reference frame,
oblique
meta-latitude, 128, 132, 136, 290
meta-longitude, 121, 128, 132, 136, 290
meta-North Pole, 121, 126–128, 141
meta-South Pole, 121
meta-spherical latitude, 286
meta-spherical longitude, 286
metric, 1
– canonical form, 18
– conformally flat, 64
– Euclidean, 6
Mimas, 637, 655
minimal atlas, 184
minimal distance mapping, 637, 638
minimal total areal distortion, 333
minimal total distance distortion, 333
mixed cylindric map projection, 569
Mollweide gauge, 595
Mollweide projection, 97, 106–109, 296
– generalized, 109, 110, 589
– spherical, 595
Moon, 637, 655
National data files, 113
Nell–Hammer projection, 586
Newton portrait, 546, 550
normal field, 644
normal perspective, 161
normal perspective mapping, 182, 186
Northing, 485, 486
oblique Mercator projection, 291
oblique conformal projection, 289
oblique equal area projection, 289
oblique equatorial plane, 97
oblique equidistant projection, 289
oblique Lambert projection, 218, 291
Oblique Mercator Projection (UOM), 357, 359–361,
369
oblique plane, 93, 126
oblique Plate Carr´ ee projection, 290
oblique Postel projection, 216
oblique quasi-spherical latitude, 144
oblique quasi-spherical longitude, 144
oblique radius, 144
oblique stereographic projection, 217
optimal cylinder projection, 279
optimal map projections, 80, 85
optimal Mercator projection, 623
optimal polycylindric projection, 623
optimal transversal Mercator projection, 331
optimal universal transverse Mercator projection,
537
order diagram, see Hasse diagram
orthogonal projection, 23, 25, 27, 28, 33–35, 190
orthographic projection, 161, 190
parabolic pseudo-cylindrical mapping, 293
parallel projection, 190
parallel transport, 126
perspective mapping, 240
perspective ratio, 174
Phobos, 637
photogrammetric surveying, 638
Plate Carr´ ee projection, 273, 276
polar aspect, 161
polar azimuthal projection, 201
polar coordinate, 248
polar decomposition, 5, 8–10
polynomial
– bivariate homogeneous, 505, 509, 512, 514
– inversion of a bivariate homogeneous, 509, 512
– inversion of a multivariate homogeneous, 516
– inversion of an univariate homogeneous, 505, 508
– multivariate homogeneous, 505, 519
– univariate homogeneous, 505, 507, 508
– vector-valued bivariate homogeneous, 512
Postel map, 161
power set, 500, 501
principal distortion, 417, 440, 443, 445
projection, see mapping
projection plane, 24, 64, 70, 72
pseudo-azimuthal projection, 202
pseudo-conic projection, 395
pseudo-cylindrical mapping equations, 570
pseudo-cylindrical projection, 19, 293
pseudo-observations, 453, 460, 463, 467
Ptolemy mapping, 379, 382–384
pullback, 4, 5, 29, 440
pushforward, 4, 29
quadrant rule, 249
Rechtswert, 485
rectified skew orthomorphic projections, 359, 377
rectilinear pseudo-cylindrical mapping, 293, 299
reference ellipsoid, 469
reference frame
– Cartan, 87, 88
– Darboux, 87, 88, 416, 417, 419, 424, 425
– meta-equatorial, 124, 126, 128
– oblique, 124, 126, 128, 129, 131, 138, 139, 141, 143,
360, 364–366
– – of the sphere, 126–128, 132
– oblique equatorial, 126
– orthogonal, 24
– transformations between oblique frames, 139
relative angular shear, 40
relative eccentricity, 361, 366, 376
remote sensing, 589
rhumb line, 273
Riemann coordinates, 415–417, 426
Riemann manifold, 1–3, 32, 43, 47, 49, 53, 74, 80, 82,
92, 95