Index
Airy criterion, 624
Airy distortion energy, 280–282, 626, 632
Airy distortion measure, 342
Airy global distortion, 417
Airy–Kavrajski criterion, 279
Airy–Kavrajski optimum, 280
Airy optimal criterion, 279
Airy optimal dilatation factor, 623
Airy optimum, 279, 331, 333, 537, 625, 631
Albers equal area conic mapping, 405
Albers mapping, 379, 389, 393, 405, 406, 413, 414
Amalthea, 637, 655
angular distortion, 37
angular shear, 37, 39–41, 43, 86, 88–91
– absolute, 41
– relative, 40–42
areal distortion, 74
areomorphism, 74, 76, 79, 85, 86, 97, 106, 114, 161
Armadillo double projection, 92
ascending node, 132
atlas
– complete, 113, 117–120
– minimal, 113, 117, 121, 148
authalic equal area projection, 257
authalic latitude, 76, 269
authalic mapping, 76
azimuthal projection, 163, 165, 223
Baltic Sea Level Project, 637, 651
Berghaus star projection, 32
Bessel ellipsoid, 339, 354, 469
best polar azimuthal projection, 197
Boltz approximation, 433
Bonne mapping, 75, 395, 398, 400, 401, 403
Bonne-pseudo-conic projection, 75
boundary condition, 534–537
boundary value problem, 426, 430, 529, 537
boundary values, 415
Buchberger algorithm, 637, 643
canonical criteria, 83, 86, 111
– a review, 80
canonical formalism, 1, 2
canonical postulate, 161
Cardan angles, 455
Cartan frame, 87, 88
Cartesian product, 497, 498
cartographic synergy, 569
Cauchy–Green matrix, 20, 21, 24, 25, 64, 87, 88, 92,
381, 382
Cauchy–Green deformation energy, 84
Cauchy–Green deformation tensor, 5, 7, 8, 12–15,
18–21, 24, 25, 29, 32, 40, 41, 47, 74, 80, 83, 86, 97,
261, 579
– polar representation, 8
Cauchy–Green distortion energy, 85
Cauchy–Riemann equations, 48, 55, 72, 97, 101, 360,
363, 369, 527, 529
chart, 113
– direct aspect, 113
– oblique aspect, 113
– transverse aspect, 113
Christoffel symbols, 162
Clairaut constant, 416, 426, 429
collinearities, 453
conformal coordinates, 48
conformal diffeomorphism, see conformeomorphism
conformal mapping, 43, 168, 225, 232, 277
conformal Mercator projection, 273
conformally flat, 527
conformeomorphism, 43, 48, 49, 53, 55, 62, 83, 85,
86, 97, 101–104, 106, 161, 527
conical orthomorphic mapping, 388
constraint optimization, 2
coordinates, 113
– meta-spherical, 126
– Cartesian, 24, 498
– conformal, 46, 48, 69, 70, 360, 363, 490
– Fermi, 415, 417, 438, 439
– Gauss–Krueger, 416, 417, 433, 440, 445, 446, 451
– oblique quasi-spherical, 144
– orthogonal, 47
– polar, 24, 33–35, 70
– Riemann, 415–417, 424, 426–428, 440–445, 451
– Soldner, 415–417, 433, 437–440, 445, 446, 451
– surface normal, 53, 637, 643, 644
cotangent space, 4, 7
Craster projection, 298
curvilinear geodetic datum transformations, 453
cylindric mapping equations, 306
cylindrical Lambert projection, 273
d’Alembert–Euler equations, see Cauchy–Riemann
equations
Darboux frame, 87, 88, 417
datum parameters, 453–455
datum problem, 453
– analysis, 454
– synthesis, 463
datum transformation, 454, 455, 463, 469
– curvilinear, 470
– rectangular, 469
Airy criterion, 624
Airy distortion energy, 280–282, 626, 632
Airy distortion measure, 342
Airy global distortion, 417
Airy–Kavrajski criterion, 279
Airy–Kavrajski optimum, 280
Airy optimal criterion, 279
Airy optimal dilatation factor, 623
Airy optimum, 279, 331, 333, 537, 625, 631
Albers equal area conic mapping, 405
Albers mapping, 379, 389, 393, 405, 406, 413, 414
Amalthea, 637, 655
angular distortion, 37
angular shear, 37, 39–41, 43, 86, 88–91
– absolute, 41
– relative, 40–42
areal distortion, 74
areomorphism, 74, 76, 79, 85, 86, 97, 106, 114, 161
Armadillo double projection, 92
ascending node, 132
atlas
– complete, 113, 117–120
– minimal, 113, 117, 121, 148
authalic equal area projection, 257
authalic latitude, 76, 269
authalic mapping, 76
azimuthal projection, 163, 165, 223
Baltic Sea Level Project, 637, 651
Berghaus star projection, 32
Bessel ellipsoid, 339, 354, 469
best polar azimuthal projection, 197
Boltz approximation, 433
Bonne mapping, 75, 395, 398, 400, 401, 403
Bonne-pseudo-conic projection, 75
boundary condition, 534–537
boundary value problem, 426, 430, 529, 537
boundary values, 415
Buchberger algorithm, 637, 643
canonical criteria, 83, 86, 111
– a review, 80
canonical formalism, 1, 2
canonical postulate, 161
Cardan angles, 455
Cartan frame, 87, 88
Cartesian product, 497, 498
cartographic synergy, 569
Cauchy–Green matrix, 20, 21, 24, 25, 64, 87, 88, 92,
381, 382
Cauchy–Green deformation energy, 84
Cauchy–Green deformation tensor, 5, 7, 8, 12–15,
18–21, 24, 25, 29, 32, 40, 41, 47, 74, 80, 83, 86, 97,
261, 579
– polar representation, 8
Cauchy–Green distortion energy, 85
Cauchy–Riemann equations, 48, 55, 72, 97, 101, 360,
363, 369, 527, 529
chart, 113
– direct aspect, 113
– oblique aspect, 113
– transverse aspect, 113
Christoffel symbols, 162
Clairaut constant, 416, 426, 429
collinearities, 453
conformal coordinates, 48
conformal diffeomorphism, see conformeomorphism
conformal mapping, 43, 168, 225, 232, 277
conformal Mercator projection, 273
conformally flat, 527
conformeomorphism, 43, 48, 49, 53, 55, 62, 83, 85,
86, 97, 101–104, 106, 161, 527
conical orthomorphic mapping, 388
constraint optimization, 2
coordinates, 113
– meta-spherical, 126
– Cartesian, 24, 498
– conformal, 46, 48, 69, 70, 360, 363, 490
– Fermi, 415, 417, 438, 439
– Gauss–Krueger, 416, 417, 433, 440, 445, 446, 451
– oblique quasi-spherical, 144
– orthogonal, 47
– polar, 24, 33–35, 70
– Riemann, 415–417, 424, 426–428, 440–445, 451
– Soldner, 415–417, 433, 437–440, 445, 446, 451
– surface normal, 53, 637, 643, 644
cotangent space, 4, 7
Craster projection, 298
curvilinear geodetic datum transformations, 453
cylindric mapping equations, 306
cylindrical Lambert projection, 273
d’Alembert–Euler equations, see Cauchy–Riemann
equations
Darboux frame, 87, 88, 417
datum parameters, 453–455
datum problem, 453
– analysis, 454
– synthesis, 463
datum transformation, 454, 455, 463, 469
– curvilinear, 470
– rectangular, 469