Contents XVII
I
Mercator projection and polycylindric projection ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 623
Optimal Mercator projection and optimal polycylindric projection of conformal type
623
I-1 The optimal Mercator projection (UM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
I-2 The optimal polycylindric projection of conformal type (UPC) . . . . . . . . . . . . . . . . 630
J
Gauss surface normal coordinates in geometry and gravity space ∗ ∗ ∗ ∗ ∗ ∗ ∗ 637
Three-dimensional geodesy, minimal distance mapping, geometric heights
637
J-1 Projective heights in geometry space: from planar/spherical to ellipsoidal mapping . . . . 638
J-2 Gauss surface normal coordinates: case study ellipsoid-of-revolution . . . . . . . . . . . . . 643
J-21 Review of surface normal coordinates for the ellipsoid-of-revolution . . . . . . . . . 644
J-22 Buchberger algorithm of forming a constraint minimum distance mapping . . . . . 648
J-3 Gauss surface normal coordinates: case study triaxial ellipsoid . . . . . . . . . . . . . . . . . 652
J-31 Review of surface normal coordinates for the triaxial ellipsoid . . . . . . . . . . . . . 652
J-32 Position, orientation, form parameters: case study Earth . . . . . . . . . . . . . . . . 653
J-33 Form parameters of a surface normal triaxial ellipsoid . . . . . . . . . . . . . . . . . . 655
Bibliography ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 657
Index ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 709