Gauss Surface Normal Coordinates in Geometry and Gravity - Map Projections: Cartographic Information Systems - page 825

Fig. J.1. Projective heights in geometry space, orthogonal projection p = π ( P ) of a topographic point X ∈ T 2

onto a local horizontal plane X 0 ∈ T 2 , minimal distance mapping δ 2 =0

X − x

Indeed, for a suitable choice of surface parameters/surface coordinates of a chart, the uncon-
strained optimization problem may be preferable to constraint optimization, however, which we
do not want to treat here.

P 2

Fig. J.2. Projective heights in geometry space, minimal distance mapping with respect to a reference plane

at X 0 ∈ T 2 , orthogonal projection p = π ( P )