By Grafarend E., Krumm F.
Within the context of Geographical info structures (GIS) the booklet deals a well timed evaluation of map projections (sphere, ellipsoidal, rotational surfaces) and geodetic datum ameliorations. For the desires of photogrammetry desktop imaginative and prescient and distant sensing area projective mappings are reviewed.
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131) 35 36 1 From Riemann manifolds to Riemann manifolds Fig. 18. Special map projection of the sphere: the Hammer equiareal modified azimuthal projection. This map projection is centered to the Greenwich meridian, with shorelines, 30◦ longitude, 15◦ latitude graticule, Tissot ellipses of distortion, “the world in one chart”. A map projection which is worth studying with all the machinery of deformation measures is the Hammer equiareal modified azimuthal projection of the sphere S2R+ presented in Fig.
11. For a further motivation, we refer to Fig. 22, which presents an image of Lichtenstein’s original publication “Zur Theorie der konformen Abbildung”. 10 (Conformal mapping). An orientation preserving diffeomorphism f : M2l → M2r is called angle preserving conformal mapping (conformeomorphism, inner product preserving) if Ψl = Ψr and Σl = Σ = 0 ⇔ Σr = σ = 0 for all points of M2l and M2r , respectively, holds. End of Definition. 11 (Conformeomorphism M2l → M2r , conformal mapping). Let f : M2l → M2r be an orientation preserving conformal mapping.
Thus, according to a standard lemma of matrix algebra, both matrices can be simultaneously diagonalized, one matrix being the unit matrix. 7 (Left and right general eigenvalue problem of the Euler–Lagrange deformation tensor). 113) is immediately obtained from the left and right general eigenvalue–eigenvector problems El Fl − Gl Fl diag K1 , K2 = 0 ⇔ El − Ki Gl f li = 0 (∀i ∈ {1, 2}) ⇔ El − Ki Gl = 0 FT l Gl Fl = I2 , K1,2 = K+,− = 1 tr El G−1 ± l 2 tr El G−1 l , − 4det El G−1 l ± End of Lemma.
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