Map Projections by Erik W. Grafarend

By Erik W. Grafarend

In the context of Geographical details structures (GIS) the ebook bargains a well timed evaluate of map projections (sphere, ellipsoidal, rotational surfaces) and geodetic datum adjustments. For the desires of photogrammetry laptop imaginative and prescient and distant sensing area projective mappings are reviewed.

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133) . gγδ u˙ γ1 u˙ δ2 The second additive measure of deformation is the angular shear or the angle of shear (Σl is of type “left” and Σr is of type “right”, respectively) Σl = Σ := Ψl − Ψr versus Σr = σ := Ψr − Ψl . 21 illustrate this second additive measure of deformation. In order to be simple, however, we have chosen the coordinate lines that are illustrated in Fig. 20. 3. Various deformation tensors of the first kind. Definitions Author Comments E1 = Cl = Sl R∗ Gr RSl = J∗l Gr Jl A. Cauchy (1889,1890) if Gr = I, then Cl = S2l = J∗l Jl E2 = Cr = Sr R∗ Gl RSr = J∗r Gl Jr G.

We pose two problems. (i) Derive the right Euler–Lagrange deformation tensor. (ii) Solve the right general eigenvalue–eigenvector problem. 34 1 From Riemann manifolds to Riemann manifolds Solution (the first and the second problem). 19 in polar coordinates. 20, we are giving the transform to the left Euler–Lagrange matrix. 18. 9 in order to compute the right Euler–Lagrange matrix 2Er = I2 − Cr in Cartesian coordinates as well as its right eigenvalues 2κi = λ2i − 1 from given right eigenvalues λ2i .

133) . gγδ u˙ γ1 u˙ δ2 The second additive measure of deformation is the angular shear or the angle of shear (Σl is of type “left” and Σr is of type “right”, respectively) Σl = Σ := Ψl − Ψr versus Σr = σ := Ψr − Ψl . 21 illustrate this second additive measure of deformation. In order to be simple, however, we have chosen the coordinate lines that are illustrated in Fig. 20. 3. Various deformation tensors of the first kind. Definitions Author Comments E1 = Cl = Sl R∗ Gr RSl = J∗l Gr Jl A. Cauchy (1889,1890) if Gr = I, then Cl = S2l = J∗l Jl E2 = Cr = Sr R∗ Gl RSr = J∗r Gl Jr G.

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