Map projections. Cartographic information systems - download pdf or read online

By Grafarend E., Krumm F.

Within the context of Geographical details structures (GIS) the publication bargains a well timed evaluate of map projections (sphere, ellipsoidal, rotational surfaces) and geodetic datum differences. For the wishes of photogrammetry computing device imaginative and prescient and distant sensing house projective mappings are reviewed.

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Right CG: Left CG: ˘ ¯ ∂u ∂u ds2 = gµν f λ (U L ) dU M dU N = ∂U M ∂U N ˘ ¯ ∂U M ∂U N dS 2 = GM N F L (uλ ) duµ duν = ∂uµ ∂uν = cM N (U L ) dU M dU N , = Cµν (uλ )duµ duν , µ cM N (U L ) := gµν (U L ) ν ∂uµ ∂uν (U L ) (U L ) . 49) ∂U M λ ∂U N λ (u ) (u ) . 3 (Left Tissot circle versus left Tissot ellipse, left Cauchy–Green deformation tensor: Ricci calculus). Left Tissot circle S1 : Left Tissot ellipse E1λ1 ,λ2 : M N – A– B UB dV dV = dS 2 = GM N UA ν M N – A– B ds2 = gµν uµ = M uN UA UB dV dV – A dV – B= = δAB dV – 1 )2 + Λ22 (dV – 2 )2 = = Λ21 (dV – 1 )2 + (dV – 2 )2 = Ω12 + Ω22 .

Third, this difference continues when we are going to compute the right Cauchy–Green matrices Cr (x, y) and Cr (α, r). Again, Cr (x, y) is a fully occupied symmetric matrix, while Cr (α, r) is diagonal. 13, we represent the right Cauchy–Green deformation tensor as a tensor of second order in the Cartesian two-basis eµ ⊗ eν for all {µ, ν} = {1, 2}. Note that R2 = span{e1 , e2 }, where {e1 , e2 O} is an orthonormal two-leg at O. Remarkably, Cr (x, y) includes the components e1 ⊗ e2 , e1 ⊗ e2 + e2 ⊗ e1 , and e2 ⊗ e2 .

Xy R2 − x2 R − (x2 + y 2 ) Right Euler–Lagrange matrix in Cartesian coordinates: » 2 – 1 1 x xy . 123) Right eigenvalues: 2κi = λ2i − 1 ∀ i ∈ {1, 2} , λ21 = R2 x2 + y 2 R2 1 , λ22 = 1 , κ1 = , κ2 = 0 . 124) Right Euler–Lagrange tensor: Er = ` ´ xy x y2 1 1 1 = − e1 ⊗ e1 2 − e1 ⊗ e2 + e2 ⊗ e1 2 − e2 ⊗ e2 2 = 2 2 2 2 2 R − (x + y ) 2 R − (x + y ) 2 R − (x2 + y 2 ) 2 x2 xy y2 1 1 = − e1 ∨ e1 2 − e1 ∨ e2 2 − e2 ∨ e2 2 2 2 2 2 2 R − (x + y ) R − (x + y ) 2 R − (x2 + y 2 ) subject to ´ 1` eµ ⊗ eν + eν ⊗ eµ .

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