By Grafarend E., Krumm F.

ISBN-10: 3540367012

ISBN-13: 9783540367017

Within the context of Geographical info platforms (GIS) the e-book bargains a well timed evaluation of map projections (sphere, ellipsoidal, rotational surfaces) and geodetic datum adjustments. For the desires of photogrammetry machine imaginative and prescient and distant sensing house projective mappings are reviewed.

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**Grafarend E., Krumm F.'s Map projections. Cartographic information systems PDF**

Within the context of Geographical info structures (GIS) the e-book bargains a well timed assessment of map projections (sphere, ellipsoidal, rotational surfaces) and geodetic datum adjustments. For the wishes of photogrammetry computing device imaginative and prescient and distant sensing house projective mappings are reviewed.

**Additional info for Map projections. Cartographic information systems**

**Example text**

U +i K2 1 Fr p K 2 + K 2 1 2 ∂/∂v ∂/∂V √ 1 K1 ∂/∂u √ −i K2 Fl Fig. 13. Left Euler–Lagrange tensor, K1 > 0, K2 < 0, left Euler–Lagrange circle S1 , left Euler–Lagrange hyperbola H1√K ,√K , left and right focal points Fl and Fr . 1 2 32 1 From Riemann manifolds to Riemann manifolds ∂/∂V √ ∂/∂v ∂/∂U κ2 √ 1 ∂/∂u κ1 1 Fig. 14. Right Euler–Lagrange tensor, κ1 > 0, κ2 > 0, right Euler–Lagrange circle S1 , right Euler–Lagrange ellipse E1√κ1 ,√κ2 . 9 (Relation between the Cauchy–Green and the Euler–Lagrange deformation tensor).

Commutative diagram, canonical representation of pairs of metric tensors, “Kartenwechsel” T and τ , canonical mapping f can from the left chart V˜l to the right chart V˜r . 2 (Left versus right Cauchy–Green deformation tensor). 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).

10, we depart from computing the left Jacobi matrix Jl . First, the partial derivatives DΛ x, DΦ x, DΛ y, and DΦ y build up the left Jacobi matrix. Second, by means of the matrix product Cl = J∗l Gr Jl , we are able to compute the left Cauchy–Green matrix for the right matrix of the metric Gr = I2 . Indeed, the chart {x, y} is covered by Cartesian coordinates whose metric is simply given by ds2 = dx2 + dy 2 . Though the special left Cauchy–Green matrix Cl = J∗l Jl looks simple, but is complicated in detail.

### Map projections. Cartographic information systems by Grafarend E., Krumm F.

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