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Rentabilidad económica de Proyectos Cartográficos Ambientales, Estructurados sobre Sistemas de Información Geográfica (SIG) X 2 Si se gira Y en ψ, se tiene (Fuente: Becerra, 2007): Z 3 X 3 ψ l Z2 ψ X Z k 3 3 i = j = X Y Z = = 3 3 3 X Z Z X 2 2 2 ψ = − k + = = sen ψ 2 l + i cos ψ sen ψ cos ψ cosψ 0 senψ j ψ X Z 3 3 Y3 = = X X 2 2 X3 X3 De la planta Y , se desprende lo siguiente: 1 0 - 406 - j cos ψ − Z sen ψ + Z Formulación de 3 Parámetros Rotacionales: 0 − senψ X 0 ⋅ Y cosψ Z 2 2 2 2 2 i ψ Y X 2 ψ ψ 3 sen ψ cos ψ k l X Z 3 Vista planta Y Z2 3 Z R ( ψ ) = 3 3 ψ Matricialm cos ψ = sen ψ cosψ 0 senψ ψ Punto a Transformar X3 ente − sen ψ ⋅ cos ψ Generaliza ndo desde el espacio 2D a 3D 0 1 0 X Z Z3 Z2 2 2 − senψ 0 cosψ
Rentabilidad económica de Proyectos Cartográficos Ambientales, Estructurados sobre Sistemas de Información Geográfica (SIG) 1 0 0 Multiplicando R ε , R ψ, R ω , se tiene: 0 0 cosψ 0 cosψ - 407 - cosω cosε senε ⋅ 0 1 0 ⋅ − senω − senε cosψ senε ⋅ senψ cosε ⋅ senψ cosε cosψ ⋅cosω 0 cosε senψ − senε senε ⋅ senψ − cosε ⋅ senω cosε ⋅ senψ ⋅cosω + senε ⋅ senω Considerando: Se tiene, matriz 3 Rotaciones: 0 − senψ − senψ cosε ⋅cosψ 0 0 cosω senε ⋅cosψ ⋅ − senω − senε ⋅cosω senω cosω 0 0 senω cosω cosψ ⋅ senω + cosω senε ⋅ senψ ⋅ senω + cosε ⋅cosω sen( α) = α ; cos( α) = 1; sen( α) ⋅ sen( α) = 0 1 E = −ω ψ ω 1 −ε −ψ ε 1 0 0 1 0 0 1 − senψ senε ⋅cosψ cosε ⋅cosψ
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Evaluación de la Rentabilidad de u
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Océano Pacifico Evaluación de la
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Rentabilidad económica de Proyecto
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