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Known are the heights of each pixel in the master (line,pixel) system.
The point P(x,y,z) corresponding to a (line,pixel) is computed with
the 3 equations (see Annex D) in such a way that
it lies on an ellipsoid of height h above the refernce ellipsoid.
When these coordinates are known, the equations of Bowring are used to
transform them to an ellipsoid system
. The
semimajor axis is denoted by a, and the semiminor axis is
denoted by b. The squared first eccentricity by:
![$\displaystyle e^2 = {a^2-b^2\over a^2}$](img513.gif) |
(1) |
The squared second eccentricity by
![$\displaystyle e'^2 = 1-e^2 = {a^2-b^2\over b^2}$](img514.gif) |
(2) |
![$\displaystyle r$](img515.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle \sqrt{x^2+y^2}$](img516.gif) |
(3) |
![$\displaystyle \nu$](img517.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle \arctan_2(z \cdot a),(r \cdot b))$](img518.gif) |
(4) |
![$\displaystyle sin3$](img519.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle \sin^3\nu$](img520.gif) |
(5) |
![$\displaystyle cos3$](img521.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle \cos^3\nu$](img522.gif) |
(6) |
|
|
|
|
![$\displaystyle \phi$](img523.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle \arctan_2((z + e'^2 \cdot b \cdot sin3),(r - e^2 \cdot a \cdot cos3))$](img524.gif) |
(7) |
![$\displaystyle \lambda$](img525.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle \arctan_2(y,x)$](img526.gif) |
(8) |
![$\displaystyle N$](img527.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle {a \over \sqrt{1 - e^2 \sin^2\phi}}$](img528.gif) |
(9) |
![$\displaystyle h$](img529.gif) |
![$\displaystyle =$](img425.gif) |
![$\displaystyle {r\over\cos\phi} - N$](img530.gif) |
(10) |
Next: Bibliography
Up: GEOCODE
Previous: Output Description
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Leijen
2009-04-14