Implementation

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 $(\phi,\lambda,h)$. The semimajor axis is denoted by a, and the semiminor axis is denoted by b. The squared first eccentricity by:

$$e^2 = {a^2-b^2\over a^2}$$ (1)

The squared second eccentricity by

$$e'^2 = 1-e^2 = {a^2-b^2\over b^2}$$ (2)

$$r = \sqrt{x^2+y^2}$$ (3)

$$\nu = \arctan_2(z \cdot a),(r \cdot b))$$ (4)

$$sin3 = \sin^3\nu$$ (5)

$$cos3 = \cos^3\nu$$ (6)

$$\phi = \arctan_2((z + e'^2 \cdot b \cdot sin3),(r - e^2 \cdot a \cdot cos3))$$ (7)

$$\lambda = \arctan_2(y,x)$$ (8)

$$N = {a \over \sqrt{1 - e^2 \sin^2\phi}}$$ (9)

$$h = {r\over\cos\phi} - N$$ (10)