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According to Wikipedia's [Geographic_coordinate_conversion#From_geodetic_to_ECEF_coordinates][1]

 

The 3D cartesian coordinates $X, Y, Z$ in Earth-centered, Earth-fixed coordinates assuming an ellipsoidal shape is given by:

 

$$X = \left(N(\phi) + h \right) \cos\phi \cos\lambda $$

 

$$Y = \left(N(\phi) + h \right) \cos\phi \sin\lambda $$

 

$$Z = \left(\frac{b^2}{a^2} N(\phi) + h \right) \sin\phi $$

 

where $\phi, \lambda, h$ are latitude, longitude, and altitude, and $a, b$ are the equatorial and polar radii of the ellipsoid used, and

 

$$N(\phi) = \frac{a^2}{\sqrt{a^2\cos^2\phi + b^2 \sin^2\phi}}. $$

According to Wikipedia's [Geographic_coordinate_conversion#From_geodetic_to_ECEF_coordinates][1]

The 3D cartesian coordinates $X, Y, Z$ in Earth-centered, Earth-fixed coordinates assuming an ellipsoidal shape is given by:

$$X = \left(N(\phi) + h \right) \cos\phi \cos\lambda $$

$$Y = \left(N(\phi) + h \right) \cos\phi \sin\lambda $$

$$Z = \left(\frac{b^2}{a^2} N(\phi) + h \right) \sin\phi $$

where $\phi, \lambda, h$ are latitude, longitude, and altitude, and $a, b$ are the equatorial and polar radii of the ellipsoid used, and

$$N(\phi) = \frac{a^2}{\sqrt{a^2\cos^2\phi + b^2 \sin^2\phi}}. $$

$$C = \sqrt{4(b^2(ux + vy) + a^2wz)^2 - (b^2(u^2 + v^2) + a^2w^2) (b^2(-a^2 + x^2 + y^2) + a^2z^2)} $$

$$C = \sqrt{(b^2(ux + vy) + a^2wz)^2 - (b^2(u^2 + v^2) + a^2w^2) (b^2(-a^2 + x^2 + y^2) + a^2z^2)} $$

$$C = \frac{1}{2}\sqrt{4(b^2(ux + vy) + a^2wz)^2 - 4(b^2(u^2 + v^2) + a^2*w^2) (b^2(-a^2 + x^2 + y^2) + a^2z^2)} $$

$$t = -\frac{1}{b^2(u^2+v^2) + a^2w^2} \left( b^2(ux + vy) + a^2wz + \frac{1}{2}\sqrt{4(b^2(ux + vy) + a^2wz)^2 - 4(b^2(u^2 + v^2) + a^2w^2) (b^2(-a^2 + x^2 + y^2) + a^2z^2)} \right)$$

$$C = \sqrt{4(b^2(ux + vy) + a^2wz)^2 - (b^2(u^2 + v^2) + a^2w^2) (b^2(-a^2 + x^2 + y^2) + a^2z^2)} $$

$$t = -\frac{1}{b^2(u^2+v^2) + a^2w^2} \left( b^2(ux + vy) + a^2wz + \sqrt{(b^2(ux + vy) + a^2wz)^2 - (b^2(u^2 + v^2) + a^2w^2) (b^2(-a^2 + x^2 + y^2) + a^2z^2)} \right)$$