Infinite distance (trigonometric): implement functions

[fgnievinski]

for interf. delay, slant distance, and height correction.

• Retirar variáveis que não constam no artigo como ... atraso trigonométrico?

Originally posted by @vitorhjr in https://github.com/vitorhjr/geo-alhazen/issues/2#issuecomment-927940709

[vitorhjr]

I implemented interf. delay, slant distance, and height correction. I commented the implementation in the issue https://github.com/vitorhjr/curv-altimetry-dev/issues/29.

I will repost here the comments about the findings.

[vitorhjr]

I have been modeling the trigonometric approach for the altimetry correction and reflection on a sphere (deposited in geo-alhazen repository and in the curv-altimetry repository, too). Those are the new trigonometric functions in the branch cor-trig:

• get_spherical_reflection_trig: compute interf. delay and slant distance;
• get_curvature_altimetry_correction_pdoppler_series_trig: compute altimetry correction
• demo_trig1: demonstration of trigonometric altimetry correction

[vitorhjr]

I found some issues when implementing the formulas from my master's thesis. I maintain wrong formulas in the code, but commented with "#WRONG".

• The correct formula for the discrepancies between direct and reflected elevation angles is $\Delta e_r = e_d - e_r^s$. In the thesis, it's presented as $\Delta e_r = -e_d - e_r^s$ (p. 69, eq. 114);
• The second formula for $D_i$ (p. 73, eq. 123) is incorrect. It should be reformulated or discarded. The first formula $D_i = D_l^s*(\sqrt\gamma- sin(g))$ is correct;
• The formula of altimetry correction on eq. 126 (p. 74) is not correct. It should be revised and reformulated. To compute altimetry correction I'm using the gradient.

[vitorhjr]

AlthoughDespite those issues, the implementation of the trigonometric formulas is correct in the algorithms.