From 4b44ce06676bb4a55526b414d447a1b73e7d0950 Mon Sep 17 00:00:00 2001
From: Orange <orange-cpp@yandex.ru>
Date: Thu, 31 Jul 2025 21:51:52 +0300
Subject: [PATCH] Documents projectile launch angle formula

Adds a comment documenting the formula used for calculating the projectile launch pitch angle.

The comment includes a link to the Stack Overflow discussion where the formula was found and the LaTeX representation of the formula for clarity.
---
 .../proj_pred_engine_legacy.hpp                      | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/include/omath/projectile_prediction/proj_pred_engine_legacy.hpp b/include/omath/projectile_prediction/proj_pred_engine_legacy.hpp
index 44eec14..8a72ee9 100644
--- a/include/omath/projectile_prediction/proj_pred_engine_legacy.hpp
+++ b/include/omath/projectile_prediction/proj_pred_engine_legacy.hpp
@@ -28,6 +28,18 @@ namespace omath::projectile_prediction
         const float m_maximum_simulation_time;
         const float m_distance_tolerance;
 
+        // Realization of this formula:
+        // https://stackoverflow.com/questions/54917375/how-to-calculate-the-angle-to-shoot-a-bullet-in-order-to-hit-a-moving-target
+        /*
+        \[
+        \theta \;=\; \arctan\!\Biggl(
+        \frac{%
+        v^{2}\;\pm\;\sqrt{\,v^{4}-g\!\left(gx^{2}+2yv^{2}\right)\,}
+        }{%
+        gx
+       }\Biggr)
+       \]
+        */
         [[nodiscard]]
         std::optional<float>
         maybe_calculate_projectile_launch_pitch_angle(const Projectile& projectile,