MGRS/UTM geodetic conversion and 3D screen-to-sphere raycasting

TerraGemini integrates a full WGS84 ellipsoid geodetic conversion engine with real-time screen-to-sphere raycasting and 3D target lock tracking.

1. Screen-to-Sphere Raycasting

When the user clicks or hovers at screen coordinate $(x_s, y_s)$, the coordinate is unprojected into spherical unit space relative to center $(c_x, c_y)$ and scale $S$:

$r_x = \frac{x_s - c_x}{S}, \quad r_y = -\frac{y_s - c_y}{S}$

If $r_x^2 + r_y^2 \le 1.0$, front-hemisphere depth $r_z = \sqrt{1.0 - (r_x^2 + r_y^2)}$ is computed and multiplied by the inverse camera rotation matrix $\mathbf{R}^{-1} = R_y(-\theta_y) R_x(-\theta_x)$ to extract geodetic latitude $\phi = \arcsin(p_y)$ and longitude $\lambda = \operatorname{atan2}(p_x, p_z)$.

2. WGS84 to MGRS (1-Meter Precision)

The geodetic coordinates are processed through a UTM projection engine (calculating meridian arc distance $M$ and 5th-order series expansions) and mapped to the Military Grid Reference System (MGRS):

• Derives the 6° UTM zone and 8° latitude band.
• Identifies the 100,000m grid square using DoD/NGA row letter offset sets.
• Produces 1-meter precision coordinates (e.g. 18T WL 83959 07350).

The locked target maintains dynamic 3D-to-2D screen tracking, rendering animated radar rings, occlusion culling on back-face rotation, and dynamic SVG leader lines anchored to the telemetry HUD.