PIT MAGIC: Lacus Mortis Pit Illumination Suite (v1.1)

A Physics-Based Spectral Radiosity Solver for Lunar Subsurface Exploration

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1. Executive Summary: The "Black Box" Problem

Lunar pits are of immense scientific value, potentially providing access to pristine basaltic stratigraphy and stable environments for future lunar bases. However, current orbital imagery (LROC NAC) is limited by extreme contrast; shadows appear as "black boxes" with zero visible detail because the Moon lacks an atmosphere to scatter light.

Pit MAGIC provides the missing link for mission success by quantifying the "Light Depth" in these shadows. It calculates how sunlight bounces off lit walls to create a faint "Glow" that reveals the pit's interior. This allows mission planners to set HDR exposure targets and identify geological features that are otherwise invisible.

Project Significance: Why This Matters

• Set HDR Exposure Targets: Predict exactly how long a rover's shutter must be open to resolve wall textures without drowning in sensor noise.
• Optimize Trajectories: Identify "High-Glow" windows where secondary reflections are at their peak, maximizing scientific ROI during circumnavigation stop-points.
• Identify Cave Entrances: Map the falloff of light into the deep recesses of the pit to differentiate deep cave entrances from simple wall overhangs.

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2. Version Evolution (Research History)

v1.0: Static Scalar Analysis

• Methodology: Grey-scale radiosity assuming a uniform lunar albedo (0.12).
• Limitation: Solar vectors were calculated in global coordinate frames, resulting in stagnant shadow models over short timeframes.
• Result: Successfully validated the primary Lambertian transport kernel.

v1.1: Dynamic Spectral Suite (Current)

• Spectral Engine: Upgraded to 3-Band (RGB) transport matching MAGIC camera bandpasses (615nm, 537nm, 450nm).
• Local ENU Transformation: Implemented a Local Tangent Plane (East-North-Up) transformation matrix (44.96°N, 25.61°E). Shadows now move realistically across the pit's local horizon.
• BVH Integration: Integrated Bounding Volume Hierarchies for $O(\log N)$ visibility checks between surface patches.
• Numerical Rigor: Migrated to float32 vectorization for high-speed processing of millions of concurrent form-factor calculations.

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📊 Part 1: Visual Gallery (Telemetry Watermarked)

I. Dynamic Shadow Progression (Multi-Day Simulation)

Figure 1: 10-day time-lapse. Note the shadow line sweeping across the floor and the "Glow" migrating between walls as the Sun arcs over the local horizon. This identifies the optimal diurnal mission window for wall imaging.

II. High-Contrast Isometric Radiosity Map

Figure 2: Spectral irradiance map ($W/m^2$). Renders include directional axes aligned with the IAU_MOON frame. The legend is relocated to the top-left to ensure zero overlap with 3D terrain data.

III. Top-Down Scientific Projection

Figure 3: Vertical projection of the radiosity distribution. Used to calculate the specific "Light Depth" available at different distances from the pit rim.

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📖 Part 2: Mission Manual (User Guide)

🚀 Setup for New Users

If you are starting from scratch or want to upload your own DTM data:

1. Install Requirements: pip install -r requirements.txt
2. Initialize: Run ./pitIllum init. This creates the folders you need.
3. Place Your Data:
   • Put your 3D Mesh (.obj) or GeoTIFF (.tif) in data/raw_lroc/.
   • Ensure SPICE kernels are in data/kernels/.
4. Analyze:

   ./pitIllum analyze --dtm data/raw_lroc/YOUR_FILE.obj --time "2026-06-21T12:00:00"

📂 Directory Rules (Do Not Break)

• lib/: Contains core physics logic. Modification will break telemetry-sync.
• data/: Subfolders (kernels, raw_lroc) must remain exactly as named for the automated loader to function.
• output/: PNG maps and 3D result models are exported here automatically.

🛠 CLI Commands

• status: Check if telemetry (SPICE kernels) and terrain data are properly loaded and synced.
• generate-test: Fabricate a synthetic pit model for physics validation.
• analyze: The primary scientific engine. Use --time for specific mission timestamps and --bounces for higher accuracy.

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🔬 Part 3: Technical Methodology

Physical Governing Equations

Pit MAGIC implements a deterministic solution to the Kajiya Rendering Equation for a vacuum environment. We model the secondary transport of photons (Radiosity) between surface patches $i$ and $j$:

$$ B_{j,\lambda} = \rho_{j,\lambda} \sum_{i} B_{i,\lambda} F_{ij} $$

Where the geometric kernel $F_{ij}$ is derived from the Lambertian Cosine Law and the Inverse Square Law:

$$ F_{ij} = \frac{\cos(\theta_i) \cdot \cos(\theta_j)}{\pi \cdot r_{ij}^2} \cdot V_{ij} \cdot A_i $$

• $V_{ij}$: Visibility term solved via BVH (Bounding Volume Hierarchy) ray-casting.
• $r_{ij}^2$: Inverse Square Law falloff across the pit void.

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🔍 Part 4: Validation & Inference

• Physics Check: Run python3 tests/validation_test.py to verify energy conservation ($\approx 0.11$ ratio).
• Structural Visibility: Areas showing $> 100 , W/m^2$ are candidates for high-resolution stratigraphy imaging without long-exposure blurring.
• Thermal Correlation: High-radiosity zones correlate with surfaces receiving more reflected energy, aiding in the calculation of local thermal inertias.

Repository: github.com/rxshira/magicPitIllum Version: 1.1 (Spectral Suite)