LiDAR Canopy Transect: Beer–Lambert Foliage Height Diversity (2D)

This is a 2D cross-section counterpart to the 3D airborne LiDAR point-cloud simulator: rather than flying a camera over an instanced-mesh forest, it renders a vertical forest transect and computes each column's canopy return directly from radiative-transfer physics. Every tree contributes a 2D Gaussian foliage-density bump in the (horizontal position, height) plane; summed together these form a continuous foliage-area-density profile that a simulated LiDAR pulse must pass through. Solving the Beer–Lambert extinction equation column by column yields an exact, energy-conserving probability distribution over return height — sampled pulses build a height histogram live, and the same Shannon-entropy Foliage Height Diversity formula MacArthur used for species diversity is applied to the resulting vertical layers. Four independent layer-weight sliders let you sculpt understory, midstory, canopy and emergent layering directly, while canopy cover and the extinction coefficient control how deeply pulses penetrate before reaching bare ground — richer, more physically transparent controls than switching between fixed 3D archetypes.