A LiDAR scanner measures depth d along a ray with bearing (azimuth θ, elevation φ) relative to the sensor. The 3D point in sensor frame coordinates is:
AP = (d·cos(θ)·cos(φ), d·sin(θ)·cos(φ), d·sin(φ))
BP = (d, θ, φ) (distance and angles)
CP = (d·sin(θ), d·cos(θ), 0) (2D horizontal only)
DInsufficient information; need the sensor's intrinsic calibration parameters
This distance-dependent density is fundamental to LiDAR. Robots often use variable voxel sizes for downsampling: coarser voxels for distant regions, finer voxels for nearby regions. This preserves detail where it matters (close to the robot) while reducing computation in the far field.