2D LiDAR Ray-Casting: Point Cloud & Occupancy Grid

Scan Parameters

Rays per scan (angular res.) 180

Max range 9.0 m

Range noise σ 0.02 m

Rotation speed 1.0 rev/s

Environment

Drag the yellow sensor to rescan from a new position (clears the map).

Live Readout

Scan angle

0.0°

Elapsed

0.0 s

Points in cloud

Occupied cells

How it works

Each simulated laser pulse is a ray from the sensor position P at angle θ. For every wall segment (A, B) in the scene, the ray-segment intersection is solved with the standard parametric line formula:

r = P + t·d          (ray, t ≥ 0)
s = A + u·(B − A)    (segment, 0 ≤ u ≤ 1)
t = ((A−P)×(B−A)) / (d×(B−A))
u = ((A−P)×d)       / (d×(B−A))

Only intersections with t ≥ 0 and 0 ≤ u ≤ 1 are valid hits; the smallest valid t across all walls is the true range. Gaussian noise (Box–Muller) is added to that range to mimic a real time-of-flight sensor before the point is plotted, exactly as the 3D version of this simulation does.

Point cloud (left) — every ray that hits a wall drops one point at the noisy hit location; thousands of points trace the room outline as the scanner rotates.
Occupancy grid (right) — a log-odds grid: cells the ray passes through are marked more "free", the cell it stops in is marked more "occupied". Averaging many noisy scans converges the grid toward the true map — the same principle real SLAM systems use.
Angular resolution — more rays per scan means finer detail but more geometry to solve per revolution, mirroring the real cost/speed trade-off of LiDAR hardware.

Sensor (drag me) Active ray Point cloud hit