📡 LiDAR Scanning

LiDAR stands for Light Detection and Ranging. It works by emitting a laser pulse and measuring how long it takes to travel to an object and reflect back (time-of-flight), or by measuring the phase shift of a continuous beam. Since light travels at a known constant speed, that time (or phase difference) converts directly into a distance measurement. This simulation approximates the same idea in 2D using geometric ray casting instead of a real time-of-flight measurement.

Ray casting fires an imaginary line from the sensor in a chosen direction and finds where it first meets an obstacle. To find that point, the simulation solves for the intersection between the ray and every wall segment in the scene using their parametric line equations, then keeps only the closest valid intersection (t and u both within range). This is the same core geometric operation used in real-time rendering, 2D games and robotics range-sensor models.

A point cloud is simply the collection of 3D (or, here, 2D) coordinates where a sensor's rays actually struck something. Every ray in this simulation that hits a wall contributes one point at that location; over many rotations, thousands of these points accumulate into a shape that traces the outline of the room and obstacles — exactly how real LiDAR units used in robotics and autonomous vehicles build up a picture of their surroundings.

An occupancy grid divides the environment into cells and tracks, per cell, the probability that it is occupied. This simulation uses a log-odds representation: every time a ray passes through a cell without stopping, that cell's free-space evidence is added; when a ray terminates in a cell, occupied evidence is added. Because each range reading includes Gaussian noise, no single scan is perfectly reliable, but averaging many noisy scans over time makes the grid converge toward an accurate map — the same principle used in real SLAM (simultaneous localization and mapping) systems.

More rays per scan means finer angular resolution, so thinner obstacles and sharper corners are less likely to be missed between two adjacent beams, and the resulting point cloud and occupancy grid look more detailed. The trade-off, just as in real hardware, is cost: more rays per revolution demands more measurements to be taken and processed in the same amount of time, which in a physical LiDAR unit means a faster (and typically more expensive) scanning mechanism or a lower maximum rotation speed.