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Hitscan is a term that is used mainly in computer games, most commonly in first person shooters. A hitscan is a calculation performed by a game to find the point at which a given line intersects a game object, and is commonly used to determine whether a bullet or projectile hit a target after being fired from a weapon.
A projectile weapon which uses unmodified hitscan information to dictate whether or not it has hit its target is often called a hitscan weapon. Deploying the weapon calls the hitscan function, and if an object is detected in the path of the projectile, a hit is registered. Since the effect is immediate, the projectiles effectively travel at infinite speed and have a linear or otherwise simple trajectory — a practical approximation of a bullet's speed and accuracy over short distances. To improve the realism, programmers may use hitscan functions in slightly different ways - for example, applying a random perturbation to the calculated path to simulate inaccuracy. As another example, the assault rifle in Half-Life 2 calls a hitscan function in the middle of a 'blazing gun' animation, creating a small amount of lag between weapon deployment and the hitting of the target to better approximate real-life ballistics.
The primary advantage is the simplicity of the simulation, it uses relatively simple mathematics to calculate hits. Although bullets do not move at infinite speed via perfectly straight trajectories, they move fast enough that a hitscan solution is normally a reasonable approximation. It leaves the question of where a weapon has hit to just one function, streamlining the programming of weapons.
In terms of game design, it readily ties cause (the player presses a 'fire' button, executing a hitscan function) to effect (the hitscan returns a result, the player sees the weapon's effect at that location). While a simplified model of real world ballistics, it makes games more accessible in that there is no need to aim slightly ahead of a moving target in order to compensate for the time it takes for the projectile to reach it. Although less realistic this model requires no understanding of real weapon handling in order to play the game, and reinforces the intuitive understanding that whatever the reticle is placed over will be hit.
Visually representing the firing effect of a hitscan weapon can be difficult - since the weapon hits its target instantaneously, any bullet or projectile that comes from the weapon is merely a 'ghost', and where it lands may not necessarily represent its actual hit. In particular, a projectile bullet effect will always lag behind the effect of its hit, a problem which can be compounded by internet latency in online multiplayer gaming.
With advances in processing and internet bandwidth, it has become more practical to simulate the ballistic nature of real-world firearms in real-time games by using a more realistic "projectile" model, spawning bullets as actual game objects with mass and velocity and continuously simulating them until they reach their target.