Field of View: How Game NPCs Actually See You

Seeing the world through triangles

Give a game character eyes and you have to answer a geometry question sixty times a second: which parts of the map can this point see right now? The brute-force answer — cast a ray to every pixel and check what it hits — is far too slow. The efficient answer is shadow casting: cast rays only to the corners of obstacles, sort the hit points by angle around the viewer, and connect them into a single polygon. Everything inside that polygon is visible; everything outside it is hidden behind a wall.

This is the same family of algorithm behind fog of war in strategy games, flashlight cones in horror games, and the vision checks that make stealth games work: if the polygon that contains the player also contains a guard's position, the guard can, in principle, see the player.

Why corners, not pixels

A visibility polygon is entirely determined by the corners of every obstacle in the scene, plus the two extreme rays that graze each obstacle's silhouette. For each corner, a ray from the viewer either stops exactly at that corner (nothing beyond it is visible in that direction) or continues past it until it hits something else. So the algorithm casts one ray directly at every corner and two more rays at a tiny angle either side of it, to catch the sliver of space that opens up just past the edge:

for each obstacle corner c:
  cast ray at angle(c) - epsilon
  cast ray at angle(c)
  cast ray at angle(c) + epsilon
sort all hit points by angle
connect them in order  →  visibility polygon

Sorting by angle around the NPC is what turns a scatter of ray/wall intersections into a single connected shape. Fan-sort the hit points, walk around them once, and each consecutive pair plus the viewer forms one triangle of the polygon — draw all the triangles as a filled shape and you get the light-coloured wedge the player actually sees, complete with sharp shadow edges exactly at obstacle corners.

Adding a field-of-view cone and a range

A full 360° visibility polygon models an omniscient sensor; real NPCs look in one direction with a limited cone and a maximum sight distance. Both are cheap additions: clip the ray-casting to angles inside [facing − fov/2, facing + fov/2], and cap every ray's length at the sight radius, treating the range boundary itself as a curved "obstacle" whose arc gets filled in with extra rays so the visibility polygon closes smoothly instead of ending in a jagged edge.

visible = angle_in_fov(target, npc.facing, npc.fovAngle)
       and distance(npc.pos, target) < npc.sightRange
       and not blocked_by_any_obstacle(npc.pos, target)

From geometry to gameplay

Once you have the visibility polygon, stealth mechanics fall out almost for free. A point-in-polygon test tells you whether the player is currently seen. Accumulating time spent inside the cone before triggering full alert (rather than an instant detection) is what makes sneaking past a guard feel fair instead of arbitrary — most shipped stealth games use a "suspicion meter" that fills while the player is inside the polygon and drains when they leave it, rather than a hard boolean.

The same visibility polygon can drive sound and light propagation too: a torch's glow, a gunshot's noise radius intersected with line-of-sight, or a security camera's rotating cone are all the identical shadow-casting computation with different rays, ranges and update rates.

Performance notes

For a scene with n obstacle corners the sort-and-sweep algorithm above runs in O(n log n) per query, dominated by the angle sort — fast enough to recompute every frame for dozens of NPCs against a few hundred wall segments, which is exactly what the simulation on this page does with rectangular obstacles you can drag and resize. Large open-world games instead precompute a static visibility structure once (a navmesh's dual graph, or a portal/cell decomposition of the level) and only run per-frame ray casts for moving obstacles, because re-sorting thousands of corners sixty times a second for every guard does add up.

Frequently asked questions

Try it live

Everything above runs in your browser — open Field of View and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.