Learning
Deconstructing the mathematical structures behind the meta.
The Geometry of War Graph Theory in FPS
Line-of-Sight as a Visibility Graph
In games like Counter-Strike 2 or Valorant, a map is mathematically defined as a polygon with holes. The "holes" are the obstacles (crates, walls, pillars).
When you "hold an angle," you are establishing a Visibility Edge between two points in the environment. The entire set of possible sightlines forms a Visibility Graph, where nodes are the corners of obstacles, and edges exist only if the line segment between them does not intersect the interior of any obstacle.
"The 'Visibility Complex' takes this further, mapping all lines of sight into a 2D topological space. Understanding this is how aimbots optimize target acquisition—they are solving a pathfinding problem on a visibility graph, not 'looking' at pixels."
"Act as a Computational Geometer. Explain the difference between a 'Visibility Graph' and a 'Visibility Complex' in the context of a 2D video game map.
Then, provide a Python script using the 'matplotlib' and 'shapely' libraries to:
1. Define a simple room with 2 rectangular obstacles.
2. Calculate the Visibility Graph from a specific player coordinate (Point P).
3. Visualize the resulting 'Line of Sight' polygon."
Visualize how the game engine determines if you are exposed.
Module: Probability Fields
Markov Chains in Loot Tables and RNG manipulation.
Module: Nash Equilibria
Game Theory applications in Pick/Ban phases.