Board Games & Game Mathematics

Game mathematics simulations cover the core computational geometry and physics algorithms that power interactive video games. Bounding-volume collision-detection simulations compare AABB–AABB, sphere–sphere, and GJK algorithms, showing the contact manifold and response impulse for each approach. Raycasting simulations build a pseudo-3D corridor from a 2D map using the same ray-DDA technique used in Wolfenstein 3D and early Doom.

Quaternion rotation visualisers demonstrate the spherical-linear interpolation (SLERP) that produces smooth camera and character animation without gimbal lock. Spatial-hashing and quad-tree demos show how broad-phase collision detection scales from O(n²) to O(n) as object count increases. These are the mathematical foundations every game programmer must master, and seeing them animated makes the algebra of cross products, dot products, and determinants immediately geometric.

Each simulation in this category is built with accuracy and interactivity in mind. The underlying mathematical models are the same ones used in academic research and professional engineering — just made accessible through a web browser. Changing parameters in real time and observing the results is one of the most effective ways to build intuition for complex scientific and engineering concepts.