AABB Collision

AABB (Axis-Aligned Bounding Box): rectangle aligned with x,y axes.

Two AABBs intersect iff they overlap on BOTH axes:

For axis overlap: a's max ≥ b's min AND a's min ≤ b's max.

Compute penetration depth:

Resolve along the smaller axis:

This is a simple positional fix. Real engines use impulses (momentum) for more realistic bouncing.

Other shapes:

• Circle: distance between centers < sum of radii.
• Capsule: rectangle + 2 semicircles. Common for character collision.
• OBB (Oriented Bounding Box): rotated. Use SAT (Separating Axis Theorem).
• Convex polygon: SAT or GJK algorithm.

Circle vs circle:

Circle vs AABB:

Find closest point on AABB to circle, compare distance to radius.

These tests are O(1) per pair. Need to optimize O(N²) for many bodies.