2D Physics Engine in C++

The brief

The gravity sim handled forces between distant bodies; this one handles the harder problem — what happens when things touch. A 2D rigid-body engine with collision detection and impulse-based resolution, built to understand what Box2D does before reaching for it.

The build

• Shapes — circles and axis-aligned bounding boxes, with all four pairwise collision tests (circle-circle, circle-AABB via closest-point clamping, AABB-AABB)
• Contact manifold — each detected collision produces a contact normal and penetration depth, the two numbers everything downstream depends on
• Impulse resolution — j = −(1+e)(v·n̂) / (1/mₐ + 1/m_b) applied along the normal, with restitution e tunable per body; positional correction (Baumgarte-style) to stop resting objects sinking
• Fixed timestep loop — simulation at a fixed Δt with render interpolation, after watching variable timesteps make identical scenes non-deterministic

What I learned

Collision detection is geometry; collision response is where the physics lives, and the impulse formula is doing more work than its one line suggests. Penetration correction is the difference between a demo and an engine — without it, every stack of boxes slowly becomes soup.