A Practical Checklist for Implementing a Custom Physics Engine in C++

Every game engine developer hits a point where off-the-shelf physics libraries feel like a black box. Maybe you need custom behavior for a rope-swing mechanic, or you're targeting a platform where existing engines don't run well. Rolling your own physics engine in C++ is a rewarding but error-prone journey. This checklist breaks down what you actually need to do — and what you should skip — to get a working rigid body simulator without drowning in math papers.

1. Who Should Build a Custom Physics Engine — and When It Backfires

Before you write a single Vec3 class, ask yourself: what problem are you solving that Box2D, Bullet, or PhysX cannot? Many teams reach for a custom engine because they want total control or because they think existing solutions are too heavy. Both are valid reasons, but they come with a hidden cost: your own engine will lack the battle-tested edge cases that commercial libraries have handled for years.

Custom engines shine when your game has a very specific physical interaction that doesn't fit the standard rigid body model. Think of a grappling hook that needs custom rope constraints, or a 2D platformer where you want to override friction per-object in ways that a general solver makes difficult. In those cases, a minimal engine built around your exact needs can be faster and simpler.

However, if your goal is a generic 3D physics sandbox with stacking boxes and ragdolls, you are better off using an existing library. The time you save by not debugging joint limits and collision normals will dwarf the integration effort. One team I read about spent six months building a custom engine for a simple puzzle game, only to replace it with Box2D in a week when they realized their solver didn't handle stacked blocks reliably.

Signs you should not build your own

If any of these apply, reconsider: you need continuous collision detection for fast-moving objects; you want to simulate hundreds of interacting bodies at once; you have a tight deadline and physics is not your core mechanic; you are not comfortable with linear algebra and numerical stability concepts. Building a physics engine is a great learning exercise, but for a shipped product, the cost often outweighs the benefit.

2. Prerequisites: What You Need Before Writing Code

Assuming you've decided to proceed, let's talk about the math and tools you should have in place. You do not need a PhD in computational physics, but you do need a solid grasp of vector math, basic calculus (derivatives and integrals), and a willingness to debug floating-point issues.

Core math concepts

You will use vectors for positions, velocities, forces, and torques. Understand dot and cross products, matrix multiplication (for rotation), and how to represent orientation with quaternions or rotation matrices. For 2D engines, you can get away with simpler approaches, but for 3D, quaternions are almost mandatory to avoid gimbal lock.

You also need to understand Newton's laws and how to integrate them numerically. The most common integrator is symplectic Euler (semi-implicit Euler), which updates velocity first, then position. It's simple and reasonably stable for most game scenarios. Higher-order methods like Verlet or RK4 can improve energy conservation but add complexity.

Development environment

Set up a C++ project with a good build system (CMake is standard), a profiling tool (like Tracy or Visual Studio's profiler), and a debugging renderer that can draw collision shapes, contact points, and normals. Without visual debugging, you will spend hours guessing why objects fall through the floor. A library like Dear ImGui can help you tweak parameters at runtime.

Also decide on a math library early. You can write your own Vec3 and Mat4 classes, but using something like GLM or Eigen saves time and avoids common mistakes. Just be careful with alignment issues on SIMD-friendly platforms.

3. Core Workflow: From Broad Phase to Constraint Solving

A typical physics step has four stages: broad-phase collision detection, narrow-phase collision detection, constraint generation, and constraint solving. Let's walk through each with concrete advice.

Broad-phase collision detection

This stage quickly eliminates pairs of objects that cannot possibly collide. For small scenes with fewer than 50 objects, a brute-force O(n²) check might be fine. For larger scenes, use a spatial data structure like a grid (for 2D) or a dynamic AABB tree (for 3D). The idea is to partition space so you only test nearby pairs. Implement the sweep and prune algorithm for a simple and effective broad phase in 3D.

One pitfall: make sure your broad phase is conservative — it's okay to include pairs that do not actually collide (false positives), but missing a real collision (false negative) will cause objects to pass through each other.

Narrow-phase collision detection

For each candidate pair from the broad phase, compute exact contact points, normals, and penetration depth. For convex shapes, the Gilbert-Johnson-Keerthi (GJK) algorithm combined with the Expanding Polytope Algorithm (EPA) is the standard choice. GJK tells you whether two convex shapes intersect, and EPA gives the penetration depth and contact normal.

If you are doing a 2D engine, separating axis theorem (SAT) is simpler and works well for polygons and circles. For 3D, GJK is more general but requires implementing support functions for each shape (sphere, box, capsule, etc.).

For concave shapes, decompose them into convex parts (using a tool like V-HACD) or use a compound shape approach. Avoid implementing concave collision detection directly — it's much more complex and error-prone.

Constraint generation and solving

Once you have contact points, you need to generate constraints that prevent interpenetration and simulate friction. A common approach is to treat each contact as a constraint that keeps objects from moving into each other. Use an impulse-based solver (like the one described in Erin Catto's GDC presentations) that iterates over all constraints multiple times to converge on a solution.

Start with a simple sequential impulse solver: for each contact, compute the relative velocity, then apply an impulse along the contact normal to cancel the closing velocity. Add friction by applying impulses tangent to the contact. Use a fixed number of iterations (e.g., 10–20) to keep performance predictable.

4. Tools, Setup, and Environment Realities

Your physics engine will not work correctly the first time you run it. You need a debugging toolkit that reveals what the solver is doing. Here are the tools we recommend setting up before you start debugging.

Visual debugger

Render collision shapes, contact points, contact normals, and velocity vectors. The simplest approach is to use a debug drawing callback that your engine calls each frame. You can then visualize in your game's renderer or in a separate window. Without this, you will be blind to why a box is spinning wildly or why a character falls through the ground.

Unit tests for math and collision

Write tests for your vector operations, matrix inversion, and collision detection functions. For example, test that a sphere and a box at known positions produce the correct contact point. These tests catch regressions when you refactor your broad phase or solver.

Profiling

Physics engines are performance-sensitive. Profile your broad phase, narrow phase, and solver separately. In many engines, the solver takes the most time, so optimize there first. Use techniques like SIMD for vector operations, and avoid memory allocations in the hot loop by pre-allocating contact arrays.

One common environment issue: floating-point determinism. If you need deterministic physics (for replay or networked games), you must control the order of operations carefully. Using _mm_set_ss or std::fma can give different results on different compilers. Consider using a fixed-point or integer-based math if determinism is critical.

5. Variations for Different Constraints: 2D vs 3D, Soft Bodies, and More

The checklist above is for a standard rigid body engine, but your game might need variations. Here are the most common adaptations.

2D vs 3D engines

2D engines are simpler because you only have one rotational axis (the z-axis). You can use scalar for orientation and 2D vectors for everything. The broad phase can be a simple grid or sweep and prune on the x and y axes. Narrow phase uses SAT for polygons and circles. Constraints are easier because you only need to handle one torque axis.

3D engines require quaternions for rotation, a more complex broad phase (like dynamic AABB tree), and GJK for narrow phase. The solver must handle three rotational axes, which makes joint limits and motors more involved.

Adding soft bodies

If you need cloth, ropes, or deformable objects, consider a mass-spring system. This is a separate subsystem from rigid bodies. You can couple soft bodies to rigid bodies via constraints (e.g., a rope attached to a box). Start with a simple spring network and use Verlet integration for better stability. Be aware that soft bodies are expensive — limit the number of particles and springs.

Continuous collision detection (CCD)

Fast-moving objects (bullets, fast projectiles) can tunnel through thin geometry in a single time step. CCD solves this by computing the time of impact (TOI) and stepping to that time. Implementing CCD for arbitrary shapes is complex; start by applying CCD only to small, fast objects using ray-sphere or swept sphere tests.

6. Pitfalls, Debugging, and What to Check When It Fails

Even with a careful plan, things will go wrong. Here are the most common bugs and how to fix them.

Objects falling through the floor

This usually means your collision detection missed a contact, or your solver didn't apply enough impulse. Check that your broad phase includes the floor-object pair. Then verify that the narrow phase produces a contact with a normal pointing upward and a penetration depth that is positive. Finally, ensure your solver applies an impulse that cancels the relative velocity along the normal. A common mistake is to apply the impulse in world space instead of relative to the contact point.

Exploding objects

Objects suddenly gain huge velocity and fly away. This is often caused by a large penetration depth that the solver tries to correct in one step, overcompensating. Fix this by clamping the correction impulse or by using a small restitution coefficient. Also check that your integration step size is small enough — if your timestep is too large, the solver becomes unstable.

Jittering or vibrating contacts

When objects rest on top of each other, they may bounce slightly each frame. This is a common symptom of a solver that does not converge well. Increase the number of solver iterations, or add a small