How Physics Engines Simulate Movement in Games

Physics engines are the software components responsible for translating the laws of physical science into the virtual environments of modern video games. This article explains how these engines simulate realistic movement by breaking down their core mechanisms, including rigid body dynamics, collision detection, collision resolution, and numerical integration. By understanding these pillars, developers can create interactive worlds where objects fall, bounce, and collide just as they would in the real world.

Rigid Body Dynamics

At the heart of any physics engine is rigid body dynamics. In game development, most objects are treated as “rigid bodies,” meaning they are perfectly solid and do not deform or change shape when forces are applied to them.

To simulate movement, the engine assigns physical properties to these virtual objects, including mass, velocity, acceleration, and center of mass. When a force—such as gravity, wind, or a player’s input—is applied to a rigid body, the engine uses Newton’s second law of motion (\(F=ma\), or Force equals mass times acceleration) to calculate how the object’s velocity and position should change.

Collision Detection

For movement to feel realistic, objects must interact with their surroundings rather than passing through them. Physics engines achieve this through a two-phase process called collision detection:

Broad-Phase Detection: To save computational power, the engine first performs a quick, approximate check. It surrounds complex game objects with simple geometric shapes like spheres or boxes (called bounding volumes). If these simple boxes do not overlap, the engine knows no collision has occurred.
Narrow-Phase Detection: If the bounding boxes do overlap, the engine performs a highly detailed, mathematically intensive calculation on the actual geometry of the objects to determine the exact point of contact, the collision angle, and how deeply the objects have penetrated each other.

Collision Resolution

Once a collision is detected, the engine must calculate the physical response, a process known as collision resolution. The engine calculates new velocities for the colliding objects based on their mass, friction, and elasticity (bounciness).

For example, a billiard ball hitting a wall will bounce off with almost equal speed due to high elasticity, while a ball of clay will stick to the wall. The engine also applies frictional forces to simulate sliding or rolling resistance, slowing objects down as they move across surfaces.

Numerical Integration

Computers cannot calculate physics continuously; instead, they calculate them in discrete steps called ticks or frames. Numerical integration is the mathematical process used to update the position and velocity of objects from one frame to the next.

The engine takes the current velocity of an object, multiplies it by the time elapsed since the last frame (delta time), and adds that value to the object’s current position. The most common integration methods are: * Euler Integration: A simple and fast method, though it can become unstable when dealing with high speeds or complex constraints. * Verlet Integration: A more stable method frequently used for simulating rope, cloth, and ragdoll physics, as it calculates position based on the history of previous frames.

Constraints and Joints

To simulate complex structures like ragdoll characters, rope bridges, or vehicle suspensions, physics engines use constraints and joints. Constraints limit the degrees of freedom of a rigid body.

For example, a hinge joint allows a door to rotate along only one axis while preventing it from flying off its frame. By linking multiple rigid bodies together with various joints and constraints, developers can create complex, lifelike movement patterns that react dynamically to the game world.