Physics Engines: Mastering Law Application In Virtual Worlds

Physics engines are an integral part of modern video games, providing an immersive experience by simulating real-world physics. They are responsible for determining the positions of objects in a scene over time, taking into account factors such as velocity, acceleration, and external forces. These engines use numerical methods to apply physical laws, such as Newton's three laws of motion, to predict object behaviour. The challenge lies in handling complex interactions, such as collisions, and ensuring that the simulation remains stable and responsive. To achieve this, physics engines employ various techniques, including impulse-based methods, constraint-based methods, and hybrid approaches. Additionally, they may utilise simplified calculations and reduced accuracy to achieve real-time performance, striking a balance between speed and precision.

Physics engines are used in video games and CGI to simulate physical systems

There are generally two classes of physics engines: real-time and high-precision. High-precision physics engines require more processing power to calculate very precise physics and are usually used by scientists and in computer-animated movies. Real-time physics engines, as used in video games and other forms of interactive computing, use simplified calculations and decreased accuracy to compute in time for the game to respond at an appropriate rate for gameplay.

The motion of rigid bodies can be modelled using Newtonian mechanics, which is founded upon Isaac Newton's famous Three Laws of Motion:

• Inertia: If no force is applied to an object, its velocity (speed and direction of motion) shall not change.
• Force, Mass, and Acceleration: The force acting on an object is equal to the mass of the object multiplied by its acceleration (the rate of change of velocity). This is given by the formula F = ma.
• Action and Reaction: "For every action, there is an equal and opposite reaction." In other words, whenever one body exerts a force on another, the second body exerts a force of the same magnitude and opposite direction on the first.

Based on these three laws, physics engines are able to reproduce the dynamic behaviour we're so familiar with, creating an immersive experience for the player.

The first general-purpose computer, ENIAC, was used as a very simple type of physics engine. It was used to design ballistics tables to help the US military estimate where artillery shells of various masses would land when fired at varying angles and gunpowder charges, also accounting for drift caused by wind.

There are two classes of physics engines: real-time and high-precision

A physics engine is a complex software system that simulates certain physical systems within a game, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics. It is a component of a larger program, such as a game, and is not usually a standalone program. The physics engine takes as input a collection of objects ("bodies") with properties such as mass, shape, and whether they are rigid or soft. It then simulates and outputs the updated positions and orientations of these objects, applying the relevant physics.

The physics of a game do not have to be identical to real life; they can be whatever the developer decides. However, the more accurate the physics, the more processing power is required. This can cause problems in games, where speed and gameplay are often prioritised over accuracy. As a result, physics engines in games often produce "perceptually correct" approximations rather than true simulations.

To achieve real-time performance, game physics engines use simplified calculations and decreased accuracy. For example, a complex object like a vase may be treated as a simple cylinder by the physics engine, which is unaware of details like handles. This can lead to limitations, such as the inability to insert a rod through the handle of the vase. Additionally, a low framerate can cause issues where small, fast-moving objects seem to teleport from one point to another, potentially missing their targets.

Physics engines use numerical methods to obtain results that are close to real-world observations

Physics engines are used to simulate the motions and reactions of objects as if they were under the constraints of real-world physics. They are a component of a larger program, such as a game, and are responsible for providing an approximate simulation of physical systems. Physics engines use numerical methods to obtain results that are close to real-world observations.

Physics simulation is a field within computer science that aims to reproduce physical phenomena using a computer. By applying numerical methods to existing theories, physics engines can generate outcomes that closely match what we observe in the real world. This allows game developers to predict and analyse how objects would behave before actually building them, which is often simpler and more cost-effective.

Physics engines take input, process it, and produce output. The input typically includes a collection of objects ("bodies") with properties such as mass, shape, and the forces acting on them. The engine then simulates the updated positions and orientations of these bodies, applying the results to the game environment.

The motion of rigid bodies, which are solids that cannot deform, is commonly simulated in games. Newtonian mechanics, founded on Isaac Newton's Three Laws of Motion, is used to model the behaviour of these bodies. This includes principles such as inertia, force, mass, acceleration, and action and reaction.

To achieve real-time simulation, physics engines use simplified calculations and decreased accuracy compared to high-precision engines used in scientific research. This trade-off between accuracy and speed ensures that games can respond at an appropriate rate for gameplay while still providing a reasonably realistic representation of physics.

In summary, physics engines utilise numerical methods and simplified calculations to produce outcomes that closely match real-world observations. This enables developers to create immersive gaming experiences while managing the computational demands of simulating complex physical interactions.

Rigid body dynamics is the most popular kind of effect simulated in games

Physics engines are responsible for simulating the motions and reactions of objects as if they were under the constraints of real-world physics. They are usually a component of a larger program, such as a game.

Rigid body dynamics, which simulate the movement and interaction of solid, inflexible objects, is the most popular kind of effect simulated in games. This is because most games are inspired by things we have in the real world, and most objects we encounter in real life are quite rigid.

The physics engine receives the specifications of the simulated bodies and some configuration parameters. It then advances the simulation by a fraction of a second, and this can be displayed on the screen. The engine can also output the updated positions and orientations of the bodies, which can then be used by client code to handle specific gameplay logic relevant to the collision.

The physics engine uses Newtonian mechanics to simulate the motion of rigid bodies. This is based on Isaac Newton's Three Laws of Motion. For example, the law of inertia states that an object will not move if it is not subject to any force. Another of Newton's laws states that a force exerted on an object is equal to its mass multiplied by its acceleration (F = ma).

Physics engines use vectors and their operations to model the motion of rigid bodies

Physics engines are used to simulate the motions and reactions of objects as if they were under the constraints of real-world physics. They are responsible for modelling the motion of objects in "the world" (the context of the engine). Most physics engines use Newtonian mechanics to simulate motion, taking into account the state of the world, the time that has passed, and the forces acting on the objects.

In a physics engine, vectors are used to represent both points and arrows. For example, a point (5,3) can be modelled as the vector [5,3], assuming the tail of the vector is at the origin (0,0). This approach offers two main advantages: it reduces the number of data types needed, and it simplifies mathematical operations. With vectors, basic operations like addition, subtraction, multiplication, dot product, cross product, and rotation become applicable to points as well.

Additionally, vectors enable the abstraction of "2D vs 3D" calculations. Instead of using separate variables for each dimension, vectors allow for unified calculations that can be easily extended from 2D to 3D. This flexibility is particularly useful when dealing with translation (movement in left/right, up/down, back/forth directions) and rotation.

To simulate motion, physics engines use Newton's equations of motion, specifically Newton's second law of motion, which relates an object's acceleration to the force applied to it. By calculating the forces acting on an object, the engine can determine its acceleration, velocity, and position over time. This process involves numerical integration techniques, such as Euler's method or Velocity Verlet integration, to update an object's position and velocity at each time step.

When dealing with rigid bodies, physics engines also need to consider angular velocity and angular acceleration. These quantities are described using vectors and matrices, with each body having a scalar mass and a body mass moment of inertia tensor. The current state of the body includes its position, orientation, linear momentum, and angular momentum. By applying forces and torques, the engine can update the body's state at each time step, simulating its motion and rotation.

In summary, physics engines use vectors and their operations to model the motion of rigid bodies by separating equations of motion into axis-specific calculations, performing basic mathematical operations on vectors, and applying Newton's laws of motion to update an object's position, velocity, and acceleration over time.

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