Physics engine is a [software](software.md) (usually a [library](library.md)) whose purpose is to simulate physics laws of mechanics, i.e. things such as forces, [rigid](rigid_body.md) and [soft](soft_body.md) body collisions, [particle](particle.md) motion, fluid dynamics etc.
{ When it comes to classic 3D rigid body physics engines, they're extremely hard to make, much harder than for example an advanced 3D rendering engine, especially when you want to make them [LRS](lrs.md) (without floating point, ...) and/or general and somewhat physically correct (being able to simulate e.g. the Dzhanibekov effect, satisfying all the conservation laws, continuous collision detection etc.). Good knowledge of mechanics and things like [quaternions](quaternion.md) and 3D rotations is just the beginning, difficulties arise in every aspect of the engine, and of those there are many. As I've found, 32 bit fixed point is not enough for a general engine (even though it is enough for a rendering engine), you'll run into precision problems as you need to represent both relatively high and low energies. You'll also run into stability issues such as stable contacts, situations with multiple objects stacked on top of each other starting to bounce on their own etc. Even things such as deciding in what order to resolve collisions are very difficult, they can lead to many bugs such as a car not being able to drive on a straight road made of several segments. Collision detection alone for all combinations of basic shapes (sphere, cuboid, cylinder, capsule, ... let alone general triangle mesh) are hard as you want to detect general cases (not only e.g. surface collisions) and you want to extract all the parameters of the collisions (collision location, depth, normal etc.) AND you want to make it fast. And of course you'll want to add acceleration structures and many other thing on top. So think twice before deciding to write your own physics engine.
A sane approach may be to write a simplified engine specifically for your program, for example a Minetest-like game may just need non-rotating capsules in a voxel environment, that's not that hard. You can also get away with a bit of cheating and faking, e.g. simulating rigid bodies as really stiff soft bodies, it may not be as efficient and precise but it's simpler to program. It may be [good enough](good_enough.md). Well, that's basically what [tinyphysicsengine](tinyphysicsengine.md) does anyway. Old playstation game Rally Cross apparently did something similar too. ~drummyfish }
Physics engine is a wide term even though one usually imagines the traditional 3D rigid body engine used in games such as [GTA](gta.md). These engines may nevertheless have different purposes, features and even basic paradigms, some may e.g. be specialized just for computing precise ballistic trajectories for the army, some may serve for simulating weather etc. Some common classifications and possible characteristics of physics engines follow:
- **[2D](2d.md) vs [3D](3d.md)**: 2D engines are generally much more simple to implement than 3D, for example because of much more simple math for rotations and collision detection. Graphics and physics are usually loosely interconnected (though they should be [decoupled](coupling.md)) in that the way in which we represent graphics (2D, general 3D, [BSP](bsp.md), [voxels](voxel.md), ...) usually also determines how we compute physics, so that there may also exist e.g. "[pseudo 3D](pseudo_3d.md)" physics engines as part of "pseudo 3D" renderers, e.g. the one used in [Doom](doom.md) etc.
- **[real time](real_time.md) vs [offline](offline.md)**: Real-time ones are mostly intended to be used in the entertainment industry, i.e. [games](game.md), movies etc. as they can compute somewhat realistic looking results quickly but for the price of dropping high accuracy (they use many [approximations](approximation.md)). Scientific engines may prefer to be offline and taking longer time to compute more precise results.
- **[rigid body](rigid_body.md) vs [soft body](soft_body.md)**: Rigid body engines don't allow bodies to deform while soft body ones do -- in real life all bodies are soft, but neglecting this detail and considering shapes rigid can have benefits (such as being able to consider the body as a whole and not having to simulate all its individual points). Of course, a complex engine may implement both rigid and soft body physics.
- **paradigm**: The basic approach to implementing the simulation, e.g. being [impulse](impulse.md)-based (applying impulses to correct errors), constraint-based (solving equations to satisfy imposed constraints), penalty-based (trying to find equilibriums of forces) etc.
- **[discrete](discrete.md) vs [continuous](continuous.md) collision detection**: Discrete collision detection only detects collisions at single points in time (at each engine tick) and are simple than those implementing continuous collision detection. Discrete engine are less accurate, consider e.g. that a very fast moving object can pass through a wall because at one instant it is in front of it while at the next tick it is behind it. Continuous collisions won't allow this to happen, but are more difficult to program, may be slower etc. For games discrete collisions are usually [good enough](good_enough.md).
- **purpose and accuracy**: The basic categories are precise, scientific and often special-purpose engines, and engines meant for entertainment and less accurate visualizations such as games and movies.
- **features: fluid, cloth, particles, [ragdoll](ragdoll.md), [inverse kinematics](inverse_kinematics.md), [GPU](gpu.md) acceleration, [determinism](determinism.md), [voxels](voxel.md), [acceleration](acceleration.md) [data structures](data_structure.md) ...**: These are a number of additional features the engine can have such as the ability to simulate fluids (which itself is a huge field of its own) or cloths, some go as far as e.g. integrating motion-captured animations of humans with physics to create smooth realistic animations e.g. of running over walking pedestrians with a car and so on.
A typical physics engine will work something like this: we create a so called **physics world**, a [data structure](data_structure.md) that represents the space in which the simulation takes place (it is similar to a [scene](scene.md) in rendering engines). We then populate this world with physics elements such as rigid bodies (which can have attributes such as mass, elasticity etc.). These bodies are normally basic geometric shapes such as spheres, cylinders, boxes or capsules, or objects composed of several such basic shapes. This is unlike with rendering engines in which we normally have triangle meshes -- in physics engines triangle meshes are extremely slow to process, so for the sake of a physics engine we approximate this mesh with some of the above basic shapes (for example a creature in a game that's rendered as a hi-poly 3D model may in the physics engine be represented just as a simple sphere). Furthermore the bodies can be **[static](static.md)** (cannot move, this is sometimes done by setting their mass to infinity) or **[dynamic](dynamic.md)** (can move); static bodies normally represent the environment (e.g. the game level), dynamic ones the entities in it (player, NPCs, projectiles, ...). Making a body static has performance benefits as its movement doesn't have to be calculated and the engine can also precalculate some things for it that will make e.g. collision detections faster. We then simulate the physics of the world in so called *ticks* (similar to [frames](frame.md) in rendering); in simple cases one tick can be equivalent to one rendering frame, but properly it shouldn't be so (physics shouldn't be affected by the rendering speed, and also for the physics simulation we can usually get away with smaller "[FPS](fps.md)" than for rendering, saving some performance). Usually one tick has set some constant time length (e.g. 1/60th of a second). In each tick the engine performs a **[collision detection](collision.md)**, i.e. it finds out which bodies are touching or penetrating other bodies (this is accelerated with things such as [bounding spheres](bounding_volume.md)). Then it performs so called **collision resolution**, i.e. updating the positions, velocities and forces so that the bodies no longer collide and react to these collisions as they would in the real world (e.g. a ball will bounce after hitting the floor). There can be many more things, for example **constraints**: we may e.g. say that one body must never get further away from another body than 10 meters (imagine it's tied to it by a rope) and the engine will try to make it so that this always holds. The engine will also offer a number of other functions such as casting rays and calculating where it hits (obviously useful for shooter games).
**Integrating physics with graphics**: you will most likely use some kind of graphics engine along with physics engine, even if just for [debugging](debugging.md). As said above, keep in mind a graphics and physics engines should be **strictly separated** ([decoupled](coupling.md), for a number of reasons such as [reusability](reusability.md), easier debugging, being able to switch graphics and physics engines etc.), even though they closely interact and may affect each other in their design, e.g. by the data structures you choose for your program (voxel graphics will imply voxel physics etc.). In your program you will have a **physics world and a graphics scene**, both contain their own elements: the scene has graphics elements such as 3D models or particle systems, the physics world has elements such as rigid bodies and force fields. Some of the graphical and physics entities are connected, for example a 3D model of a tree may be connected to a physics rigid body of a cone shape. NOT ALL graphics elements have counterparts in the physics simulation (e.g. a smoke effect or light aren't present in the physics simulation) and vice versa (e.g. player in a first-person game has no 3D model but still has some physics shape). The connection between graphics and physics elements should be done **above** both engines (i.e. do NOT add pointers to physics object to graphics elements etc.). This means that e.g. in a game you create a higher abstract environment -- for example a level -- which stands above the graphics scene and physics world and has its own game elements, each game element may be connected to a graphics or physics element. These game elements have attributes such as a position which gets updated according to the physics engine and which is transferred to the graphics elements for rendering. Furthermore remember that **graphics and physics should often run on different "FPS"**: graphics engines normally try to render as fast as they can, i.e. reach the highest [FPS](fps.md), while physics engines often have a time step, called a **tick**, of fixed time length (e.g. 1/30th of a second) -- this is so that they stay [deterministic](determinism.md), accurate and also because physics may also run on much lower FPS without the user noticing ([interpolation](interpolation.md) can be used in the graphics engine to smooth out the physics animation for rendering). "[Modern](modern.md)" engines often implement graphics and physics in separate [threads](thread.md), however this is not [suckless](suckless.md), in most cases we recommend the [KISS](kiss.md) approach of a single thread (in the main loop keep a timer for when the next physics tick should be simulated).
## Existing Engines
One of the best and most famous [FOSS](foss.md) 3D physics engines is [Bullet](bullet_physics.md) ([zlib](zlib.md) license), it has many features (rigid and soft bodies, GPU acceleration, constraints, ...) and has been used in many projects ([Blender](blender.md), [Godot](godot.md), ...). [Box2D](box2d.md) is a famous 2D physics engine under [MIT](mit.md) license, written in [C++](cpp.md).
