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A physics engine is
computer software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists ...
that provides an approximate
simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...
of certain
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment. The environment is ignored except for its effects on the ...
s, such as
rigid body dynamics In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of a ...
(including
collision detection Collision detection is the computational problem of detecting the intersection of two or more objects. Collision detection is a classic issue of computational geometry and has applications in various computing fields, primarily in computer grap ...
),
soft body dynamics Soft-body dynamics is a field of computer graphics that focuses on visually realistic physical simulations of the motion and properties of deformable objects (or ''soft bodies''). The applications are mostly in video games and films. Unlike in sim ...
, and
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
, of use in the domains of
computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...
,
video game Video games, also known as computer games, are electronic games that involves interaction with a user interface or input device such as a joystick, controller, keyboard, or motion sensing device to generate visual feedback. This fee ...
s and film ( CGI). Their main uses are in video games (typically as
middleware Middleware is a type of computer software that provides services to software applications beyond those available from the operating system. It can be described as "software glue". Middleware makes it easier for software developers to implement co ...
), in which case the simulations are in
real-time Real-time or real time describes various operations in computing or other processes that must guarantee response times within a specified time (deadline), usually a relatively short time. A real-time process is generally one that happens in defined ...
. The term is sometimes used more generally to describe any software system for simulating physical phenomena, such as high-performance scientific simulation.


Description

There are generally two classes of physics
engine An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power gen ...
s:
real-time Real-time or real time describes various operations in computing or other processes that must guarantee response times within a specified time (deadline), usually a relatively short time. A real-time process is generally one that happens in defined ...
and high-precision. High-precision physics engines require more processing power to calculate very precise physics and are usually used by scientists and 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 game play.


Scientific engines

One of the first general purpose computers,
ENIAC ENIAC (; Electronic Numerical Integrator and Computer) was the first programmable, electronic, general-purpose digital computer, completed in 1945. There were other computers that had these features, but the ENIAC had all of them in one packa ...
, was used as a very simple type of physics engine. It was used to design ballistics tables to help the United States military estimate where
artillery Artillery is a class of heavy military ranged weapons that launch munitions far beyond the range and power of infantry firearms. Early artillery development focused on the ability to breach defensive walls and fortifications during siege ...
shells of various mass would land when fired at varying angles and gunpowder charges, also accounting for drift caused by wind. The results were calculated a single time only, and were tabulated into printed tables handed out to the artillery commanders. Physics engines have been commonly used on supercomputers since the 1980s to perform
computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate th ...
modeling, where particles are assigned
force vector In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
s that are combined to show circulation. Due to the requirements of speed and high precision, special computer processors known as
vector processor In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called ...
s were developed to accelerate the calculations. The techniques can be used to model weather patterns in
weather forecasting Weather forecasting is the application of science and technology forecasting, to predict the conditions of the Earth's atmosphere, atmosphere for a given location and time. People have attempted to predict the weather informally for millennia a ...
, wind tunnel data for designing air- and watercraft or motor vehicles including racecars, and thermal cooling of computer processors for improving
heat sink A heat sink (also commonly spelled heatsink) is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, th ...
s. As with many calculation-laden processes in computing, the accuracy of the simulation is related to the resolution of the simulation and the precision of the calculations; small fluctuations not modeled in the simulation can drastically change the predicted results. Tire manufacturers use physics simulations to examine how new
tire tread The tread of a tire or track refers to the rubber on its circumference that makes contact with the road or the ground. As tires are used, the tread is worn off, limiting its effectiveness in providing traction. A worn tire can often be retrea ...
types will perform under wet and dry conditions, using new tire materials of varying flexibility and under different levels of weight loading.


Game engines

In most computer games, speed of the processors and
gameplay Gameplay is the specific way in which players interact with a game, and in particular with video games. Gameplay is the pattern defined through the game rules, connection between player and the game, challenges and overcoming them, plot and pla ...
are more important than accuracy of simulation. This leads to designs for physics engines that produce results in real-time but that replicate real world physics only for simple cases and typically with some approximation. More often than not, the simulation is geared towards providing a "perceptually correct" approximation rather than a real simulation. However some game engines, such as
Source Source may refer to: Research * Historical document * Historical source * Source (intelligence) or sub source, typically a confidential provider of non open-source intelligence * Source (journalism), a person, publication, publishing institute o ...
, use physics in puzzles or in combat situations. This requires more accurate physics so that, for example, the momentum of an object can knock over an obstacle or lift a sinking object. Physically-based character animation in the past only used
rigid body dynamics In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of a ...
because they are faster and easier to calculate, but modern games and movies are starting to use soft body physics. Soft body physics are also used for particle effects, liquids and cloth. Some form of limited
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
simulation is sometimes provided to simulate water and other liquids as well as the flow of fire and explosions through the air.


Collision detection

Objects in games interact with the player, the environment, and each other. Typically, most 3D objects in games are represented by two separate meshes or shapes. One of these meshes is the highly complex and detailed shape visible to the player in the game, such as a vase with elegant curved and looping handles. For purpose of speed, a second, simplified invisible mesh is used to represent the object to the physics engine so that the physics engine treats the example vase as a simple cylinder. It would thus be impossible to insert a rod or fire a projectile through the handle holes on the vase, because the physics engine model is based on the cylinder and is unaware of the handles. The simplified mesh used for physics processing is often referred to as the collision geometry. This may be a
bounding box In geometry, the minimum or smallest bounding or enclosing box for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure ...
, sphere, or
convex hull In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ...
. Engines that use bounding boxes or bounding spheres as the final shape for collision detection are considered extremely simple. Generally a bounding box is used for broad phase collision detection to narrow down the number of possible collisions before costly mesh on mesh collision detection is done in the narrow phase of collision detection. Another aspect of precision in discrete collision detection involves the
framerate Frame rate (expressed in or FPS) is the frequency (rate) at which consecutive images ( frames) are captured or displayed. The term applies equally to film and video cameras, computer graphics, and motion capture systems. Frame rate may also be ...
, or the number of moments in time per second when physics is calculated. Each frame is treated as separate from all other frames, and the space between frames is not calculated. A low framerate and a small fast-moving object causes a situation where the object does not move smoothly through space but instead seems to teleport from one point in space to the next as each frame is calculated. Projectiles moving at sufficiently high speeds will miss targets, if the target is small enough to fit in the gap between the calculated frames of the fast moving projectile. Various techniques are used to overcome this flaw, such as ''
Second Life ''Second Life'' is an online multimedia platform that allows people to create an avatar for themselves and then interact with other users and user created content within a multi player online virtual world. Developed and owned by the San Fra ...
''s representation of projectiles as arrows with invisible trailing tails longer than the gap in frames to collide with any object that might fit between the calculated frames. By contrast, continuous collision detection such as in
Bullet A bullet is a kinetic projectile, a component of firearm ammunition that is shot from a gun barrel. Bullets are made of a variety of materials, such as copper, lead, steel, polymer, rubber and even wax. Bullets are made in various shapes and co ...
or Havok does not suffer this problem.


Soft-body dynamics

An alternative to using bounding box-based rigid body physics systems is to use a
finite element The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat t ...
-based system. In such a system, a 3-dimensional, volumetric
tessellation A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional ...
is created of the 3D object. The tessellation results in a number of finite elements which represent aspects of the object's physical properties such as toughness, plasticity, and volume preservation. Once constructed, the finite elements are used by a
solver A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates t ...
to model the stress within the 3D object. The stress can be used to drive fracture, deformation and other physical effects with a high degree of realism and uniqueness. As the number of modeled elements is increased, the engine's ability to model physical behavior increases. The visual representation of the 3D object is altered by the finite element system through the use of a
deformation shader Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * De ...
run on the CPU or GPU. Finite Element-based systems had been impractical for use in games due to the performance overhead and the lack of tools to create finite element representations out of 3D art objects. With higher performance processors and tools to rapidly create the volumetric tessellations, real-time finite element systems began to be used in games, beginning with '' Star Wars: The Force Unleashed'' that used
Digital Molecular Matter Digital Molecular Matter (DMM) is a proprietary middleware physics engine developed by Pixelux for generating realistic destruction and deformation effects. The offline version can support high-resolution simulations for use in film special effect ...
for the deformation and destruction effects of wood, steel, flesh and plants using an algorithm developed by Dr. James O'Brien as a part of his PhD thesis.


Brownian motion

In the real world, physics is always active. There is a constant
Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...
jitter to all particles in our universe as the forces push back and forth against each other. For a
game physics Computer animation physics or game physics are laws of physics as they are defined within a simulation or video game, and the programming logic used to implement these laws. Game physics vary greatly in their degree of similarity to real-world phy ...
engine, such constant active precision is unnecessarily wasting the limited CPU power, which can cause problems such as decreased
framerate Frame rate (expressed in or FPS) is the frequency (rate) at which consecutive images ( frames) are captured or displayed. The term applies equally to film and video cameras, computer graphics, and motion capture systems. Frame rate may also be ...
. Thus, games may put objects to "sleep" by disabling the computation of physics on objects that have not moved a particular distance within a certain amount of time. For example, in the 3D
virtual world A virtual world (also called a virtual space) is a computer-simulated environment which may be populated by many users who can create a personal avatar, and simultaneously and independently explore the virtual world, participate in its activities ...
Second Life ''Second Life'' is an online multimedia platform that allows people to create an avatar for themselves and then interact with other users and user created content within a multi player online virtual world. Developed and owned by the San Fra ...
, if an object is resting on the floor and the object does not move beyond a minimal distance in about two seconds, then the physics calculations are disabled for the object and it becomes frozen in place. The object remains frozen until physics processing reactivates for the object after collision occurs with some other active physical object.


Paradigms

Physics engines for video games typically have two core components, a
collision detection Collision detection is the computational problem of detecting the intersection of two or more objects. Collision detection is a classic issue of computational geometry and has applications in various computing fields, primarily in computer grap ...
/ collision response system, and the dynamics simulation component responsible for solving the forces affecting the simulated objects. Modern physics engines may also contain fluid simulations, animation
control systems A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial c ...
and asset integration tools. There are three major paradigms for the physical simulation of solids: * Penalty methods, where interactions are commonly modelled as mass-spring systems. This type of engine is popular for deformable, or soft-body physics. * Constraint based methods, where constraint equations are solved that estimate physical laws. * Impulse based methods, where
impulse Impulse or Impulsive may refer to: Science * Impulse (physics), in mechanics, the change of momentum of an object; the integral of a force with respect to time * Impulse noise (disambiguation) * Specific impulse, the change in momentum per uni ...
s are applied to object interactions. Finally, hybrid methods are possible that combine aspects of the above paradigms.


Limitations

A primary limit of physics engine
realism Realism, Realistic, or Realists may refer to: In the arts *Realism (arts), the general attempt to depict subjects truthfully in different forms of the arts Arts movements related to realism include: *Classical Realism *Literary realism, a move ...
is the approximated result of the constraint resolutions and collision result due to the slow convergence of algorithms. Collision detection computed at a too low frequency can result in object passing through each other and then be repelled with an abnormal correction force. In the other hand, approximated results of reaction force is due to the slow convergence of typical Projected Gauss Seidel solver resulting in abnormal bouncing. Any type of free-moving compound physics object can demonstrate this problem, but it is especially prone to affecting chain links under high tension and wheeled objects with actively physical bearing surfaces. Higher precision reduces the positional/force errors, but at the cost of greater CPU power needed for the calculations.


Physics processing unit (PPU)

A
physics processing unit A physics processing unit (PPU) is a dedicated microprocessor designed to handle the calculations of physics, especially in the physics engine of video games. It is an example of hardware acceleration. Examples of calculations involving a PPU mig ...
(PPU) is a dedicated microprocessor designed to handle the calculations of physics, especially in the physics engine of
video game Video games, also known as computer games, are electronic games that involves interaction with a user interface or input device such as a joystick, controller, keyboard, or motion sensing device to generate visual feedback. This fee ...
s. Examples of calculations involving a PPU might include
rigid body dynamics In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of a ...
,
soft body dynamics Soft-body dynamics is a field of computer graphics that focuses on visually realistic physical simulations of the motion and properties of deformable objects (or ''soft bodies''). The applications are mostly in video games and films. Unlike in sim ...
,
collision detection Collision detection is the computational problem of detecting the intersection of two or more objects. Collision detection is a classic issue of computational geometry and has applications in various computing fields, primarily in computer grap ...
,
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
, hair and clothing simulation,
finite element analysis The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...
, and fracturing of objects. The idea is that specialized processors offload time-consuming tasks from a computer's CPU, much like how a
GPU A graphics processing unit (GPU) is a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device. GPUs are used in embedded systems, mobi ...
performs graphics operations in the main CPU's place. The term was coined by
Ageia Ageia, founded in 2002, was a fabless semiconductor company. In 2004, Ageia acquired NovodeX, the company who created PhysX – a Physics Processing Unit chip capable of performing game physics calculations much faster than general purpose CPUs ...
's marketing to describe their PhysX chip to consumers. Several other technologies in the CPU-GPU spectrum have some features in common with it, although Ageia's solution was the only complete one designed, marketed, supported, and placed within a system ''exclusively'' as a PPU.


General-purpose computing on graphics processing unit (GPGPU)

Hardware acceleration for physics processing is now usually provided by graphics processing units that support more general computation, a concept known as
general-purpose computing on graphics processing units General-purpose computing on graphics processing units (GPGPU, or less often GPGP) is the use of a graphics processing unit (GPU), which typically handles computation only for computer graphics, to perform computation in applications traditiona ...
(GPGPU).
AMD Advanced Micro Devices, Inc. (AMD) is an American multinational semiconductor company based in Santa Clara, California, that develops computer processors and related technologies for business and consumer markets. While it initially manufactur ...
and
NVIDIA Nvidia CorporationOfficially written as NVIDIA and stylized in its logo as VIDIA with the lowercase "n" the same height as the uppercase "VIDIA"; formerly stylized as VIDIA with a large italicized lowercase "n" on products from the mid 1990s to ...
provide support for rigid body dynamics computations on their latest graphics cards. NVIDIA's GeForce 8 Series supports a GPU-based Newtonian physics acceleration technology named ''Quantum Effects Technology''. NVIDIA provides an SDK Toolkit for
CUDA CUDA (or Compute Unified Device Architecture) is a parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for general purpose processing, an approach ...
(
Compute Unified Device Architecture CUDA (or Compute Unified Device Architecture) is a parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for general purpose processing, an approach ...
) technology that offers both a low and high-level API to the GPU. For their GPUs,
AMD Advanced Micro Devices, Inc. (AMD) is an American multinational semiconductor company based in Santa Clara, California, that develops computer processors and related technologies for business and consumer markets. While it initially manufactur ...
offers a similar SDK, called
Close to Metal In computing, Close To Metal ("CTM" in short, originally called ''Close-to-the-Metal'') is the name of a beta version of a low-level programming interface developed by ATI, now the AMD Graphics Product Group, aimed at enabling GPGPU computing. CT ...
(CTM), which provides a thin hardware interface.
PhysX PhysX is an open-source realtime physics engine middleware SDK developed by Nvidia as a part of Nvidia GameWorks software suite. Initially, video games supporting PhysX were meant to be accelerated by PhysX PPU (expansion cards designed by ...
is an example of a physics engine that can use GPGPU based hardware acceleration when it is available.


Engines


Real-time physics engines

;Open source *
Advanced Simulation Library Advanced Simulation Library (ASL) is free and open-source hardware-accelerated multiphysics simulation platform. It enables users to write customized numerical solvers in C++ and deploy them on a variety of massively parallel architecture ...
- open source hardware accelerated multiphysics simulation software *
Box2D Box2D is a free open source 2-dimensional physics simulator engine written in C++ by Erin Catto and published under the MIT license. It has been used in ''Crayon Physics Deluxe'', ''Limbo'', '' Rolando'', '' Incredibots'', '' Angry Birds'', ' ...
*
Bullet A bullet is a kinetic projectile, a component of firearm ammunition that is shot from a gun barrel. Bullets are made of a variety of materials, such as copper, lead, steel, polymer, rubber and even wax. Bullets are made in various shapes and co ...
* Chipmunk physics engine - 2D physics engine *
Newton Game Dynamics Newton Game Dynamics is an open-source physics engine for realistically simulating rigid bodies in games and other real-time applications. Its solver is deterministic and not based on traditional LCP or iterative methods. Newton Game Dynamic ...
*
Open Dynamics Engine The Open Dynamics Engine (ODE) is a physics engine written in C/C++. Its two main components are a rigid body dynamics simulation engine and a collision detection engine. It is free software licensed both under the BSD license and the LGPL. O ...
* PAL (Physics Abstraction Layer) - A uniform API that supports multiple physics engines *
PhysX PhysX is an open-source realtime physics engine middleware SDK developed by Nvidia as a part of Nvidia GameWorks software suite. Initially, video games supporting PhysX were meant to be accelerated by PhysX PPU (expansion cards designed by ...
*
Project Chrono Project Chrono is a physics engine developed by University of Wisconsin-Madison and University of Parma and members of its open source community. It supports simulating rigid and soft body dynamics, collision detection, vehicle dynamics, fluid- ...
- An open source simulation engine for multi-physics applications. *
Siconos SICONOS is an Open Source scientific software primarily targeted at modeling and simulating non-smooth dynamical systems (NSDS): * Mechanical systems (Rigid body or solid) with Unilateral contact and Coulomb friction as we find in Non-smooth mec ...
Modeling and the simulation of mechanical systems with contact, impact and Coulomb's friction * SOFA (Simulation Open Framework Architecture) *
Tokamak physics engine The Tokamak Game Physics SDK is an open-source physics engine. At its beginnings, Tokamak was free for non commercial uses only. Since May 2007, it has become open sourced under a BSD licenses, BSD License. Now it can be used under BSD or Zlib ...
;Public domain *
Phyz Phyz (Dax Phyz) is a public domain, 2.5D physics engine with built-in editor and DirectX graphics and sound. In contrast to most other real-time physics engines, it is vertex based and stochastic. Its integrator is based on a SIMD-enabled assembl ...
(Dax Phyz) - 2.5D physics simulator/editor. ;Closed source/limited free distribution *
Digital Molecular Matter Digital Molecular Matter (DMM) is a proprietary middleware physics engine developed by Pixelux for generating realistic destruction and deformation effects. The offline version can support high-resolution simulations for use in film special effect ...
* Havok *
Vortex In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
by CMLabs Simulations * AGX Multiphysics by
Algoryx Simulation AB Algoryx Simulation AB was formed in 2007 in Umeå, Sweden as a spin-off company from Umeå University. Algoryx currently has three products: Algodoo (formerly Phun), Dynamics for SpaceClaim, and AGX Multiphysics, a professional physics engine fo ...
*
Algodoo Algodoo () is a physics-based 2D sandbox freeware from Algoryx Simulation AB (known simply as Algoryx) as the successor to the popular physics application Phun. It was released on September 1, 2009 and is presented as a learning tool, an open e ...
by
Algoryx Simulation AB Algoryx Simulation AB was formed in 2007 in Umeå, Sweden as a spin-off company from Umeå University. Algoryx currently has three products: Algodoo (formerly Phun), Dynamics for SpaceClaim, and AGX Multiphysics, a professional physics engine fo ...
*Rubikon by
Valve Corporation Valve Corporation is an American video game developer, video game publisher, publisher, and digital distribution company headquartered in Bellevue, Washington. It is the developer of the software distribution platform Steam (service), Steam an ...


High precision physics engines

* VisSim - Visual Simulation engine for linear and nonlinear dynamics


See also

*
Game physics Computer animation physics or game physics are laws of physics as they are defined within a simulation or video game, and the programming logic used to implement these laws. Game physics vary greatly in their degree of similarity to real-world phy ...
*
Ragdoll physics Ragdoll physics is a type of procedural animation used by physics engines, which is often used as a replacement for traditional static death animations in video games and animated films. As computers increased in power, it became possible to d ...
*
Procedural animation A procedural animation is a type of computer animation, used to automatically generate animation in real-time to allow for a more diverse series of actions than could otherwise be created using predefined animations. Procedural animation is us ...
*
Rigid body dynamics In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of a ...
*
Soft body dynamics Soft-body dynamics is a field of computer graphics that focuses on visually realistic physical simulations of the motion and properties of deformable objects (or ''soft bodies''). The applications are mostly in video games and films. Unlike in sim ...
*
Physics processing unit A physics processing unit (PPU) is a dedicated microprocessor designed to handle the calculations of physics, especially in the physics engine of video games. It is an example of hardware acceleration. Examples of calculations involving a PPU mig ...
*
Cell microprocessor Cell is a multi-core microprocessor microarchitecture that combines a general-purpose PowerPC core of modest performance with streamlined coprocessing elements which greatly accelerate multimedia and vector processing applications, as well as m ...
*
Linear complementarity problem In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. ...
Impulse/constraint physics engines require a solver for such problems to handle multi-point collisions. *
Finite Element Analysis The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...


References


Further reading

* Bourg, David M. (2002)
Physics for Game Developers"> Physics for Game Developers
'. O'Reilly & Associates.


External links

* {{DEFAULTSORT:Physics Engine Computer graphics Video game development Articles containing video clips