computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, a 4D vector is a 4-component

vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

data type In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these ...

. Uses include

homogeneous coordinates In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. ...

for 3-dimensional space in

computer graphics Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...

, and ''red green blue alpha'' (

RGBA RGBA stands for red green blue alpha. While it is sometimes described as a color space, it is actually a three-channel RGB color model supplemented with a fourth ''alpha channel''. Alpha indicates how opaque each pixel is and allows an image to ...

) values for

bitmap In computing, a bitmap (also called raster) graphic is an image formed from rows of different colored pixels. A GIF is an example of a graphics image file that uses a bitmap. As a noun, the term "bitmap" is very often used to refer to a partic ...

images with a color and

alpha channel In computer graphics, alpha compositing or alpha blending is the process of combining one image with a background to create the appearance of partial or full transparency. It is often useful to render picture elements (pixels) in separate pass ...

(as such they are widely used in computer graphics). They may also represent

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...

s (useful for rotations) although the algebra they define is different.

Computer hardware support

Some

microprocessor A microprocessor is a computer processor (computing), processor for which the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, a ...

s have hardware support for 4D vectors with instructions dealing with 4

lane In road transport, a lane is part of a roadway that is designated to be used by a single line of vehicles to control and guide drivers and reduce traffic conflicts. Most public roads (highways) have at least two lanes, one for traffic in eac ...

''single instruction, multiple data'' (

SIMD Single instruction, multiple data (SIMD) is a type of parallel computer, parallel processing in Flynn's taxonomy. SIMD describes computers with multiple processing elements that perform the same operation on multiple data points simultaneousl ...

) instructions, usually with a

128-bit General home computing and gaming utility emerged at 8-bit word sizes, as 28=256 Word (computer architecture), words, a natural unit of data, became possible. Early 8-bit CPUs (such as the Zilog Z80 and MOS Technology 6502, used in the 1977 Co ...

data path and 32-bit floating point fields. Specific instructions (e.g., 4 element

dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. N ...

) may facilitate the use of one 128-bit register to represent a 4D vector. For example, in chronological order: Hitachi SH4,

PowerPC PowerPC (with the backronym Performance Optimization With Enhanced RISC – Performance Computing, sometimes abbreviated as PPC) is a reduced instruction set computer (RISC) instruction set architecture (ISA) created by the 1991 Apple Inc., App ...

VMX128 extension, and Intel

x86 x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel, based on the 8086 microprocessor and its 8-bit-external-bus variant, the 8088. Th ...

SSE4. Some 4-element vector engines (e.g., the PS2 vector units) went further with the ability to broadcast components as multiply sources, and

cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and ...

support. Earlier generations of

graphics processing unit A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal ...

(GPU) shader pipelines used ''

very long instruction word Very long instruction word (VLIW) refers to instruction set architectures that are designed to exploit instruction-level parallelism (ILP). A VLIW processor allows programs to explicitly specify instructions to execute in parallel, whereas conve ...

'' (VLIW)

instruction set In computer science, an instruction set architecture (ISA) is an abstract model that generally defines how software controls the CPU in a computer or a family of computers. A device or program that executes instructions described by that ISA, s ...

s tailored for similar operations.

Software support

SIMD use for 4D vectors can be conveniently wrapped in a '' vector maths library'' (commonly implemented in C or C++) commonly used in

video game development Video game development (sometimes shortened to gamedev) is the process of creating a video game. It is a multidisciplinary practice, involving programming, design, art, audio, user interface, and writing. Each of those may be made up of more speci ...

, along with 4×4 matrix support. These are distinct from more general linear algebra libraries in other domains focussing on

matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...

of arbitrary size. Such libraries sometimes support 3D vectors padded to 4D or loading 3D data into 4D registers, with arithmetic mapped efficiently to SIMD operations by per platform

intrinsic function In computer software, in compiler theory, an intrinsic function, also called built-in function or builtin function, is a function ( subroutine) available for use in a given programming language whose implementation is handled specially by the com ...

implementations. There is choice between AOS and SOA approaches given the availability of 4 element registers, versus SIMD instructions that are usually tailored toward homogenous data. Shading languages for

(GPU) programming usually have a 4D datatypes (along with 2D, 3D) with x-y-z-w accessors including '' permutes'' or ''swizzle'' access, e.g., allowing easy swapping of RGBA or ARGB formats, accessing two 2D vectors packed into one 4D vector, etc. Modern GPUs have since moved to scalar

single instruction, multiple threads Single instruction, multiple threads (SIMT) is an execution model used in parallel computing where single instruction, multiple data (SIMD) is combined with zero-overhead multithreading, i.e. multithreading where the hardware is capable of switch ...

(SIMT) pipelines (for more efficiency in ''

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 traditional ...

'' (GPGPU)) but still support this programming model.

References

{{DEFAULTSORT:4D Vector Mathematical structures Vectors (mathematics and physics) Computer hardware Data types

Computer hardware support

Software support

See also

References