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4-component vector data type in computer science
In computer science, a 4D vector is a 4-component vector data type. Uses include homogeneous coordinates for 3-dimensional space in computer graphics
4D_vector
Parallel computing data layout methods
with such support. AoS vs. SoA presents a choice when considering 3D or 4D vector data on machines with four-lane SIMD hardware. SIMD ISAs are usually designed
AoS_and_SoA
Special orthogonal group
with the group of orientation-preserving isometric linear mappings of a 4D vector space with inner product over the real numbers onto itself. With respect
Rotations in 4-dimensional Euclidean space
Rotations_in_4-dimensional_Euclidean_space
vector A unit vector in 3D space. 4D vector A common datatype in graphics code, holding homogeneous coordinates or RGBA data, or simply a 3D vector with
Glossary_of_computer_graphics
RGB color model with an opacity channel
areas and anti-aliasing of the edges of opaque regions. Each pixel is a 4D vector. The term does not define what RGB color space is being used. It also
RGBA_color_model
Geometric space with four dimensions
experiences of everyday life. Single locations in Euclidean 4D space can be given as vectors or 4-tuples, i.e., as ordered lists of numbers such as (x,
Four-dimensional_space
Central processing unit by Sony Computer Entertainment and Toshiba
vertex shader pipelines. Each VPU features 32 128-bit vector SIMD registers (holding 4D vector data), 16 16-bit fixed-point registers, four floating point
Emotion_Engine
3D computer graphics software
Cinema 4D is a 3D software suite developed by the German company Maxon. As of R21, only a single version of Cinema 4D is available. It replaces all previous
Cinema_4D
Four-dimensional number system
Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described
Quaternion
Vector function in optics
sphere of directions, produces a vector-valued function of 3D space called the vector irradiance field. The vector direction at each point in the field
Light_field
Mathematical objects more general than vectors
\right|^{2}\mathbf {\nabla } _{\mathbf {y} },} where y i {\displaystyle y_{i}} is a 4D vector, i = 1 , 2 , 3 , 4 {\displaystyle i=1,2,3,4} , y = ( r , τ ) , | y | 2
Harmonic_tensors
Property of a mathematical space
that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially
Dimension
Four-dimensional analogue of the cube
symbol {4,3,3} with hyperoctahedral symmetry of order 384. Constructed as a 4D hyperprism made of two parallel cubes, it can be named as a composite Schläfli
Tesseract
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
space and 4D Minkowski space", From local isometries to global symmetries: bridging Killing vectors and Lie algebras through induced vector fields, Universidade
Killing_vector_field
4D analogue of electric current density
with the dimension of electric charge per time per area. Also known as vector current, it is used in the context of four-dimensional spacetime, rather
Four-current
Representation of the supersymmetry algebra
Julius Wess and Bruno Zumino. The most commonly used supermultiplets are vector multiplets, chiral multiplets (in d = 4 , N = 1 {\displaystyle d=4,{\mathcal
Supermultiplet
Theory of supergravity in four dimensions
In supersymmetry, 4D N = 1 {\displaystyle {\mathcal {N}}=1} supergravity is the theory of supergravity in four dimensions with a single supercharge. It
4D_N_=_1_supergravity
Theorem used in quantum mechanics for angular momentum calculations
all possible 4d orbitals (i.e., the 5 states m = −2, −1, 0, 1, 2 and their quantum superpositions) form a 5-dimensional abstract vector space. Rotating
Wigner–Eckart_theorem
Algorithm for modelling sequential data
numerical representations called tokens, and each token is converted into a vector via lookup from a word embedding table. At each layer, each token is then
Transformer_(deep_learning)
Mathematical description of spacetime used in relativity
is the four-velocity of the particle, satisfying u2 = 1 and s is the 4D spin vector, which is also the Pauli–Lubanski pseudovector satisfying s2 = −1 and
Minkowski_spacetime
Ways to represent 3D rotations
needs to track a target. Consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
4D relativistic energy and momentum
four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum
Four-momentum
Geospatial vector data format
The shapefile format is a geospatial vector data format for geographic information system (GIS) software. It is developed and regulated by Esri as a mostly
Shapefile
Sum of directed areas in exterior algebra
mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar
Bivector
Four-dimensional analog of the dodecahedron
to give another vector. Quaternions extend the vectorial structure of 4D real space by allowing the multiplication of two 4D vectors ( w , x , y , z )
120-cell
Generalized sphere of dimension n (mathematics)
the following algorithm. Generate an n {\displaystyle n} -dimensional vector of normal deviates (it suffices to use N ( 0 , 1 ) {\displaystyle N(0
N-sphere
Gauge theory with supersymmetry
space. This superspace is a Z 2 {\displaystyle {\mathbb {Z} _{2}}} -graded vector space W = W 0 ⊕ W 1 {\displaystyle {\mathcal {W}}={\mathcal {W}}^{0}\oplus
Supersymmetric_gauge_theory
How many linearly independent smooth nowhere-zero vector fields can be on an n-sphere
In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and
Vector_fields_on_spheres
Approach to dimensionality reduction
vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D)
Multilinear_subspace_learning
Four-vector analogue of the gradient operation
{\boldsymbol {\partial }}} is the four-vector analogue of the gradient ∇ → {\displaystyle {\vec {\boldsymbol {\nabla }}}} from vector calculus. In special relativity
Four-gradient
Path of an object through spacetime
\Delta \tau } defines a vector, the tangent vector of the world line at the point p {\displaystyle p} . It is a four-dimensional vector, defined in the point
World_line
Data type that represents an ordered collection of elements (values or variables)
analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively
Array_(data_type)
Surface-to-air missile
The IRIS-T SL (Infra Red Imaging System Tail/Thrust Vector Controlled Surface Launched) is a family of short and high to medium air defense surface-to-air
IRIS-T_SL
Movement of an object which leaves at least one point unchanged
of change of a vector independently influence only the magnitude or orientation of the vector respectively. Hence, a rotating vector always has a non-zero
Rotation
Minimal supergravity in four dimensions
In supersymmetry, pure 4D N = 1 {\displaystyle {\mathcal {N}}=1} supergravity describes the simplest four-dimensional supergravity, with a single supercharge
Pure_4D_N_=_1_supergravity
Graded vector space with applications to theoretical physics
In mathematics, a super vector space is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space, that is, a vector space over a field K {\displaystyle
Super_vector_space
Theory of supersymmetry in four dimensions
In supersymmetry, 4D N = 1 {\displaystyle {\mathcal {N}}=1} global supersymmetry is the theory of global supersymmetry in four dimensions with a single
4D_N_=_1_global_supersymmetry
Process used in video coding/compression
image processing, motion estimation is the process of determining motion vectors that describe the transformation from one 2D image to another; usually
Motion_estimation
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Unified field theory
\phi } . Then decompose the 5D metric so that the 4D metric is framed by the electromagnetic vector potential, with the scalar field at the fifth diagonal
Kaluza–Klein_theory
On closed convex subsets in Hilbert space
theorem is a famous result of convex analysis that says that for every vector x {\displaystyle x} in a Hilbert space H {\displaystyle H} and every nonempty
Hilbert_projection_theorem
Type of CT scanning
Radiosurgery. Springer. p. 191. ISBN 9781461483632. The ITV can be assessed with a 4D CT scan or fluoroscopy... Jeremic, Branislav (2011). Advances in Radiation
4DCT
Polyhedron with 8 triangles and 6 squares
its edges. In other words, it has the same length vectors in three-dimensional space, known as vector equilibrium.[citation needed] The rigid struts and
Cuboctahedron
Technique for the generative modeling of a continuous probability distribution
Transformer model, and so it is a DiT. It uses rectified flow. Stable Video 4D (2024–07) is a latent diffusion model for videos of 3D objects. Imagen (2022)
Diffusion_model
Supergravity in eleven dimensions
theory can also be acquired by introducing an auxiliary nondynamical Killing vector field, with this theory reducing to massive type IIA supergravity upon dimensional
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Computer markup language
Well-known text (WKT) is a text markup language for representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used
Well-known text representation of geometry
Well-known_text_representation_of_geometry
3D reconstruction technique
the input point, B i {\displaystyle \mathrm {B} _{i}} are the frequency vectors, and a i {\displaystyle a_{i}} are coefficients. This allows for rapid
Neural_radiance_field
Algebraic structure designed for geometry
identification of Euclidean points with 1D subspaces in the 4D null cone of the 5D CGA vector subspace. This allows all conformal transformations to be
Geometric_algebra
Theory in supersymmetric gauge theory
{\displaystyle {\mathcal {N}}=2} vector supermultiplet, analogous to the field content of Yang–Mills theory being a single vector gauge field (in particle theory
Seiberg–Witten_theory
Determining the position and orientation of a robot by analyzing associated camera images
Construct optical flow field (Lucas–Kanade method). Check flow field vectors for potential tracking errors and remove outliers. Estimation of the camera
Visual_odometry
Correspondence between quaternions and 3D rotations
{R}}i+c_{\rm {R}}j+d_{\rm {R}}k} can represent any rotation in 4D space. Given a four-dimensional vector v → {\displaystyle {\vec {v}}} , expressed as a quaternion
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Geometric space with five dimensions
geometry, such a space extends the familiar three spatial dimensions plus time (4D spacetime) by introducing an additional degree of freedom, which is often
Five-dimensional_space
PhotoCap Vector 78 56 34 xV4 0 pbt pdt pea peb pet pgt pict pjt pkt pmt PhotoCap Template 50 41 52 31 PAR1 0 Apache Parquet columnar file format 45 4D 58 32
List_of_file_signatures
Planar surface that forms part of the boundary of a solid object
formed from a subset of three or more vertices of a 2-face. The facets of a 4D polytope or 3-honeycomb are its 3-faces or cells. The facets of a 5D polytope
Face_(geometry)
Notation in quantum physics
(coupling of j of three electrons). 4d 5 / 2 3 4d 3 / 2 2 ( 9 2 , 2 ) 11 / 2 {\displaystyle {\text{4d}}_{5/2}^{3}{\text{4d}}_{3/2}^{2}~\ {{\left({\frac {9}{2}}
Term_symbol
Type of diagnosis assisted by computers
classifier Artificial neural network Radial basis function network (RBF) Support vector machine (SVM) Principal component analysis (PCA) If the detected structures
Computer-aided_diagnosis
Israeli company
(Hebrew: ואיאר הדמאה בע"מ) is an Israeli semiconductor company that produces 4D imaging radar sensors. Initially developed to provide a more effective means
Vayyar
supersymmetric theories are: In an N = 1 {\displaystyle {\mathcal {N}}=1} 4D SUSY theory involving only chiral superfields, the superpotential is immune
Supersymmetry nonrenormalization theorems
Supersymmetry_nonrenormalization_theorems
Model of optics describing light as geometric rays
perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's
Geometrical_optics
Theory of interwoven space and time by Albert Einstein
lightlike 4-vector is orthogonal to itself. Invariance of the magnitude of a vector: The magnitude of a vector is the inner product of a 4-vector with itself
Special_relativity
Euclidean geometry without distance and angles
transformations (that is bijective mappings), the translations, which forms a vector space (over a given field, commonly the real numbers), and such that for
Affine_geometry
Term in supersymmetric theories
theoretical physics, the D-term is the final term in the expansion of a vector superfield over fermionic coordinates. A superfield is a field that depends
D-term
Construction for n-dimensional noise functions
requires fewer multiplications. Simplex noise scales to higher dimensions (4D, 5D) with much less computational cost: the complexity is O ( n 2 ) {\displaystyle
Simplex_noise
Set of rules defining correctly structured programs
which have elements grouped linearly as vectors or in table form as matrices—and higher dimensions (3D or cubed, 4D or cubed over time, etc.). Arrays containing
APL_syntax_and_symbols
4DIndx – 4D database Data Index file 4DR – 4D database Data resource file (in old 4D versions) 4DZ – 4D database Structure file (compiled in 4D Project
List_of_file_formats
No-go theorem pertaining the triviality of space-time and internal symmetries
This non-relativistic SU ( 6 ) {\displaystyle {\text{SU}}(6)} model united vector and pseudoscalar mesons of different spin into a 35-dimensional multiplet
Coleman–Mandula_theorem
Element representing a value on a grid in three dimensional space
complements to traditional 3D vector modeling. A generalization of a voxel is the toxel, or temporal voxel. This is used in the case of a 4D data set, such as an
Voxel
Superconformal Yang–Mills theory
bosons, not 16. Therefore, N = 4 SYM has 1 + 4 + 6 = 11 fields, namely: one vector field (the spin-1 gauge boson), four spinor fields (the spin-1/2 fermions)
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Samples within a data set identified for a particular purpose
outlining an object (sometimes known as the Volume of Interest (VOI)) in a volume 4D dataset: the outline of an object at or during a particular time interval
Region_of_interest
Type of supersymmetric quantum field theory
superpotential leads to a renormalizable theory. It is a special case of 4D N = 1 global supersymmetry. The treatment in this article largely follows
Wess–Zumino_model
Quantum mechanics with supersymmetry
Note that ℑ { W } {\displaystyle \Im \{W\}} acts like an electromagnetic vector potential. Let's also call the spin down state "bosonic" and the spin up
Supersymmetric quantum mechanics
Supersymmetric_quantum_mechanics
superconformal field theory 6D (2,0) superconformal field theory Pure 4D N = 1 supergravity 4D N = 1 supergravity Type I supergravity Type IIA supergravity Type
List of quantum field theories
List_of_quantum_field_theories
Algebraic structure used in theoretical physics
{\displaystyle \mathrm {Hom} } , composed of all linear maps) of a super vector space forms a superalgebra under composition. The set of all square supermatrices
Superalgebra
Topological structure of 4D spacetime
Topological structure of 4D spacetime
Spacetime_topology
Piece of information about the content of an image
as the elements of one single vector, commonly referred to as a feature vector. The set of all possible feature vectors constitutes a feature space. A
Feature_(computer_vision)
1994 book by Michio Kaku
10th Dimension Cover depicting the artist's 2D conception of a 3D face of a 4D Hypercube house upon a 3D landscape Author Michio Kaku Language English Genre
Hyperspace_(book)
Base space for supersymmetric theories
is also commonly used as a synonym for the super vector space. This is taken to be an ordinary vector space, together with additional coordinates taken
Superspace
Supersymmetric generalization of the Poincaré algebra
and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra
Super-Poincaré_algebra
Characteristic classes of vector bundles
geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches of
Chern_class
Modern theory of gravitation that combines supersymmetry and general relativity
let's recapitulate some important details about general relativity. We have a 4D differentiable manifold M with a Spin(3,1) principal bundle over it. This
Supergravity
supported vector-register width to 128/256 bits - however, as of March 2025, this option has been removed, making support for 512-bit vector-register width
List_of_x86_SIMD_instructions
Mathematical descriptions of a rotation group
surface of a 4D disc, which is also a 3D variety. For doing this equivalence, we will have to define how will we represent a rotation with this 4D-embedded
Charts_on_SO(3)
Upgraded series of the Su-27 fighter aircraft
produced and used for tests and demonstrations; one example had thrust-vectoring engines and was in turn redesignated the Su-37. A sole Su-35UB two-seat
Sukhoi_Su-35
Theorem in theoretical physics
ISBN 978-0521356756. Akhond, M.; et al. (2021). "The Hitchhiker's Guide to 4d N=2 Superconformal Field Theories". SciPost Phys. Lect. Notes. arXiv:2112
Haag–Łopuszański–Sohnius theorem
Haag–Łopuszański–Sohnius_theorem
Non-orientable mathematical surface
cannot define a consistent direction perpendicular to the surface (normal vector) that varies continuously over the whole shape. The Klein bottle is related
Klein_bottle
Concept in machine learning
sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds
Tensor_(machine_learning)
Constructing product by means of computer
use of computer software. CAD software for mechanical design uses either vector-based graphics to depict the objects of traditional drafting, or may also
Computer-aided_design
is a bosonic abelian vector normal subalgebra of dimension d, normally identified with translations of spacetime. It is a vector representation of L.
Supersymmetry_algebra
Mathematical operation
lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different
Lattice_reduction
Open-source deep learning library
scalars termed vectors. DataVec is designed to vectorize CSVs, images, sound, text, video, and time series. Deeplearning4j includes a vector space modeling
Deeplearning4j
Four-dimensional geometrical object
matrix, all incidence counts between elements are shown. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full
Runcinated_5-cell
Angular momentum in special and general relativity
instantaneous three-dimensional position vector x = (x, y, z) and momentum vector p = (px, py, pz), is defined as the axial vector L = x × p {\displaystyle \mathbf
Relativistic_angular_momentum
}} The tensor T ν α {\displaystyle T^{\nu }{}_{\alpha }} is traceless (in 4D): T α α = 0. {\displaystyle T^{\alpha }{}_{\alpha }=0.} Proof Starting with
Electromagnetic stress–energy tensor
Electromagnetic_stress–energy_tensor
Ten-dimensional supergravity
Yang–Mills 4D N = 1 N = 4 super Yang–Mills Super QCD MSSM NMSSM 6D (2,0) superconformal ABJM superconformal Supergravity Pure 4D N = 1 supergravity 4D N = 1
Type_IIB_supergravity
Biomedical imaging technology
3 orthogonal planes within a 3D volume throughout the cardiac cycle. Such 4D imaging encodes the velocity of flowing blood at each voxel in the volume
Cardiac magnetic resonance imaging
Cardiac_magnetic_resonance_imaging
General relativity in M-theory
one spinor and one vector index, which means that gravitinos transform as a tensor product of a spinorial representation and the vector representation of
Higher-dimensional supergravity
Higher-dimensional_supergravity
Image edge detection algorithm
Sobel–Feldman operator is either the corresponding gradient vector or the norm of this vector. The Sobel–Feldman operator is based on convolving the image
Sobel_operator
Supersymmetric generalization of quantum chromodynamics
contains one Majorana spinor supercharge. The particle content consists of vector supermultiplets, which include gluons and gluinos and also chiral supermultiplets
Super_QCD
Superconformal quantum field theory
Yang–Mills 4D N = 1 N = 4 super Yang–Mills Super QCD MSSM NMSSM 6D (2,0) superconformal ABJM superconformal Supergravity Pure 4D N = 1 supergravity 4D N = 1
ABJM superconformal field theory
ABJM_superconformal_field_theory
of relativity, that Hsu & Hsu say, when applied to 4D spacetime, implies the invariance of the 4D-spacetime interval s 2 = w 2 − r 2 {\displaystyle s^{2}=w^{2}-r^{2}}
Formulations of special relativity
Formulations_of_special_relativity
4D VECTOR
4D VECTOR
4D VECTOR
4D VECTOR
Boy/Male
African, Arabic, German, Swahili
Leader; Officer; Prince; Commander; Colonel
Female
English
English name derived from the name of the precious green gemstone, the birthstone of May, from Greek smaragdos, EMERALD means "green gem." The emerald was once believed to have the power to protect chastity, ward off evil spirits, cure dysentery, epilepsy, and help poor eyesight.Â
Boy/Male
Muslim/Islamic
A gift or a present
Girl/Female
Muslim
Small
Boy/Male
Scottish
Night.
Girl/Female
Indian, Malayalam
Soft; Grass
Boy/Male
Indian, Telugu
Good Look
Boy/Male
Tamil
Apne Dam par
Boy/Male
Muslim
Leader, President, Head, Chief
Male
Portuguese
Variant spelling of Portuguese Hélder, ÉLDER means "slanting surface."
4D VECTOR
4D VECTOR
4D VECTOR
4D VECTOR
4D VECTOR
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
A spiral whose polar equation is r2/ = a; that is, a curve the square of whose radius vector varies inversely as the angle which the radius vector makes with a given line.
n.
An old French gold coin of the value of 3s. 4d. sterling, or about 80 cents.
n.
Same as Radius vector.
n.
The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
n.
An ideal straight line joining the center of an attracting body with that of a body describing an orbit around it, as a line joining the sun and a planet or comet, or a planet and its satellite.
n.
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.