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Geometric transformation that preserves lines but not angles nor the origin
affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space
Affine_transformation
Topics referred to by the same term
Look up affine in Wiktionary, the free dictionary. Affine may describe any of various topics concerned with connections or affinities. It may refer to:
Affine
Euclidean space without distance and angles
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent
Affine_space
Construct allowing differentiation of tangent vector fields of manifolds
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector
Affine_connection
Mathematical concept
In affine differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point The term affine sphere
Affine_sphere
Euclidean geometry without distance and angles
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance
Affine_geometry
Linear combination whose coefficients sum to 1
In mathematics, an affine combination of x1, ..., xn is a linear combination ∑ i = 1 n α i ⋅ x i = α 1 x 1 + α 2 x 2 + ⋯ + α n x n , {\displaystyle \sum
Affine_combination
Resource-sensitive logic allowing each assumption to be used at most once
Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with
Affine_logic
In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold
Affine_manifold
Topics referred to by the same term
Affine algebra may refer to: Affine Lie algebra, a type of Kac–Moody algebras The Lie algebra of the affine group Reduced finitely-generated algebra over
Affine_algebra
In mathematics, an affine Hecke algebra is the algebra associated to an affine Weyl group, and can be used to prove Macdonald's constant term conjecture
Affine_Hecke_algebra
Algebraic variety defined within an affine space
geometry, an affine variety or affine algebraic variety is a certain kind of algebraic variety that can be described as a subset of an affine space. More
Affine_variety
Mathematical object studied in the field of algebraic geometry
An irreducible affine algebraic set is also called an affine variety. (Some authors use the phrase affine variety to refer to any affine algebraic set
Algebraic_variety
Branch of mathematics
an affine variety to A1, we can define regular maps from one affine variety to another. First we will define a regular map from a variety into affine space:
Algebraic_geometry
Type of substitution cipher
The affine cipher is a type of monoalphabetic substitution cipher, where each letter in an alphabet is mapped to its numeric equivalent, encrypted using
Affine_cipher
Type of fiber bundle
mathematics, an affine bundle is a fiber bundle whose typical fiber, fibers, trivialization morphisms and transition functions are affine. Let π ¯ : Y ¯
Affine_bundle
Serre's theorem on affineness (also called Serre's cohomological characterization of affineness or Serre's criterion on affineness) is a theorem due to
Serre's_theorem_on_affineness
Group of all affine transformations of an affine space
In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into
Affine_group
Fundamental space of geometry
not distinct) in the complex affine space. Therefore, most of algebraic geometry is built in complex affine spaces and affine spaces over algebraically closed
Euclidean_space
Type of Kac–Moody algebras
affine Lie algebra, one can also form the associated affine Kac-Moody algebra, as described below. From a purely mathematical point of view, affine Lie
Affine_Lie_algebra
Generalization of algebraic variety
particular, it is not affine. A simple reason to go beyond affine schemes is that an open subset of an affine scheme need not be affine. For example, let
Scheme_(mathematics)
Number line and triangular tiling's symmetry mathematical structure
The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling of
Affine_symmetric_group
geometry, affine differential geometry is the study of differential invariants of curves, surfaces, and higher-dimensional submanifolds under affine transformations
Affine_differential_geometry
Species of tree
Scaphium affine is a tree species in the family Malvaceae, subfamily Sterculioideae (previously placed in the Sterculiaceae and synonyms include Sterculia
Scaphium_affine
Mathematical discipline
quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra
Quantum_affine_algebra
Axiomatically defined geometrical space
In geometry, an affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Given any
Affine plane (incidence geometry)
Affine_plane_(incidence_geometry)
Straight path on a curved surface or a Riemannian manifold
having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain
Geodesic
Algebra term in mathematics
In mathematics, a double affine Hecke algebra, or Cherednik algebra, is an algebra containing the Hecke algebra of an affine Weyl group, given as the
Double_affine_Hecke_algebra
Two-dimensional geometrical space
geometry, an affine plane is a two-dimensional affine space. There are two ways to formally define affine planes, which are equivalent for affine planes over
Affine_plane
Multi-dimensional generalization of triangle
the k + 1 points u 0 , … , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent, which means that the k vectors u 1 − u 0 , … , u k − u 0 {\displaystyle
Simplex
Mathematical concept
term affine Grassmannian. In one it is the manifold of all k-dimensional affine subspaces of Rn (described on this page), while in the other the affine Grassmannian
Affine Grassmannian (manifold)
Affine_Grassmannian_(manifold)
Coordinate system using perpendicular axes
the spherical and cylindrical coordinates for three-dimensional space. An affine line with a chosen Cartesian coordinate system is called a number line.
Cartesian_coordinate_system
Finitelt generated commutative monoid
In abstract algebra, a branch of mathematics, an affine monoid is a commutative monoid that is finitely generated, and is isomorphic to a submonoid of
Affine_monoid
Let Y → X be an affine bundle modelled over a vector bundle Y → X. A connection Γ on Y → X is called the affine connection if it as a section Γ : Y →
Connection_(affine_bundle)
Manifold or algebraic variety of dimension n in a space of dimension n+1
embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. Hypersurfaces share, with surfaces in a three-dimensional
Hypersurface
Topics referred to by the same term
Affine cone may refer to: Convex cone § Affine convex cones Cone (algebraic geometry) This disambiguation page lists articles associated with the title
Affine_cone
Affine space over the complex numbers
Affine geometry, broadly speaking, is the study of the geometrical properties of lines, planes, and their higher dimensional analogs, in which a notion
Complex_affine_space
Species of plant
Exacum affine, known commercially as the Persian violet, is a species of plant in the family Gentianaceae. It is endemic to Socotra, part of Yemen, though
Exacum_affine
Family of type systems based on substructural logic
categories. Affine types are a version of linear types allowing to discard (i.e. not use) a resource, corresponding to affine logic. An affine resource can
Substructural_type_system
Algorithm for solving linear programming problems
In mathematical optimization, affine scaling is an algorithm for solving linear programming problems. Specifically, it is an interior point method, discovered
Affine_scaling
In comparison with General Relativity, dynamic variables of metric-affine gravitation theory are both a pseudo-Riemannian metric and a general linear connection
Metric-affine gravitation theory
Metric-affine_gravitation_theory
Species of shrub
Melastoma affine, also known by the common names blue tongue, straits rhododendron or native lassiandra, is a shrub of the family Melastomataceae. Distributed
Melastoma_affine
Chern's conjecture for affinely flat manifolds was proposed by Shiing-Shen Chern in 1955 in the field of affine geometry. As of 2025, it remains an unsolved
Chern's conjecture (affine geometry)
Chern's_conjecture_(affine_geometry)
Type of vector field
An affine vector field (sometimes affine collineation or affine) is a projective vector field preserving geodesics and preserving the affine parameter
Affine_vector_field
Gauge theory with affine connections
Affine gauge theory is classical gauge theory where gauge fields are affine connections on the tangent bundle over a smooth manifold X {\displaystyle
Affine_gauge_theory
Smallest affine subspace that contains a subset
mathematics, the affine hull or affine span of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is the smallest affine set containing
Affine_hull
In the fields of computer vision and image analysis, the Harris affine region detector belongs to the category of feature detection. Feature detection
Harris_affine_region_detector
mathematics, an affine root system is a root system of affine-linear functions on a Euclidean space. They are used in the classification of affine Lie algebras
Affine_root_system
In mathematics, the affine Grassmannian of an algebraic group G over a field k is an ind-scheme—a colimit of finite-dimensional schemes—which can be thought
Affine_Grassmannian
Species of thyme-moss from old-growth boreal forests
Plagiomnium affine, the many-fruited thyme-moss, is a species of thyme-moss found in old-growth boreal forests in North America, Europe and Asia, growing
Plagiomnium_affine
Topology on prime ideals and algebraic varieties
which allows one to build general algebraic varieties by gluing together affine varieties in a way similar to that in manifold theory, where manifolds are
Zariski_topology
affine differential geometry, the affine focal set of a smooth submanifold M embedded in a smooth manifold N is the caustic generated by the affine normal
Affine_focal_set
Species of bird
The black-faced laughingthrush (Trochalopteron affine) is a bird species in the family Leiothrichidae. It is found in the Eastern Himalayas. Its range
Black-faced_laughingthrush
Species of flowering plant
Pseudognaphalium affine is a species of flowering plant belonging to the genus Pseudognaphalium. The species is widely distributed in East Asia, Southeast
Pseudognaphalium_affine
Central object in linear algebra; mapping vectors to vectors
linear transformations on the n+1-dimensional space Rn+1. These include both affine transformations (such as translation) and projective transformations. For
Transformation_matrix
subscheme of some projective space. An affine space is a Zariski-open subset of a projective space, and since any closed affine subset U {\displaystyle U} can
Quasi-projective_variety
Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine
Affine_arithmetic
Curve defined as zeros of polynomials
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in
Algebraic_curve
Mathematical structure
is an affine Weyl group, the Coxeter complex is a subdivision of the affine plane and one speaks of affine, or Euclidean, buildings. An affine building
Building_(mathematics)
Affine shape adaptation is a methodology for iteratively adapting the shape of the smoothing kernels in an affine group of smoothing kernels to the local
Affine_shape_adaptation
Surface with vanishing affine mean curvature
In affine differential geometry, an affine maximal surface is a locally strongly convex hypersurface in an equiaffine manifold whose affine mean curvature
Affine_maximal_surface
Sum of terms, each multiplied with a scalar
under them, so affine subsets, convex cones, and convex sets are generalizations of vector subspaces: a vector subspace is also an affine subspace, a convex
Linear_combination
Group that admits a formal description in terms of reflections
translates of these hyperplanes. The affine Coxeter group (or affine Weyl group) is then the group generated by the (affine) reflections about all the hyperplanes
Coxeter_group
Type of mathematical object
such as when H is closed in G and both are affine. The multiplicative group Gm has the punctured affine line as its underlying scheme, and as a functor
Group_scheme
Species of moss
Sphagnum affine, the imbricate bogmoss, is a species of peat moss or sphagnum moss which is exploited to make commercial peat products. This moss type
Sphagnum_affine
Species of orchid
Dendrobium affine, commonly known as the white butterfly orchid, malakmalak or matngala in Australian Aboriginal languages, is an epiphytic orchid in the
Dendrobium_affine
In mathematics, an affine representation of a topological Lie group G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism
Affine_representation
Species of fish
Myctophum affine, the metallic lanternfish, is a species of lanternfish native to the Atlantic Ocean. Myctophum affine grows to a length of 7.9 centimetres
Myctophum_affine
Geometric system with a finite number of points
finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity. Other significant types
Finite_geometry
Method of defining surface detail on a computer-generated graphic or 3D model
triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable
Texture_mapping
Algebraic variety with a group structure
of algebraic groups is given by the affine algebraic groups, those whose underlying algebraic variety is an affine variety; they are exactly the algebraic
Algebraic_group
The Hessian affine region detector is a feature detector used in the fields of computer vision and image analysis. Like other feature detectors, the Hessian
Hessian affine region detector
Hessian_affine_region_detector
Linear combination of points where all coefficients are non-negative and sum to 1
of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1. In other words
Convex_combination
mathematics, an affine braid group is a braid group associated to an affine Coxeter system. Their group rings have quotients called affine Hecke algebras
Affine_braid_group
Transformation of a body from a reference configuration to a current configuration
surface will always remain within. An affine deformation is a deformation that can be completely described by an affine transformation. Such a transformation
Deformation_(physics)
Species of beetle
Mezium affine is a species of beetle in the family Ptinidae. Its common names include shiny spider beetle, northern spider beetle, and hood spider beetle
Mezium_affine
Concept in differential geometry
can be applied to real-world data. Affine holonomy groups are the groups arising as holonomies of torsion-free affine connections; those which are not Riemannian
Holonomy
Ideal generated by differences of monomials
two monomials. An affine or projective algebraic variety defined by a toric prime ideal or a homogeneous toric ideal is an affine or projective toric
Toric_ideal
Type of mathematical function
each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine".) If the domain of the function
Piecewise_linear_function
Real numbers with + and - infinity added
authors use Affinely extended real number system and Affinely extended real number line, although the extended real numbers do not form an affine line. Read
Extended_real_number_line
Concept in mathematics
also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Particular task in computer vision
detector that is invariant to affine transformations. In practice, affine invariant interest points can be obtained by applying affine shape adaptation to a blob
Blob_detection
mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such
Affine_geometry_of_curves
Species of moss
Lepidopilum affine is a species of moss in the family Callicostaceae. It is endemic to Ecuador. Its natural habitat is subtropical or tropical moist lowland
Lepidopilum_affine
Concept in algebraic geometry
In algebraic geometry, a finite morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion
Finite_morphism
Type of 2D conformal field theory
associated to a Lie group (or supergroup), and its symmetry algebra is the affine Lie algebra built from the corresponding Lie algebra (or Lie superalgebra)
Wess–Zumino–Witten_model
double affine braid group is a group containing the braid group of an affine Weyl group. Their group rings have quotients called double affine Hecke algebras
Double_affine_braid_group
Special affine curvature, also known as the equiaffine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve
Affine_curvature
Mathematical set with some added structure
n-dimensional affine subspace. It is homogeneous. An affine space need not be included into a linear space, but is isomorphic to an affine subspace of a
Space_(mathematics)
Species of woodlouse
Armadillidium vulgare Latreille, 1804 Synonyms tripus magnus Armadillidium affine Armadillidium armeniense Armadillidium brevicaudatum Armadillidium commutatum
Armadillidium_vulgare
Species of fig
Synonyms Urostigma religiosum (L.) Gasp. Ficus caudata Stokes Ficus peepul Griff. Ficus rhynchophylla Steud. Ficus superstitiosa Link Urostigma affine Miq.
Ficus_religiosa
Symmetry group of a configuration in space
faithfully is an affine space group. Combining these results shows that classifying space groups in n dimensions up to conjugation by affine transformations
Space_group
Subspace of n-space whose dimension is (n-1)
properties from Euclidean space are no longer relevant. For example, in affine space, there is no concept of distance, so there are no reflections or motions
Hyperplane
point. For example, the point associated to the zero ideal for any integral affine scheme. F(n), F(D) 1. If X is a projective scheme with Serre's twisting
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Species of moth
Pyropteron affine is a moth of the family Sesiidae. It is found in most of Europe, except Ireland, Great Britain, the Netherlands, Denmark, Fennoscandia
Pyropteron_affine
Theoretical attempts to unify the forces of nature
the affine connection as the fundamental structure field rather than the metric tensor which was the original focus of general relativity. Affine connection
Classical unified field theories
Classical_unified_field_theories
Function that applies a set to itself
transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations
Transformation_(function)
Approximation of a function by its tangent line at a point
approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce
Linear_approximation
algebra Clifford algebra Geometric algebra Affine space Affine transformation Affine group Affine geometry Affine coordinate system Flat (geometry) Cartesian
Outline_of_linear_algebra
Economic model
In economics, affine pricing is a situation where buying more than zero of a good gains a fixed benefit or cost, and each purchase after that gains a per-unit
Affine_pricing
AFFINE
AFFINE
AFFINE
AFFINE
Boy/Male
Welsh
Legendary son of Greidyawl.
Boy/Male
Hindu, Indian, Marathi
Lord Vishnu
Girl/Female
Gaelic American Latin English Scottish
Joy.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Shiva
Girl/Female
Arabic, Muslim
Pigeon
Male
German
German name derived from Latin Aloisius, ALOÃS means "famous warrior."
Boy/Male
Tamil
Divine
Female
Egyptian
, daughter of a chief named Iuaa.
Girl/Female
Hindu
Delight Moon, Full of Honey
Boy/Male
Russian
Great.
AFFINE
AFFINE
AFFINE
AFFINE
AFFINE
v. t.
To refine.
a.
Joined in affinity or by any tie.