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Homogeneous coordinates

Index Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry. [1]

148 relations: Affine coordinate system, Affine transformation, Algebraic curve, Algebraic geometry, Algebraic variety, Apollonian circles, Artificial neuron, August Ferdinand Möbius, Axis–angle representation, B-spline, Back-face culling, Barycentric coordinate system, Bézout's theorem, Bitangents of a quartic, Blocking set, Blowing up, Borel–Weil–Bott theorem, Camera matrix, Camera resectioning, Canonical bundle, Cayley transform, Cayley–Klein metric, Circle, Circular algebraic curve, Circular points at infinity, Clip coordinates, Complete intersection, Complex projective plane, Complex projective space, Conic bundle, Conic section, Conversion between quaternions and Euler angles, Coordinate system, Cross-ratio, Cubic plane curve, Cubic surface, Diophantine equation, Diophantine geometry, Dual curve, Duality (projective geometry), Edwards curve, Elliptic curve, Enumerative geometry, Fano plane, Fermat curve, Fubini–Study metric, Fundamental matrix (computer vision), Geometric algebra, Glossary of arithmetic and diophantine geometry, Glossary of computer graphics, ..., Graphics pipeline, Grassmannian, Hesse pencil, History of Lorentz transformations, Holor, Homogeneity (disambiguation), Homogeneous coordinate ring, Homogeneous space, Homography, Hyperbolic space, Hyperplane at infinity, Hyperplane section, Hypersurface, Image rectification, Imaginary line (mathematics), Imaginary point, Incidence (geometry), Isotropic line, Julius Plücker, Karl Wilhelm Feuerbach, Kirkman's schoolgirl problem, Klein quartic, Laguerre formula, Laguerre–Forsyth invariant, Lie sphere geometry, Line at infinity, Line bundle, Line clipping, Line coordinates, Linear algebra, Linear fractional transformation, Linear system of divisors, Line–line intersection, List of geometry topics, List of German inventors and discoverers, Mass point geometry, Matrix representation of conic sections, Möbius transformation, Monge cone, Mordell–Weil theorem, Motor variable, Non-uniform rational B-spline, Oriented projective geometry, Orthographic projection, Pinhole camera model, Plane at infinity, Plücker coordinates, Plücker matrix, Polar curve, Projection, Projective connection, Projective geometry, Projective line, Projective line over a ring, Projective linear group, Projective space, Projective variety, Quadratic form, Quadric, Quaternion, Quaternionic projective space, Qvist's theorem, Rational motion, Rational normal curve, Real hyperelliptic curve, Real point, Real projective line, Real projective plane, Resultant, Reye configuration, Rotation (mathematics), Rotation matrix, Scaling (geometry), Segre embedding, Segre's theorem, Semicubical parabola, Shadow mapping, Shadow volume, Silhouette edge, Singleton bound, Smooth projective plane, Spherical wave transformation, Stereographic projection, Surface (mathematics), Tangent, Tautological bundle, Transformation matrix, Translation (geometry), Trilinear coordinates, Twisted cubic, Unit hyperbola, Unital (geometry), Veronese surface, Vertex (computer graphics), Wiman's sextic, 2D computer graphics, 3D projection, 4D vector. Expand index (98 more) »

Affine coordinate system

In mathematics, an affine coordinate system is a coordinate system on an affine space where each coordinate is an affine map to the number line.

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Affine transformation

In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.

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Algebraic curve

In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry.

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Apollonian circles

Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa.

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Artificial neuron

An artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network.

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August Ferdinand Möbius

August Ferdinand Möbius (17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer.

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Axis–angle representation

In mathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector indicating the direction of an axis of rotation, and an angle describing the magnitude of the rotation about the axis.

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B-spline

In the mathematical subfield of numerical analysis, a B-spline, or basis spline, is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.

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Back-face culling

In computer graphics, back-face culling determines whether a polygon of a graphical object is visible.

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Barycentric coordinate system

In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.

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Bézout's theorem

Bézout's theorem is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves which do not share a common component (that is, which do not have infinitely many common points).

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Bitangents of a quartic

In the theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places.

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Blocking set

In geometry, specifically projective geometry, a blocking set is a set of points in a projective plane which every line intersects and which does not contain an entire line.

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Blowing up

In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace.

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Borel–Weil–Bott theorem

In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles.

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Camera matrix

In computer vision a camera matrix or (camera) projection matrix is a 3 \times 4 matrix which describes the mapping of a pinhole camera from 3D points in the world to 2D points in an image.

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Camera resectioning

Camera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video.

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Canonical bundle

In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n.

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Cayley transform

In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things.

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Cayley–Klein metric

In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space is defined using a cross-ratio.

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Circle

A circle is a simple closed shape.

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Circular algebraic curve

In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y).

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Circular points at infinity

In projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane that are contained in the complexification of every real circle.

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Clip coordinates

The clip coordinate system is a homogeneous coordinate system in the graphics pipeline.

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Complete intersection

In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements.

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Complex projective plane

In mathematics, the complex projective plane, usually denoted P2(C), is the two-dimensional complex projective space.

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Complex projective space

In mathematics, complex projective space is the projective space with respect to the field of complex numbers.

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Conic bundle

In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution of a Cartesian equation of the form Theoretically, it can be considered as a Severi–Brauer surface, or more precisely as a Châtelet surface.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Conversion between quaternions and Euler angles

Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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Cross-ratio

In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line.

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Cubic plane curve

In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation.

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Cubic surface

A cubic surface is a projective variety studied in algebraic geometry.

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Diophantine equation

In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).

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Diophantine geometry

In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of rational numbers or a finite field, or more general commutative ring such as the integers.

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Dual curve

In projective geometry, a dual curve of a given plane curve is a curve in the dual projective plane consisting of the set of lines tangent to.

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Duality (projective geometry)

In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept.

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Edwards curve

x^2+y^2.

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Elliptic curve

In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.

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Enumerative geometry

In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory.

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Fano plane

In finite geometry, the Fano plane (after Gino Fano) is the finite projective plane of order 2.

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Fermat curve

In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation Therefore, in terms of the affine plane its equation is An integer solution to the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa.

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Fubini–Study metric

In mathematics, the Fubini–Study metric is a Kähler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form.

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Fundamental matrix (computer vision)

In computer vision, the fundamental matrix \mathbf is a 3×3 matrix which relates corresponding points in stereo images.

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Geometric algebra

The geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements called multivectors, which is a superset of both the scalars F and the vector space V. Mathematically, a geometric algebra may be defined as the Clifford algebra of a vector space with a quadratic form.

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Glossary of arithmetic and diophantine geometry

This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry.

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Glossary of computer graphics

This is a glossary of terms relating computer graphics.

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Graphics pipeline

In computer graphics, a computer graphics pipeline, rendering pipeline or simply graphics pipeline, is a conceptual model that describes what steps a graphics system needs to perform to render a 3D scene to a 2D screen.

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Grassmannian

In mathematics, the Grassmannian is a space which parametrizes all -dimensional linear subspaces of the n-dimensional vector space.

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Hesse pencil

In mathematics, the syzygetic pencil or Hesse pencil, named for Otto Hesse, is a pencil (one-dimensional family) of cubic plane elliptic curves in the complex projective plane, defined by the equation Each curve in the family is determined by a pair of parameter values (\lambda,\mu) (not both zero) and consists of the points in the plane whose homogeneous coordinates (x,y,z) satisfy the equation for those parameters.

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History of Lorentz transformations

The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval -x_0^2+\cdots+x_n^2 and the Minkowski inner product -x_0^2 y_0^2+\cdots+x_n^2 y_n^2.

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Holor

A holor (Greek ὅλος "whole") is a mathematical entity that is made up of one or more independent quantities ("merates" as they are called in the theory of holors).

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Homogeneity (disambiguation)

Homogeneity is a sameness of constituent structure.

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Homogeneous coordinate ring

In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ring where I is the homogeneous ideal defining V, K is the algebraically closed field over which V is defined, and is the polynomial ring in N + 1 variables Xi.

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Homogeneous space

In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively.

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Homography

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.

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Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

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Hyperplane at infinity

In geometry, any hyperplane H of a projective space P may be taken as a hyperplane at infinity.

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Hyperplane section

In mathematics, a hyperplane section of a subset X of projective space Pn is the intersection of X with some hyperplane H. In other words, we look at the subset XH of those elements x of X that satisfy the single linear condition L.

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Hypersurface

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.

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Image rectification

Image rectification is a transformation process used to project images onto a common image plane.

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Imaginary line (mathematics)

In complex geometry, an imaginary line is a straight line that only contains one real point.

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Imaginary point

In geometry, in the context of a real geometric space extended to (or embedded in) a complex projective space, an imaginary point is a point not contained in the embedded space.

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Incidence (geometry)

In geometry, an incidence relation is a binary relation between different types of objects that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used.

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Isotropic line

In the geometry of quadratic forms, an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any pair of its points is zero.

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Julius Plücker

Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist.

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Karl Wilhelm Feuerbach

Karl Wilhelm von Feuerbach (30 May 1800 – 12 March 1834) was a German geometer and the son of legal scholar Paul Johann Anselm Ritter von Feuerbach, and the brother of philosopher Ludwig Feuerbach.

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Kirkman's schoolgirl problem

Kirkman's schoolgirl problem is a problem in combinatorics proposed by Rev.

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Klein quartic

In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus with the highest possible order automorphism group for this genus, namely order orientation-preserving automorphisms, and automorphisms if orientation may be reversed.

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Laguerre formula

The Laguerre formula (named after Edmond Laguerre) provides the acute angle \phi between two proper real lines, as follows: where.

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Laguerre–Forsyth invariant

In projective geometry, the Laguerre–Forsyth invariant is a cubic differential that is an invariant of a projective plane curve.

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Lie sphere geometry

Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere.

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Line at infinity

In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane.

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Line bundle

In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space.

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Line clipping

In computer graphics, line clipping is the process of removing lines or portions of lines outside an area of interest.

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Line coordinates

In geometry, line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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Linear fractional transformation

In mathematics, the phrase linear fractional transformation usually refers to a Möbius transformation, which is a homography on the complex projective line P(C) where C is the field of complex numbers.

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Linear system of divisors

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.

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Line–line intersection

In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or a line.

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List of geometry topics

This is a list of geometry topics, by Wikipedia page.

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List of German inventors and discoverers

---- This is a list of German inventors and discoverers.

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Mass point geometry

Mass point geometry, colloquially known as mass points, is a geometry problem-solving technique which applies the physical principle of the center of mass to geometry problems involving triangles and intersecting cevians.

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Matrix representation of conic sections

In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections.

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Möbius transformation

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

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Monge cone

In the mathematical theory of partial differential equations (PDE), the Monge cone is a geometrical object associated with a first-order equation.

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Mordell–Weil theorem

In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A(K) of ''K''-rational points of A is a finitely-generated abelian group, called the Mordell-Weil group.

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Motor variable

In mathematics, a function of a motor variable is a function with arguments and values in the split-complex number plane, much as functions of a complex variable involve ordinary complex numbers.

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Non-uniform rational B-spline

Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces.

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Oriented projective geometry

Oriented projective geometry is an oriented version of real projective geometry.

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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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Pinhole camera model

The pinhole camera model describes the mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light.

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Plane at infinity

In projective geometry, a plane at infinity is the hyperplane at infinity of a three dimensional projective space or to any plane contained in the hyperplane at infinity of any projective space of higher dimension.

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Plücker coordinates

In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3.

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Plücker matrix

The Plücker matrix is a special skew-symmetric 4 × 4 matrix, which characterizes a straight line in projective space.

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Polar curve

In algebraic geometry, the first polar, or simply polar of an algebraic plane curve C of degree n with respect to a point Q is an algebraic curve of degree n−1 which contains every point of C whose tangent line passes through Q. It is used to investigate the relationship between the curve and its dual, for example in the derivation of the Plücker formulas.

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Projection

Projection, projections or projective may refer to.

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Projective connection

In differential geometry, a projective connection is a type of Cartan connection on a differentiable manifold.

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Projective geometry

Projective geometry is a topic in mathematics.

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Projective line

In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity.

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Projective line over a ring

In mathematics, the projective line over a ring is an extension of the concept of projective line over a field.

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Projective linear group

In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V).

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Projective space

In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.

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Projective variety

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective ''n''-space Pn over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety.

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Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

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Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Quaternionic projective space

In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by and is a closed manifold of (real) dimension 4n.

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Qvist's theorem

In projective geometry Qvist's theorem, named after the Finnish mathematician Bertil Qvist, is a statement on ovals in finite projective planes.

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Rational motion

In kinematics, the motion of a rigid body is defined as a continuous set of displacements.

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Rational normal curve

In mathematics, the rational normal curve is a smooth, rational curve of degree in projective n-space.

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Real hyperelliptic curve

A hyperelliptic curve is a class of algebraic curves.

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Real point

In geometry, a real point is a point in the complex projective plane with homogeneous coordinates for which there exists a nonzero complex number such that,, and are all real numbers.

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Real projective line

In geometry, a real projective line is an extension of the usual concept of line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity".

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Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

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Resultant

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients).

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Reye configuration

In mathematics, the Reye configuration, introduced by, is a configuration of 12 points and 16 lines.

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Rotation (mathematics)

Rotation in mathematics is a concept originating in geometry.

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Rotation matrix

In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

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Scaling (geometry)

In Euclidean geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions.

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Segre embedding

In mathematics, the Segre embedding is used in projective geometry to consider the cartesian product (of sets) of two projective spaces as a projective variety.

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Segre's theorem

In projective geometry Segre's theorem, named after the Italian mathematician Beniamino Segre, is the statement.

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Semicubical parabola

In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve defined by an equation of the form.

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Shadow mapping

Shadow mapping or shadowing projection is a process by which shadows are added to 3D computer graphics.

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Shadow volume

Shadow volume is a technique used in 3D computer graphics to add shadows to a rendered scene.

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Silhouette edge

In computer graphics, a silhouette edge on a 3D body projected onto a 2D plane (display plane) is the collection of points whose outwards surface normal is perpendicular to the view vector.

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Singleton bound

In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code C with block length n, size M and minimum distance d.

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Smooth projective plane

In geometry, smooth projective planes are special projective planes.

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Spherical wave transformation

Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames.

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Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

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Surface (mathematics)

In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.

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Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Tautological bundle

In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: the fiber of the bundle over a vector space V (a point in the Grassmannian) is V itself.

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Transformation matrix

In linear algebra, linear transformations can be represented by matrices.

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Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

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Trilinear coordinates

In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle.

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Twisted cubic

In mathematics, a twisted cubic is a smooth, rational curve C of degree three in projective 3-space P3.

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Unit hyperbola

In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x^2 - y^2.

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Unital (geometry)

In geometry, a unital is a set of n3 + 1 points arranged into subsets of size n + 1 so that every pair of distinct points of the set are contained in exactly one subset.

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Veronese surface

In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics.

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Vertex (computer graphics)

A vertex (plural vertices) in computer graphics is a data structure that describes certain attributes, like the position of a point in 2D or 3D space, at multiple points on a surface.

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Wiman's sextic

In mathematics, Wiman's sextic is a degree 6 plane curve with four nodes studied by.

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2D computer graphics

2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them.

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3D projection

3D projection is any method of mapping three-dimensional points to a two-dimensional plane.

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4D vector

In computer science, a 4D vector is a 4-component vector data type.

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Redirects here:

Homogeneous Coordinates, Homogeneous co-ordinates, Homogeneous coordinate, Homogeneous coordinate system, Homogenous coordinates, Projective coordinates.

References

[1] https://en.wikipedia.org/wiki/Homogeneous_coordinates

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