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Branch of mathematics concerned with the movement of shapes and sets
mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing
Transformation_geometry
Geometric transformation that preserves lines but not angles nor the origin
In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines
Affine_transformation
Property of objects which are scaled or mirrored versions of each other
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely
Similarity_(geometry)
Bijection of a set using properties of shapes in space
The study of geometry may be approached by the study of these transformations, such as in transformation geometry. Geometric transformations can be classified
Geometric_transformation
Euclidean geometry without distance and angles
through P.) is fundamental in affine geometry. Comparisons of figures in affine geometry are made with affine transformations, which are mappings that preserve
Affine_geometry
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Type of geometry
mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared
Projective_geometry
Isomorphism of projective spaces in geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces
Homography
Rational function of the form (az + b)/(cz + d)
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f ( z ) = a z + b c z + d {\displaystyle
Möbius_transformation
Function that applies a set to itself
Infinitesimal transformation Linear transformation List of transforms Rigid transformation Transformation geometry Transformation semigroup Transformation group
Transformation_(function)
Overview of and topical guide to geometry
Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation geometry
Outline_of_geometry
Study of angle-preserving transformations
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines
Inversive_geometry
Central object in linear algebra; mapping vectors to vectors
(computer vision) Rigid transformation Transformation (function) Transformation geometry Gentle, James E. (2007). "Matrix Transformations and Factorizations"
Transformation_matrix
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Study of angle-preserving transformations of a geometric space
conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is
Conformal_geometry
Concept in physics and mathematics
Galilean geometry. This is the passive transformation point of view. In special relativity the homogeneous and inhomogeneous Galilean transformations are,
Galilean_transformation
Distance-preserving mathematical transformation
mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective
Isometry
Topics referred to by the same term
points in geometry Infinitesimal transformation, a limiting case of a geometrical transformation Chemical transformation Phase transformation, a physical
Transformation
Planar movement within a Euclidean space without rotation
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given
Translation_(geometry)
Topics referred to by the same term
Similarity transformation may refer to: Similarity (geometry), for shape-preserving transformations Matrix similarity, for matrix transformations of the form
Similarity_transformation
Geometrical property
In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object
Symmetry_(geometry)
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Differential_geometry
Geometric transformation
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale
Scaling_(geometry)
Study of geometry using a coordinate system
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts
Analytic_geometry
Coordinate system using perpendicular axes
In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely
Cartesian_coordinate_system
Branch of differential geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds. An example of a Riemannian manifold is a surface, on which
Riemannian_geometry
Family of linear transformations
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that
Lorentz_transformation
Mathematical model of the physical space
coordinates (analytic geometry), the use of transformation groups (Erlangen program), or the use of calculus (differential geometry). The Elements is mainly
Euclidean_geometry
Branch of geometry
"contact transformation". Similarly, the line-sphere correspondence and other transformations of the Lie sphere geometry are contact transformations. While
Contact_geometry
parallelism. Affine geometry of curves The study of curve properties that are invariant under affine transformations. Affine differential geometry A type of differential
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Topics referred to by the same term
dodges an attack Layoff Child displacement Offset (disambiguation) Transformation (geometry) This disambiguation page lists articles associated with the title
Displacement
Transformation of a geometric space preserving structure
In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a
Motion_(geometry)
Unique point and line of a conic section
section is the transformation of each point in the plane into its polar line and each line in the plane into its pole. In projective geometry, this affords
Pole_and_polar
Method for specifying point positions
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points
Coordinate_system
Mathematical function that preserves angles
conformal maps are described by linear fractional transformations in each case. In Riemannian geometry, two Riemannian metrics g {\displaystyle g} and h
Conformal_map
Topics referred to by the same term
a congruent transformation (or congruence transformation) is: Another term for an isometry; see congruence (geometry). A transformation of the form A
Congruent_transformation
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
Branch of mathematics
projective geometry (along with other types of geometry) from the viewpoint that the geometry on a space is encoded in a certain class of transformations on the
Algebraic_geometry
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
Research program on the symmetries of geometry
invariant under projective transformations (something familiar in geometrical perspective). The way the multiple languages of geometry then came back together
Erlangen_program
Mathematical formulation of vector pairs used in physics (rigid body dynamics)
the transformation. In transformation geometry, the elemental concept of transformation is the reflection (mathematics). In planar transformations a translation
Screw_theory
Subfield of conformal geometry
further developed the field of Möbius geometry. Informally, Möbius geometry is the study of geometric transformations turning hyperspheres back into hyperspheres
Möbius_geometry
Completion of the usual space with "points at infinity"
projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix
Projective_space
Shape with three sides
three sides connected at three corners. It is one of the basic shapes in geometry and the simplest of polygons. The corners, also called vertices, are zero-dimensional
Triangle
Conic solid with a polygonal base
p. 23, ISBN 978-1-134-13953-8. Johnson, Norman W. (2018), Geometries and Transformations, Cambridge University Press, ISBN 978-1-107-10340-5. See Chapter
Pyramid_(geometry)
Geometric surface
In geometry, a pseudosphere is a surface in R 3 {\displaystyle \mathbb {R} ^{3}} . It is the most famous example of a pseudospherical surface. A pseudospherical
Pseudosphere
Geometric surface
(geometry)". Archived from the original on 2011-07-23. Retrieved 2009-11-12. Rogers and Schief (2002). Bäcklund and Darboux transformations: geometry and
Dini's_surface
Generalized scaling operation in geometry
affine transformations with the property that the image of every line g is a line parallel to g. In projective geometry, a homothetic transformation is a
Homothety
Procedure to convert 3D scenes to 2D images
However, more complex transformations such as vertex blending are possible. Freely programmable geometry shaders that modify the geometry can also be executed
Graphics_pipeline
under affine transformations. Its equiaffine form, often called equiaffine differential geometry, studies invariants under affine transformations that preserve
Affine_differential_geometry
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Mathematical transformation that preserves distances
mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that
Rigid_transformation
Möbius transformation generalized to rings other than the complex numbers
a linear fractional transformation (or fractional–linear transformation/map) is, roughly speaking, an invertible transformation of the form z ↦ a z +
Linear fractional transformation
Linear_fractional_transformation
Field of mathematics dealing with three-dimensional Euclidean spaces
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional
Solid_geometry
Four-sided polygon
In geometry, a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri
Quadrilateral
Geometry founded on spheres
projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which preserve it. This geometry can be difficult to visualize
Lie_sphere_geometry
Special class of linear fractional transformations
In projective geometry, a special conformal transformation is a linear fractional transformation that is not an affine transformation. Thus the generation
Special conformal transformation
Special_conformal_transformation
VLSI chip
typically a portion of a transformation matrix. Clark anticipated that a pipeline of twelve Geometry Engines would comprise a Geometry System "to accomplish
Geometry_Engine
Graph of space and time in special relativity
Minkowski Diagram, and used as a standard illustration of the transformation geometry of special relativity. E. T. Whittaker has pointed out that the
Spacetime_diagram
India's national-level mathematics contest conducted by the (AMTI)
numbers. Geometry: Geometry of triangles and circles. (Trigonometric methods, vector methods, complex number methods, transformation geometry methods can also
National Mathematics Talent Contest
National_Mathematics_Talent_Contest
Formula for area of a grid polygon
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points
Pick's_theorem
Invariant in projective geometry
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
Cross-ratio
Polyhedron with 8 triangles and 6 squares
J.D. (1971). "A geometric transformation concept for expanding rigid structures". NASA Report: Advanced structural geometry studies, Part 2. Vol. CR-1735
Cuboctahedron
Mathematical function, in linear algebra
two vector spaces are the same, a linear map is also called a linear transformation or linear endomorphism. A linear map is a homomorphism of vector spaces
Linear_map
Branch of mathematics
For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations
Linear_algebra
Linear map that preserves areas
Bianchi in 1879.) Such transformations of pseudospherical surfaces were discussed in detail in the lectures on differential geometry by Gaston Darboux (1894)
Squeeze_mapping
Design technique
after all necessary transformations have been applied. 3D computer graphics Camera matrix Computer graphics Cross section (geometry) Cross-sectional view
3D_projection
French mathematician (1834–1886)
foundations of a geometry of oriented spheres (Laguerre geometry and Laguerre plane), including the Laguerre transformation or transformation by reciprocal
Edmond_Laguerre
Book on philosophy of mathematics
space & time: curvature calculus; differential geometry --Without cycling Change Real analysis; transformation group --With cycling Repetition pi; trigonometry;
Mathematics, Form and Function
Mathematics,_Form_and_Function
Coordinate system used in projective geometry
system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates
Homogeneous_coordinates
Maths textbook
(ISBN 0-486-63830-8), including the subtitle Circle Geometry, Moebius Transformation, Non-Euclidean Geometry. The Basic Library List Committee of the Mathematical
Geometry_of_Complex_Numbers
based image geometry correction system). Calculation of the image geometry correction transformation The image geometry correction transformation can be calculated
Image_geometry_correction
Creating a complex 3D surface or object by combining primitive objects
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a
Constructive_solid_geometry
Line or vector perpendicular to a curve or a surface
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve
Normal_(geometry)
American professor and author
include transformational geometry in cornrow braiding, spiral arcs in graffiti, least common multiples in percussion rhythms, and analytic geometry in Native
Ron_Eglash
Geometric transformation combining reflection and translation
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide")
Glide_reflection
Compact astronomical body
determine whether such an event occurred. For non-rotating black holes, the geometry of the event horizon is precisely spherical, while for rotating black holes
Black_hole
Concept in mathematics
In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times
Integral_geometry
Type of geometric transformation
In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed
Shear_mapping
Relation between sides of a right triangle
theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of
Pythagorean_theorem
German mathematician (1905–1988)
Legendre–Fenchel transformation Convex minimization Fenchel's duality theorem Geometry Convex geometry Brunn–Minkowski theorem Differential geometry Fenchel's
Werner_Fenchel
Property that is not changed by mathematical transformations
areas of mathematics such as geometry, topology, algebra and discrete mathematics. Some important classes of transformations are defined by an invariant
Invariant_(mathematics)
Mathematical model combining space and time
connected to certain types of sphere, hyperbolic, or conformal geometries and their transformation groups already developed in the 19th century, in which invariant
Spacetime
Generalization of affine connections
geometry and pseudogroup geometry is that the symmetry for a Cartan geometry relates infinitesimally close points by an infinitesimal transformation in
Cartan_connection
James R. (1997), "An eye for similarity transformations", in King, James R.; Schattschneider, Doris (eds.), Geometry Turned On: Dynamic Software in Learning
Dilation_(metric_space)
Geometry without the parallel postulate
Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally
Absolute_geometry
Family of geometric objects with a common property
Schwerdtfeger, Hans (1979) [1962], Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry, Dover, pp. 8–10. Young, John
Pencil_(geometry)
Branch of computational geometry
Hoberman into transformational geometry as a design idiom, and applications of this design idiom within the domain of architectural geometry. Architectural
Geometric_design
Term in geometry
lie on one line. The proper setting for this concept is in projective geometry where there will be no special cases due to parallel lines since all lines
Perspective_(geometry)
Relation of space and time in relativity theory
In geometry, given a pair of conjugate hyperbolas, two conjugate diameters are hyperbolically orthogonal. This relationship of diameters was described
Hyperbolic_orthogonality
Mathematical transformation
S2CID 37549350. Nielsen, Frank (2010-09-01). "Legendre transformation and information geometry" (PDF). Retrieved 2016-01-24. Touchette, Hugo (2005-07-27)
Legendre_transformation
Mathematical invariance under transformations
is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these
Symmetry
Theorem in complex analysis
theory Nevanlinna theory Geometric function theory Teichmüller theory Several complex variables Complex geometry Complex dynamics Mathematics portal v t e
Argument_principle
Transformation of coordinates that moves the origin
equations of curves using the methods of analytic geometry. To use the method of coordinate geometry, the axes are placed at a convenient position with
Translation_of_axes
Theorem of dynamical systems
the example of the springs). More precisely, there exists a canonical transformation to action-angle coordinates in which the transformed Hamiltonian is
Liouville–Arnold_theorem
Distinction between meanings of Euclidean space transformations
Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative
Active and passive transformation
Active_and_passive_transformation
Concept in projective geometry
In projective geometry, a correlation is a transformation of a d-dimensional projective space that maps subspaces of dimension k to subspaces of dimension
Correlation (projective geometry)
Correlation_(projective_geometry)
Branch of mathematics that studies the properties of groups
certain structure. The theory of transformation groups forms a bridge connecting group theory with differential geometry. A long line of research, originating
Group_theory
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Skeletonized version of algebraic geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication
Tropical_geometry
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