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Geometric transformation
affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor
Scaling_(geometry)
Changing the resolution of a digital image
pixel number (scaling down), this usually results in a visible quality loss. From the standpoint of digital signal processing, the scaling of raster graphics
Image_scaling
Topics referred to by the same term
Look up scaling in Wiktionary, the free dictionary. Scaling may refer to: Scaling (geometry), a linear transformation that enlarges or diminishes objects
Scaling
Generalized scaling operation in geometry
also conformal because it is composed of translation and uniform scale. Scaling (geometry) a similar notion in vector spaces Homothetic center, the center
Homothety
Topics referred to by the same term
Manufacturer Something which has undergone a scale transformation Scale model#Scales Scaling (geometry) Scale (disambiguation) This disambiguation page lists
Scaled
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
VLSI chip
twelve Geometry Engines would comprise a Geometry System "to accomplish 4 × 4 matrix multiplications; line, character, and polygon clipping; and scaling of
Geometry_Engine
Type of metric geometry
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined
Taxicab_geometry
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Property of objects which are scaled or mirrored versions of each other
other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation
Similarity_(geometry)
Ratio of distance on a map to the corresponding distance on the ground
point scale across a map. The foundations for quantitative map scaling goes back to ancient China with textual evidence that the idea of map scaling was
Scale_(map)
Planar movement within a Euclidean space without rotation
graphics#Translation Advection Change of basis Parallel transport Rotation matrix Scaling (geometry) Transformation matrix Translational symmetry LIMA, 2001 Edmund Taylor
Translation_(geometry)
Study of angle-preserving transformations of a geometric space
that are defined up to scale. Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry. A conformal manifold is
Conformal_geometry
American mathematician (1943–2024)
possibilities for the small-scale geometry around points with large curvature, and hence to systematically modify the geometry so as to continue the Ricci
Richard_S._Hamilton
Distance-preserving mathematical transformation
theorem 3D isometries that leave the origin fixed Partial isometry Scaling (geometry) Semidefinite embedding Space group Symmetry in mathematics "We shall
Isometry
Topics referred to by the same term
space Dilation (morphology), an operation in mathematical morphology Scaling (geometry), including: Homogeneous dilation (homothety), the scalar multiplication
Dilation
Topics referred to by the same term
refer to: Canvas stretching, the lengthening of a canvas by pulling Scaling (geometry) in one direction Stretching (body piercing), the deliberate expansion
Stretching_(disambiguation)
Infinitely detailed mathematical structure
Multifractal scaling: characterized by more than one fractal dimension or scaling rule Fine or detailed structure at arbitrarily small scales. A consequence
Fractal
Type of program in computer graphics
Shaders act on data such as vertices and primitives, generate or morph geometries and fragments, and calculate the colors in a rendered image. Shaders can
Shader
Property shared by codirectional lines
In geometry, direction, also known as spatial direction, vector direction or relative direction, is the common characteristic of all rays which coincide
Direction_(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
Real-valued number of spatial dimensions
into the square. Such familiar scaling relationships obey equation (1), where ε {\displaystyle \varepsilon } is the scaling factor, D {\displaystyle D} the
Fractal_dimension
Number functioning as an exponent
more than 8 bits are required to scale them down and store them in a fixed-point format. Logarithm Scaling (geometry) Scientific notation Linz & Wang
Scale factor (computer science)
Scale_factor_(computer_science)
Set of related ordination techniques used in information visualization
known as Principal Coordinates Analysis (PCoA), Torgerson Scaling or Torgerson–Gower scaling. It takes an input matrix giving dissimilarities between pairs
Multidimensional_scaling
Form of computer-aided engineering
Open CASCADE Polygon mesh Polygonal modeling Ray tracing (graphics) Scaling (geometry) SIGGRAPH Stanford bunny Triangle mesh Utah teapot Voxel B-rep "What
3D_modeling
Algebraic operation
multiplication Multiplication of vectors Product (mathematics) Scalar division Scaling (geometry) Lay, David C. (2006). Linear Algebra and Its Applications (3rd ed
Scalar_multiplication
Non-Euclidean geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel
Elliptic_geometry
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
Parametrizes complex structures on a surface
complete. This is the metric most commonly used for the study of the metric geometry of Teichmüller space. In particular it is of interest to geometric group
Teichmüller_space
Branch of geometry
Descriptive geometry is a type of technical drawing and the branch of geometry which allows the representation of three-dimensional objects in two dimensions
Descriptive_geometry
Field of knowledge
properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the quantitative
Mathematics
Line segment joining two adjacent vertices in a polygon or polytope
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon,
Edge_(geometry)
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
Feature of some electrical appliances
such as cache memory and main memory. With dynamic voltage scaling and dynamic frequency scaling, the CPU core voltage, clock rate, or both, can be altered
Power_management
Verification of geometric constraints on electronic designs
design rules and DRC is greatest for ICs, which have micro- or nano-scale geometries; for advanced processes, some fabs also insist upon the use of more
Design_rule_checking
Function between two metric spaces that only respects their large-scale geometry
between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale details. Two metric spaces are quasi-isometric
Quasi-isometry
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
Form of an object
(PDF) on 2021-11-16. Retrieved 2019-09-25. Here, scale means only uniform scaling, as non-uniform scaling would change the shape of the object (e.g., it
Shape
Computer format for representing real numbers
multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 123 with an implicit scaling factor of 1/100
Fixed-point_arithmetic
metric space is locally a discrete topological space, but its large-scale geometry exhibits meaningful structure. For instance, the volume of a ball of
Infinite_group
Mathematical set with some added structure
meaningful in Euclidean geometry but meaningless in projective geometry. A different situation appeared in the 19th century: in some geometries the sum of the
Space_(mathematics)
Features that do not change if length or energy scales are multiplied by a common factor
all along the curve. Some fractals may have multiple scaling factors at play at once; such scaling is studied with multi-fractal analysis. Periodic external
Scale_invariance
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
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
further reduced cubic scaling law E∝ρ3 is common, such as with aerogels and aerogel composites. The dependence of scaling on geometry is seen in periodic
Reversibly assembled cellular composite materials
Reversibly_assembled_cellular_composite_materials
image geometry correction, the spatial transformation consists of spatially defined 2-dimensional image re-sampling or scaling filter. The scaling operation
Image_geometry_correction
Local and global geometry of the universe
geometry and cosmic topology. Local geometry is defined primarily by its curvature, general relativity explains how spatial curvature (local geometry)
Shape_of_the_universe
Historical development of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry
History_of_geometry
Matrices similar to diagonal matrices
n-Schatten norm. Note that n ≥ 2 {\displaystyle n\geq 2} Defective matrix Scaling (geometry) Triangular matrix Semisimple operator Diagonalizable group Jordan
Diagonalizable_matrix
geometric topology, Busemann functions are used to study the large-scale geometry of geodesics in Hadamard spaces and in particular Hadamard manifolds
Busemann_function
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)
Austrian physicist (born 1961)
Vienna. She is known for her groundbreaking research on the atomic scale geometry and electronic structure of metal-oxide surfaces. Diebold was born on
Ulrike_Diebold
Mathematical study of triangle properties (19th century–present)
In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed
Modern_triangle_geometry
Quadrilateral symmetric across a diagonal
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and
Kite_(geometry)
Set of mathematical concepts in quantum gravity
gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable to the
Quantum_geometry
Geometric line segment whose endpoints lie on a circular arc
In geometry, a chord (from Latin chorda 'catgut, string') of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord
Chord_(geometry)
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
Geometric operation which truncates the edges of polyhedra
In geometry, a chamfer or edge-truncation is a topological operator that modifies one polyhedron into another. It separates the faces by reducing them
Chamfer_(geometry)
Power scaling of a laser is increasing its output power without changing the geometry, shape, or principle of operation. Power scalability is considered
Laser_power_scaling
Musical keyboard layout designed by Paul von Jankó
overcome two limitations on the traditional piano keyboard: the large-scale geometry of the keys (stretching beyond a ninth, or even an octave, can be difficult
Jankó_keyboard
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
Game engine
generate normal maps for finer details. Nanite automatically manages LoDs by scaling models dynamically based on draw distance, screen resolution, and performance
Unreal_Engine_5
Counterintuitive observation
coastline approaches infinity. Richardson had believed, based on Euclidean geometry, that a coastline would approach a fixed length, as do similar estimations
Coastline_paradox
Study of geometries as axiomatic systems
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean
Foundations_of_geometry
Concept in geometry and topology
large-scale structure of metric spaces and topological spaces to be defined. The concern of traditional geometry and topology is with the small-scale structure
Coarse_structure
Geometric shape
In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called
Cone
Vector representing the position of a point with respect to a fixed origin
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its
Position_(geometry)
Property of a mathematical space
back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William
Dimension
Topological model
invariant to rotation, translation and scaling transformations. The matrix provides an approach for classifying geometry relations. Roughly speaking, with
DE-9IM
Algorithm for solving linear programming problems
gradient descent steps in a re-scaled version of the problem, then scaling the step back to the original problem. The scaling ensures that the algorithm can
Affine_scaling
Bijection of a set using properties of shapes in space
distances (e.g., resizing); Affine transformations preserve parallelism (e.g., scaling, shear); Projective transformations preserve collinearity; Each of these
Geometric_transformation
EDA file format for integrated circuits
the subroutine number and a subroutine scaling factor. There are no arguments to the DF statement. The scaling factor for a subroutine consists of a numerator
Caltech_Intermediate_Form
Conic solid with a polygonal base
Prismatoids", Discrete & Computational Geometry, 18: 13–52, doi:10.1007/PL00009307. O'Leary, Michael (2010), Revolutions of Geometry, John Wiley & Sons, p. 10,
Pyramid_(geometry)
In geometry, a centre (Commonwealth English) or center (American English) (from Ancient Greek κέντρον (kéntron) 'pointy object') of an object is a point
Centre_(geometry)
Musical scale comprising seven notes
LLC. ISBN 978-0-8258-5699-0. Tymoczko, Dmitri (2011). "Chapter 4". A Geometry of Music. New York: Oxford. "Musicstudents.com - Free Sheet Music and Play-Along
Major_scale
Technique used in realtime rendering
In real-time computer graphics, geometry instancing is the practice of rendering multiple copies of the same mesh in a scene at once. This technique is
Geometry_instancing
Measure of angles
fixed-point format, with the same scaling factor; or a fraction of half-turn between −1.0 (inclusive) and +1.0 (exclusive) with scaling factor 1/2n−1. Either way
Binary_angular_measurement
One of eight divisions of a Euclidean 3D coordinate system
An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It
Octant_(solid_geometry)
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric
List of interactive geometry software
List_of_interactive_geometry_software
Simple curve of Euclidean geometry
mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Annulus: a ring-shaped object, the region bounded
Circle
French-American mathematician (1924–2010)
"fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory
Benoit_Mandelbrot
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)
Mathematical treatise by Euclid
and theorems with their proofs that covers plane and solid Euclidean geometry, elementary number theory, and incommensurability. These include the Pythagorean
Euclid's_Elements
Completion of the usual space with "points at infinity"
generally preferred. There are two classes of definitions. In synthetic geometry, point and line are primitive entities that are related by the incidence
Projective_space
Research institute
chemistry and material science. Geometry and complex systems (Jürgen Jost) Pattern formation, energy landscapes and scaling laws (Felix Otto) Nonlinear algebra
Max Planck Institute for Mathematics in the Sciences
Max_Planck_Institute_for_Mathematics_in_the_Sciences
Study of random spatial patterns
In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This
Stochastic_geometry
Hard skeletal covering of fish
filefish. Some filefish appear scaleless because their scales are so small. Prominent scaling appears on tuna only along the lateral line and in the corselet
Fish_scale
Set of points equidistant from a center
(sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from
Sphere
System that relates geologic strata to time
controlled by the amount and type of sediment in a sedimentary basin, and the geometry of that basin. The principle of cross-cutting relationships that states
Geologic_time_scale
Scales used by rail transport models
gauge. Conversely, modeling standard gauge in Lego trains would yield a scaling of (37.5:1435 =) 1:38.3. Live steam model railways are not standardized
Rail transport modelling scales
Rail_transport_modelling_scales
Depth of an impact crater
crater. Using the following concepts, a crater is measured: Measurement Scales Geometry Graphing data Drawing conclusions A method of measuring a crater is
Crater_depth
Board with pegs used as a geometric demonstration
is a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other
Geoboard
Interactive online visualization tool
The Scale of the Universe is an interactive online visualization tool and website created in January 2010 by twin brothers Cary and Michael Huang. It
The_Scale_of_the_Universe
Geometry definition file format
OBJ (or .OBJ) is a geometry definition file format first developed by Wavefront Technologies for The Advanced Visualizer animation package. It is an open
Wavefront_.obj_file
French mathematician (1928–2014)
mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative
Alexander_Grothendieck
Constructing product by means of computer
to edit geometry without a history tree. With direct modeling, once a sketch is used to create geometry it is incorporated into the new geometry, and the
Computer-aided_design
Model for predicting molecular geometry
vəˈsɛpər/ VESP-ər, və-SEP-ər) is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their
VSEPR_theory
Geometric space with four dimensions
ordinary space is called Euclidean space because it corresponds to Euclid's geometry, which was originally abstracted from the spatial experiences of everyday
Four-dimensional_space
Approximate power law relating animal metabolic rate to mass
3⁄4 exponent. Before Kleiber's observation of the 3/4 power scaling, a 2/3 power scaling was largely anticipated based on the "surface law", which states
Kleiber's_law
Smallest convex set containing a given set
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined
Convex_hull
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SCALING GEOMETRY
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