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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
Geometric transformation that preserves lines but not angles nor the origin
homothety, similarity, reflection, rotation, hyperbolic rotation, shear mapping, and compositions of them in any combination and sequence. Viewing an
Affine_transformation
Linear map that preserves areas
the Cartesian plane, but is not a rotation or shear mapping. For a fixed positive real number a, the mapping ( x , y ) ↦ ( a x , y / a ) {\displaystyle (x
Squeeze_mapping
Theorem about right triangles
rectangle of equal area with sides p and q with the help of three shear mappings (shear mappings preserve the area): Hartmut Wellstein, Peter Kirsche: Elementargeometrie
Geometric_mean_theorem
Topics referred to by the same term
lens) Shear mapping, a particular type of mapping in linear algebra, also called transvection Shear matrix in geometry, a linear transformation shearing a
Shear
Translation which preserves parallelism
rotation}}\end{matrix}}} The mathematical model representing simple shear is a shear mapping restricted to the physical limits. It is an elementary linear transformation
Simple_shear
Area interpreted positively or negatively
{\ell }{k}}b,\ b)} shear mapping ∼ ( k a + ℓ b , 1 k b ) {\displaystyle \thicksim (ka+\ell b,\ {\tfrac {1}{k}}b)} squeeze mapping ∼ ( k a + ℓ b , 1
Signed_area
Concepts from linear algebra
to that point. The linear transformation in this example is called a shear mapping. Points in the top half are moved to the right, and points in the bottom
Eigenvalues_and_eigenvectors
Transformation that preserves area measure of regions
the converse is not true. In fact, shear mapping and squeeze mapping are counterexamples to the converse. Shear mapping takes a rectangle to a parallelogram
Equiareal_map
Concept in mathematics
hyperbolic angle is invariant under squeeze mapping, and a difference of slopes is invariant under shear mapping. Ergodic theory is the study of invariant
Invariant_measure
Mathematical term
the idea of angle follows from the difference of slopes. Consider the shear mapping ( u , v ) = ( x , y ) ( 1 v 0 1 ) . {\displaystyle (u,v)=(x
Slope
Central object in linear algebra; mapping vectors to vectors
right and the y axis points up. For shear mapping (visually similar to slanting), there are two possibilities. A shear parallel to the x axis has x ′ = x
Transformation_matrix
Operation on mathematical functions
Composition of a shear mapping (red) and a clockwise rotation by 45° (green). On the left is the original object. Above is shear, then rotate. Below is
Function_composition
Relation between sides of a right triangle
287–288. ISBN 978-1-107-02430-4. See for example Pythagorean theorem by shear mapping Archived 2016-10-14 at the Wayback Machine, Saint Louis University website
Pythagorean_theorem
Euclidean geometry without distance and angles
involves rapidity instead of velocity, and substitutes squeeze mapping for the shear mapping used earlier. This affine geometry was developed synthetically
Affine_geometry
Group of all affine transformations of an affine space
another one. Case 4 corresponds to a shear mapping combined with a dilation. Case 5 corresponds to a shear mapping combined with a dilation. Case 6 corresponds
Affine_group
Group of real 2×2 matrices with unit determinant
and is a shear mapping. If | t r ( A ) | > 2 {\displaystyle |\mathrm {tr} (A)|>2} , then A is called hyperbolic, and is a squeeze mapping. The names
SL2(R)
monodromy round the singular fiber acts on the vanishing cycles, by a shear mapping. The classical, geometric theory of Solomon Lefschetz was recast in
Vanishing_cycle
Topics referred to by the same term
Skewness, a measure of the asymmetry of a probability distribution Shear mapping Skew, also synclinal or gauche in alkane stereochemistry Skew ray (optics)
Skew
Angle of downward strokes in handwriting
input towards a population average or towards 90 degrees. Graphonomics Shear mapping Downey, June Etta (1919). Graphology and the Psychology of Handwriting
Slant_(handwriting)
Book by the Scottish D'Arcy Wentworth Thompson 1917
carapace of the crab Geryon variously to that of Corystes by a simple shear mapping, and to Scyramathia, Paralomis, Lupa, and Chorinus (Pisinae) by stretching
On_Growth_and_Form
Mathematical function, in linear algebra
{A} ={\begin{pmatrix}2&0\\0&2\end{pmatrix}}=2\mathbf {I} } horizontal shear mapping: A = ( 1 m 0 1 ) {\displaystyle \mathbf {A} ={\begin{pmatrix}1&m\\0&1\end{pmatrix}}}
Linear_map
Matrix which differs from the identity matrix by one elementary row operation
j\\1&k=l\\m&k=i,l=j\end{cases}}} These transformations are a kind of shear mapping, also known as a transvections. The inverse of this matrix is given
Elementary_matrix
Exception to a proposed general rule
isometries are mappings that preserve area, but the converse is false as shown by the counterexamples of shear mapping and squeeze mapping. Other examples
Counterexample
Circumellipse of a triangle whose center is the triangle's centroid
inverse shear mapping maps C ′ {\displaystyle C'} back to C {\displaystyle C} and point D {\displaystyle D} is fixed, because it is a point on the shear axis
Steiner_ellipse
dimension Examples of vector spaces Linear map Shear mapping or Galilean transformation Squeeze mapping or Lorentz transformation Linear subspace Row and
Outline_of_linear_algebra
View of mathematicians to consolidate two or more theories into a more generalized one
on slope differences, is invariant because of area preservation of a shear mapping. Early in the 20th century, many parts of mathematics began to be treated
Unifying theories in mathematics
Unifying_theories_in_mathematics
Font style with cursive typeface and slanted design
characters in general text in place of presentational markup. Boldface Shear mapping It has been suggested that his choice to publish such small, cheap editions
Italic_type
Topics referred to by the same term
Transvection (genetics) The creation of a transvectant in invariant theory A shear mapping in linear algebra Raising and lowering indices This disambiguation page
Transvection
Scottish biologist, mathematician, and classics scholar
December 2010. Retrieved 16 February 2011. Waterston, Charles D; Macmillan Shearer, A (2006). Biographical Index of Former Fellows of the Royal Society of
D'Arcy_Wentworth_Thompson
Two geometries based on axioms closely related to those specifying Euclidean geometry
{\displaystyle x^{\prime }=x+vt,\quad t^{\prime }=t} are equivalent to a shear mapping in linear algebra: ( x ′ t ′ ) = ( 1 v 0 1 ) ( x t ) . {\displaystyle
Non-Euclidean_geometry
Three-dimensional homogeneous flattening of a body
principal stretch. Simple shear Squeeze mapping Reish, Nathaniel E.; Gary H. Girty. "Definition and Mathematics of Pure Shear". San Diego State University
Pure_shear
Overview of and topical guide to geometry
Translation Glide reflection Similarity Similarity transformation Homothety Shear mapping 2D computer graphics 2D geometric model Altitude Brahmagupta's formula
Outline_of_geometry
Key layout for musical instruments
The two pitch arrays are trivially obtained from each other by direct shear mapping. This note layout created by Euler is utilised in Neo-Riemannian theory
Harmonic_table_note_layout
Technology capable of matching a face from an image against a database of faces
Research Organisation (ISRO) is developing a new technology called Crime Mapping Analytics and Predictive System (CMAPS). The project aims to deploy space
Facial_recognition_system
Texture mapping technique
normal mapping, or Dot3 bump mapping, is a texture mapping technique used for faking the lighting of bumps and dents – an implementation of bump mapping. It
Normal_mapping
Data analysis technique
different directions to teach models positional invariance. Scaling Shear Mapping Cropping: Removing sections of the image to focus on particular features
Data_augmentation
Method of defining surface detail on a computer-generated graphic or 3D model
complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and
Texture_mapping
Real numbers adjoined with a nil-squaring element
of a rotation in the dual number plane is equivalent to a vertical shear mapping since (1 + pε)(1 + qε) = 1 + (p + q)ε. In absolute space and time the
Dual_number
Video software application produced by Apple Inc.
'anchor point' that acts as the center of rotation or enlargement. Shear mapping Drop shadow Four Corner, which changes the perspective of objects. Crop
Motion_(software)
Method to draw shadows in computer graphic images
Shadow mapping or shadowing projection is a process by which shadows are added to 3D computer graphics. This concept was introduced by Lance Williams
Shadow_mapping
Concept in physics and mathematics
the language of linear algebra, this transformation is considered a shear mapping, and is described with a matrix acting on a vector. With motion parallel
Galilean_transformation
Vector satisfying some of the criteria of an eigenvector
spaces Hamel dimension Examples of vector spaces Linear map Shear mapping Squeeze mapping Linear subspace Row and column spaces, Null space Rank–nullity
Generalized_eigenvector
Set of imaging methods for determining soft-tissue hardness
elasticity mapping using shear waves is often replaced by SWE. The principal difference between SWEI and ARFI is that SWEI is based on the use of shear waves
Elastography
Canadian computer scientist and author (1956–2018)
research contributions to computer graphics, including algorithms for shear mapping and pre–image compression filtering; the Paeth filter implemented in
Alan_W._Paeth
Result of repeatedly applying a mathematical function
the smallest positive exponent that produces the identity. Below is a shear mapping with infinite order. Below that are their compositions, which both have
Iterated_function
List of alternatives to Darwinian natural selection
geometric transformation of one fish's body form into another with a 20° shear mapping. He did not discuss the evolutionary causes of such a change, raising
Alternatives to Darwinian evolution
Alternatives_to_Darwinian_evolution
Medical imaging methodology
Shear wave elastography (SWE), as a type of elastography, is a non-invasive medical imaging technique used to quantitatively assess the elasticity and
Shear_wave_elastography
radiation or mechanical shearing seems to be more random. It has been used to genetically map several organisms. HAPPY mapping has also been adapted to
Happy_mapping
Group of flat spacetime symmetries
that acts on absolute time and space. Instead of boosts, it features shear mappings to relate co-moving frames of reference. In general relativity, i.e
Poincaré_group
Soviet mathematician (1921–1988)
relativity." The approach taken is elementary; simple manipulations by shear mapping lead on page 68 to the conclusion that "the difference between the Galilean
Isaak_Yaglom
being a shear mapping when acting on the dual number plane. Other angles in the plane are generated by such action, and since shear mapping preserves
Laguerre_transformations
Attempt to explain evolution by forces other than natural selection
geometric transformation of one fish's body form into another with a 20° shear mapping. He does not discuss the evolutionary causes of such a structural change
Structuralism_(biology)
Simulation of the appearance of being three-dimensional
techniques. Parallax mapping (also called offset mapping or virtual displacement mapping) is an enhancement of the bump mapping and normal mapping techniques implemented
2.5D
Gravitational deflection of light
terms, the convergence and shear. The convergence term magnifies the background objects by increasing their size, and the shear term stretches them tangentially
Weak_gravitational_lensing
Homeomorphism between plane domains
Gareth Wyn; Mahadevan, L. (2013), "Planar morphometry, shear and optimal quasi-conformal mappings", Proceedings of the Royal Society A: Mathematical, Physical
Quasiconformal_mapping
Parametrizes complex structures on a surface
dimension 6 g − 6 + 2 k {\displaystyle 6g-6+2k} . These coordinates are called shear coordinates. For closed surfaces, a pair of pants can be decomposed as the
Teichmüller_space
Process of finding a spatial transformation that aligns two point clouds
transformations include affine transformations such as scaling and shear mapping. However, in the context of point set registration, non-rigid registration
Point-set_registration
Computer graphics technique
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Physically_based_rendering
Origin point beneath an air explosion
Earthquake Epicenters, Hypocenters, Faults and Lineaments in Montana". Digital Mapping Techniques '00 -- Workshop Proceedings. United States Geological Survey
Hypocenter
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Cone_tracing
Representing a 3D-modeled object or dataset as a 2D projection
technique. A combination of these techniques is possible. For instance, a shear warp implementation could use texturing hardware to draw the aligned slices
Volume_rendering
Type of program in computer graphics
outputting the same color, to applying a lighting value, to doing bump mapping, shadows, specular highlights, translucency and other phenomena. They can
Shader
3D projection in which points in 3D space are linearly mapped onto a 2D plane
projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional projection
Planar_projection
Type of application software
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Graphics_software
3D computer graphics rendering technique
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Checkerboard_rendering
3D computer graphics rendering method
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Ray_marching
Computer graphics method
Metropolis light transport, and ways of combining path tracing with photon mapping. Video games often use biased versions of path tracing to improve performance
Path_tracing
Computer graphics rendering technique
the images. Spectral rendering is often used in ray tracing or photon mapping to more accurately simulate the scene, often for comparison with an actual
Spectral_rendering
Natural hazard involving ground movement
This is essentially due to a decrease in the shear strength of the slope material, an increase in the shear stress borne by the material, or a combination
Landslide
Fault zone in Cameroon
The Foumban Shear Zone, or Central Cameroon Shear Zone (CCSZ), is a fault zone in Cameroon that has been correlated with the Pernambuco fault in northeastern
Foumban_Shear_Zone
Graphics that use a three-dimensional representation of geometric data
features, such as ray tracers and other rendering alternatives and texture mapping facilities. Some also contain features that support or allow animation
3D_computer_graphics
Planar movement within a Euclidean space without rotation
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Translation_(geometry)
Screen-space shading technique
shading. These features also allow them to correctly apply HDR luminance mapping to anti-aliased edges, where in earlier versions of the API any benefit
Deferred_shading
Set of overlapping DNA segments that together represent a consensus region of DNA
by Rodger Staden (1979). The bottom-up DNA sequencing strategy involves shearing genomic DNA into many small fragments ("bottom"), sequencing these fragments
Contig
Simulation of reflective surfaces
usually be computed faster by using simpler methods such as environment mapping. Reflections on shiny surfaces like wood or tile can add to the photorealistic
Reflection (computer graphics)
Reflection_(computer_graphics)
Simulation of light in computer graphics
Object oriented lighting, also known as local illumination, is defined by mapping a single light source to a single object. This technique is fast to compute
Computer_graphics_lighting
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Fragment_(computer_graphics)
3D computer graphics image rendering method
complexity with costly pixel operations (i.e. perspective-correct texture mapping without hardware assist). This use preceded the widespread adoption of
Scanline_rendering
Chaotic map from the torus into itself
That is, with a unit equal to the width of the square image, the image is sheared one unit up, then two units to the right, and all that lies outside that
Arnold's_cat_map
Type of weather map
narrow zone where wind direction changes over a short distance, known as a shear line, depicted as a blue line of single alternating dots and dashes. Mesoscale
Surface_weather_analysis
Shading language for WebGPU
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
WebGPU_Shading_Language
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Diffusion_curve
Visibility in 3D computer graphics
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Hidden-surface_determination
Only rendering polygons facing towards the camera
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Back-face_culling
Computer software architecture in 3D computer graphics
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Reyes_rendering
Excluding certain graphical elements from being rendered in a scene
overflow of depth-buffer values. Some early texture mapping hardware (using forward texture mapping) in video games suffered from complications associated
Clipping_(computer_graphics)
Design technique
(graphical) Plan (drawing) Planar projection Technical drawing Tesseract Texture mapping Timeline of early 3D computer graphics hardware Transform, clipping, and
3D_projection
improper rotations and most generally similarity transformations. However, shear transformations and non-uniform scaling are not. Conformal linear transformations
Conformal linear transformation
Conformal_linear_transformation
Graphics mode on the Super NES video game console
produce any combination of translation, scaling, reflection, rotation, and shearing. However, many games create additional effects by setting a different transformation
Mode_7
casts beams from the light source into the environment. Similar to photon mapping, backwards beam tracing may be used to efficiently model lighting effects
Beam_tracing
DNA visualization technique
the optical mappings. The modern optical mapping platform works as follows: Genomic DNA is obtained from lysed cells, and randomly sheared to produce a
Optical_mapping
Computer graphics algorithm
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Warnock_algorithm
Computer graphics technique
Carmack's Reverse[citation needed]. In modern real-time rendering, Shadow mapping techniques and their variations have become more widely used, due to their
Shadow_volume
Sub-discipline of civil engineering
creating a shearing action with the third layer of fluid, and so on. As the fluid passes further along with the plate, the zone in which shearing action occurs
Hydraulic_engineering
Geometric transformation
n<1} , it is a contraction. If m × n = 1, the transformation is a squeeze mapping. Mathematics portal 2D computer graphics#Scaling Digital zoom Dilation
Scaling_(geometry)
Type of video game graphics
Path Rendering Checkerboard Scanline Rotation Scaling Shadow mapping Shadow volume Shear matrix Shader Texel Translation Volume rendering Voxel Software
Isometric_video_game_graphics
Method of spatial measurement using laser
forestry, atmospheric physics, laser guidance, airborne laser swathe mapping (ALSM), and laser altimetry. It is used to make digital 3D representations
Lidar
Fundamental unit of a texture map
centroid. When texturing a 3D surface or surfaces (a process known as texture mapping), the renderer maps texels to appropriate pixels in the geometric fragment
Texel_(graphics)
Concept in physics
diagonal term involving the convergence and a trace-free term involving the shear γ {\displaystyle \gamma ~} A = ( 1 − κ ) [ 1 0 0 1 ] − γ [ cos 2 ϕ sin
Gravitational lensing formalism
Gravitational_lensing_formalism
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