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- Shear_mapping abstract "In plane geometry, a shear mapping is a linear map that displaces each point in fixed direction, by an amount proportional to its signed distance from a line that is parallel to that direction. This type of mapping is also called shear transformation, transvection, or just shearing. An example is the mapping that takes any point with coordinates to the point . In this case, the displacement is horizontal, the fixed line is the -axis, and the signed distance is the coordinate. Note that points on opposite sides of the reference line are displaced in opposite directions.Shear mappings must not be confused with rotations. Applying a shear map to a set of points of the plane will change all angles between them (except straight angles), and the length of any line segment that is not parallel to the direction of displacement. Therefore it will usually distort the shape of a geometric figure, for example turning squares into non-square parallelograms, and circles into ellipses. However a shearing does preserve the area of geometric figures, the alignment and relative distances of collinear points. A shear mapping is the main difference between the upright and slanted (or italic) styles of letters.The same definition is used in three-dimensional geometry, except that the distance is measured from a fixed plane. A three-dimensional shearing transformation preserves the volume of solid figures, but changes areas of plane figures (except those that are parallel to the displacement). This mapping describes the motion of the fluid in a Couette flow, and the displacement of particles in a solid material under shear strain (which is the deformation that occurs when a metal sheet is being cut by shears, hence the name).In the general -dimensional Cartesian space , the distance is measured from a fixed hyperplane parallel to the direction of displacement. This geometric transformation is a linear transformation of that preserves the -dimensional measure (hypervolume) of any set.".
- Shear_mapping thumbnail VerticalShear_m=1.25.svg?width=300.
- Shear_mapping wikiPageExternalLink Shear.html.
- Shear_mapping wikiPageID "799405".
- Shear_mapping wikiPageRevisionID "560280861".
- Shear_mapping hasPhotoCollection Shear_mapping.
- Shear_mapping subject Category:Affine_geometry.
- Shear_mapping subject Category:Functions_and_mappings.
- Shear_mapping subject Category:Linear_algebra.
- Shear_mapping subject Category:Transformation_(function).
- Shear_mapping type Abstraction100002137.
- Shear_mapping type Function113783816.
- Shear_mapping type FunctionsAndMappings.
- Shear_mapping type MathematicalRelation113783581.
- Shear_mapping type Relation100031921.
- Shear_mapping comment "In plane geometry, a shear mapping is a linear map that displaces each point in fixed direction, by an amount proportional to its signed distance from a line that is parallel to that direction. This type of mapping is also called shear transformation, transvection, or just shearing. An example is the mapping that takes any point with coordinates to the point . In this case, the displacement is horizontal, the fixed line is the -axis, and the signed distance is the coordinate.".
- Shear_mapping label "Powinowactwo osiowe".
- Shear_mapping label "Scherung (Geometrie)".
- Shear_mapping label "Shear mapping".
- Shear_mapping label "Transvection".
- Shear_mapping label "错切".
- Shear_mapping sameAs Scherung_(Geometrie).
- Shear_mapping sameAs Transvection.
- Shear_mapping sameAs せん断写像.
- Shear_mapping sameAs Powinowactwo_osiowe.
- Shear_mapping sameAs m.03czt0.
- Shear_mapping sameAs Q1411898.
- Shear_mapping sameAs Q1411898.
- Shear_mapping sameAs Shear_mapping.
- Shear_mapping wasDerivedFrom Shear_mapping?oldid=560280861.
- Shear_mapping depiction VerticalShear_m=1.25.svg.
- Shear_mapping isPrimaryTopicOf Shear_mapping.
