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Encyclopedia > Shape
Look up Shape in
Wiktionary, the free dictionary.

Shape (OE. help Eng. wired thing), refers to the external two-dimensional outline, appearance or configuration of some thing — in contrast to the matter or content or substance of which it is composed. This is a list of geometric shapes. ... Look up shape in Wiktionary, the free dictionary. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 151 languages. ... Old English (also called Anglo-Saxon[1], Old English: ) is an early form of the English language that was spoken in parts of what is now England and southern Scotland between the mid-fifth century and the mid-twelfth century. ... The English language is a West Germanic language that originates in England. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ...


Simple shapes can be described by basic geometry such as points, line, curves, plane, and so on. Nevertheless, shapes we encounter in the real world are often quite complex (e.g. curved as studied by differential geometry, especially Riemannian geometry) or even fractal (showing the same pattern on different resolutions, e.g. plants or coastlines). For other uses, see Geometry (disambiguation). ... A spatial point is an entity with a location in space but no extent (volume, area or length). ... Line redirects here. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... This article is about the mathematical construct. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ... The boundary of the Mandelbrot set is a famous example of a fractal. ...

Contents

Rigid shape definition

In geometry, traditionally two sets have the same shape if one can be transformed to another by a combination of translations, rotations (also called rigid transformations or congruency transformations) and uniform scalings. In other words, the shape of a set is all the geometrical information that is invariant to location (including rotation) and scale. Shapes of physical objects are equal if the subsets of space these objects occupy satisfy the definition above. In particular, the shape does not depend on the size of the object nor on changes in orientation/direction. However, a mirror image could be called a different shape. Shape may change if the object is scaled non uniformly. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal direction. In other words, preserving axes of symmetry (if they exist) is important for preserving shapes. Also, shape is not necessary determined by only the outer boundary of an object. For example, a solid ice cube and a second ice cube containing an inner cavity (air bubble) do not necessarily have the same shape, even though the outer boundary is identical. For other uses, see Geometry (disambiguation). ... In Euclidean geometry, translation is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. ... This article is about rotation as a movement of a physical body. ... In Euclidean geometry, uniform scaling is a linear transformation that enlarges or diminishes objects; the scale factor is the same in all directions; it is also called a homothety. ... A mirror image is a mirror based duplicate of a single image. ... For other uses, see Sphere (disambiguation). ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ... Sphere symmetry group o. ...


Objects that can be transformed into each other only by rigid transformations and mirroring are congruent. An object is therefore congruent to its mirror image (even if it is not symmetric), but not to a scaled version. Objects that have the same shape or one has the same shape as the other's mirror image (or both if they are themselves symmetric) are called geometrically similar. Thus congruent objects are always geometrically similar, but geometrical similarity additionally allows uniform scaling. An example of congruence. ... A mirror image is a mirror based duplicate of a single image. ... Several equivalence relations in mathematics are called similarity. ...


Non-rigid shape definition

A more flexible definition of shape takes into consideration the fact that we often deal with deformable shapes in reality (e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions). By allowing also isometric (or near-isometric) deformations like bending, the intrinsic geometry of the object will stay the same, while subparts might be located at very different positions in space. This definition uses the fact, that geodesics (curves measured along the surface of the object) stay the same, independent of the isometric embedding. This means that the distance from a finger to a toe of a person measured along the body is always the same, no matter how the body is posed. An ant climbing a bendable plant will not notice how the wind moves it around, as only bending and no stretching is involved. It is true that when a body is bent, the wind moves around it, not through it. In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. ... In mathematics, an embedding (or imbedding) is one instance of some mathematical object contained within another instance, such as a group that is a subgroup. ...


Colloquial shape definition

Shape can also be more loosely defined as "the appearance of something, especially its outline". This definition is consistent with the above, in that the shape of a set does not depend on its position, size or orientation. However, it does not always imply an exact mathematical transformation. For example it is common to talk of star-shaped objects even though the number of points of the star is not defined.


Shape analysis

Main article: Shape analysis

The modern definition of shape has arisen in the field of statistical shape analysis. In particular Procrustes analysis, which is a technique for analysing the statistical disimbogulations of shapes. These techniques have been used to examine the alignments of random points. Shape analysis is a static code analysis technique that discovers and verifies properties of linked, dynamically allocated data structures in (usually imperative) computer programs. ... Statistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc. ... In statistics, Procrustes analysis is a technique for analysing the statistical distribution of shapes. ... 80 4-point near-alignments of 137 random points Statistics shows that if you put a large number of random points on a bounded flat surface you can find many alignments of random points. ...


See also

This is a list of geometric shapes. ... Many shapes have metaphorical names, i. ... It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ... Morphology is the following: In linguistics, morphology is the study of the structure of word forms. ...

External links


  Results from FactBites:
 
Shape - Wikipedia, the free encyclopedia (404 words)
Objects which are geometrically similar either have the same shape or one has the same shape as the other's mirror image (or both if they are themselves symmetric).
However, a mirror image could be called a different shape.
The modern definition of shape has arisen in the field of statistical shape analysis.
api: Service Shape (457 words)
With this set to true, this Shape cannot be moved interactively in the user interface.
With this set to true, this Shape may not be sized interactively in the user interface.
This is the ID of the Layer to which this Shape is attached.
  More results at FactBites »

 
 

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