The comparative lack of rigidity of the two-dimensional case with that of higher dimensions owes to the analytical fact that the asymptotic developments of the infinitesimal automorphisms of the structure are relatively unconstrained.

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar equations, sequence plots, differential equation fields, and three-dimensional ( two independent variable ) functions.

Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, and bioinformatics.

For such models, economists often use two-dimensional graphs instead of functions.

This series is used to define the scales for graphs and for instruments that display in a two-dimensional form with a graticule, such as oscilloscopes.

Also referred to as " two-dimensional characters " or " flat characters ," they play a supporting role to the main character, who as a rule should be round, or complex.

The formal elements, those aesthetic effects created by design, upon which figurative art is dependent, include line, shape, color, light and dark, mass, volume, texture, and perspective, although it should be pointed out that these elements of design could also play a role in creating other types of imagery -- for instance abstract, or non-representational or non-objective two-dimensional artwork.

His many achievements include work on planetary orbits, measuring the mean density of the Earth, a method of solution of two-dimensional problems in solid mechanics and, in his role as Astronomer Royal, establishing Greenwich as the location of the prime meridian.

The characteristics of such a wing can be measured on a section of wing spanning the width of a wind tunnel, since the walls block spanwise flow and create what is effectively two-dimensional flow.

As a result, its name was adopted as the most common German-language term for the style: Jugendstil (" Jugend-style "), although, during the early 20th century, the word was applied to only two-dimensional examples of the graphic arts, especially the forms of organic typography and graphic design found in and influenced by German magazines like Jugend, Pan, and Simplicissimus.

* MST Workshop, an interactive visual programming language for creating mathematical solutions, rapid prototyping, two-dimensional and three-dimensional graphic applications

The vectors of a two-dimensional graphic, each encoding a direction from the previous pixel along with a flag indicating whether the new pixel should be illuminated or not, were encoded up to three in a byte.

Icon designs can be simple, with flat two-dimensional drawing or a black silhouette, or complex, presenting a combination of graphic design elements such as one or more linear and radial color gradients, projected shadows, contour shades, and three-dimensional perspective effects.

In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure " painted " on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies.

PVP is a branched polymer, meaning its structure is more complicated than linear polymer, though it too lies in a two-dimensional plane.

From the 1950s onward, Hans Keller developed a ' two-dimensional ' method of analysis that explicitly considered form and structure from the point of view of listener expectations.

Note that these depictions of two-dimensional surfaces are merely easily visualizable analogs to the 3-dimensional structure of ( local ) space.

Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.

Zenneck improved the Braun cathode ray tube, by adding a second deflection structure at right angles to the first, which allowed two-dimensional viewing of a waveform.

Supergalactic coordinates are coordinates in a spherical coordinate system which was designed to have its equator aligned with the supergalactic plane, a major structure in the local universe formed by the preferential distribution of nearby galaxy clusters ( such as the Virgo cluster, the Great Attractor and the Pisces-Perseus supercluster ) towards a ( two-dimensional ) plane.

The stress analysis can be simplified in cases where the physical dimensions and the loading conditions allows the structure to be assumed as one-dimensional or two-dimensional.

Haworth worked out the correct structure of a number of sugars, and is known among organic chemists for his development of the Haworth projection that translates three-dimensional sugar structures into convenient two-dimensional graphical form.

In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral ( functional integration ) description of quantum gravity.

A later study, while agreeing that the pigmented area represented something originally inside the body, found no defined structure and noted that any organs would have been distorted by the processes that flattened the skeleton into an essentially two-dimensional form.

This two-dimensional structure is built via self-assembly and encloses the whole cell surface.

An arbitrary graph embedding on a two-dimensional surface may be represented as a cubic graph structure known as a graph-encoded map.

A typographic grid is a two-dimensional structure made up of a series of intersecting vertical and horizontal axes used to structure content.

These depth samples are explicitly stored in a two-dimensional spatial data structure.

The irregular Z-buffer solves this problem by storing sample locations explicitly in a two-dimensional spatial data structure, and later querying this structure to determine which samples lie within a projected triangle.

They also mapped the pulsar's two-dimensional beam structure using the fact that the system's precession leads to varying pulse shapes.

It is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image.

Abbott's best-known work is his 1884 novella Flatland: A Romance of Many Dimensions which describes a two-dimensional world and explores the nature of dimensions.

Whereas most video games use monocular cues to achieve the illusion of three dimensions on a two-dimensional screen, The Virtual Boy creates an illusion of depth through the effect known as parallax.

The analysis so far has been two dimensional ; it turns out that an unperturbed orbit is two-dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two-dimensional plane into the required angle relative to the poles of the planetary body involved.

However, present observations cannot exclude the possibilities that the universe has more dimensions and that its spacetime may have a multiply connected global topology, in analogy with the cylindrical or toroidal topologies of two-dimensional spaces.

This led to the development of a two-dimensional gender identity model, in which masculinity and femininity were conceptualized as two separate, orthogonal dimensions, coexisting in varying degrees within an individual.

Just as an ordinary sphere ( or 2-sphere ) is a two-dimensional surface that forms the boundary of a ball in three dimensions, a 3-sphere is an object with three dimensions that forms the boundary of a ball in four dimensions.

Although the stages are rendered in three dimensions, players can only move on a two-dimensional plane.

It is also possible to use a two-dimensional ( 2-D ) gel which spreads the proteins from a single sample out in two dimensions.

Considering a two-dimensional deformation of an infinitesimal rectangular material element with dimensions by ( Figure 1 ), which after deformation, takes the form of a rhombus.

The main result for the supercritical phase in three and more dimensions is that, for sufficiently large N, there is an infinite open cluster in the two-dimensional slab Z < sup > 2 </ sup > × < sup > d − 2 </ sup >.

The image to the left shows sample images from this dataset ( to save space, not all input images are shown ), and a plot of the two-dimensional points that results from using a NLDR algorithm ( in this case, Manifold Sculpting was used ) to reduce the data into just two dimensions.

In this book Jouffret described hypercubes and complex polyhedra in four dimensions projected onto a two-dimensional page.

Naturally the analogues of contour integrals will be harder to handle: when n = 2 an integral surrounding a point should be over a three-dimensional manifold ( since we are in four real dimensions ), while iterating contour ( line ) integrals over two separate complex variables should come to a double integral over a two-dimensional surface.

A further classical example is the space of lines in projective space of three dimensions ( equivalently, the space of two-dimensional subspaces of a four-dimensional vector space ).

This symmetry makes it possible to classify two-dimensional CFTs much more precisely than in higher dimensions.

The analogy is seen directly in three dimensions, by taking and: the two-dimensional leaves of a book are enumerated by a ( one-dimensional ) page number.

Digitizing is the primary way of storing images in a form suitable for transmission and computer processing, whether scanned from two-dimensional analog originals or captured using an image sensor-equipped device such as a digital camera, tomographical instrument such as a CAT scanner, or acquiring precise dimensions from a real-world object, such as a car, using a 3D scanning device.

The data generated by flow-cytometers can be plotted in a single dimension, to produce a histogram, or in two-dimensional dot plots or even in three dimensions.

Quantum dots defined by lithographically patterned gate electrodes, or by etching on two-dimensional electron gases in semiconductor heterostructures can have lateral dimensions exceeding 100 nm.