Two-Dimensional

(adjective)

Existing in two dimensions. Not creating the illusion of depth.

Related Terms

Examples of Two-Dimensional in the following topics:

  • Surfaces in Space

    • A surface is a two-dimensional, topological manifold.
    • The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space $R^3$— for example, the surface of a ball.
    • On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
    • To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined.
    • For example, the surface of the Earth is (ideally) a two-dimensional surface, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian).

  • Shape and Volume

    • Shape refers to an area in a two-dimensional space that is defined by edges; volume is three-dimensional, exhibiting height, width, and depth.
    • Shape refers to an area in two-dimensional space that is defined by edges.
    • In two-dimensional art, the "picture plane" is the flat surface that the image is created upon, such as paper, canvas, or wood.
    • Combining two or more shapes can create a three-dimensional shape.
    • While three-dimensional forms, such as sculpture, have volume inherently, volume can also be simulated, or implied, in a two-dimensional work such as a painting.

  • Two-Dimensional Space

    • Two-dimensional, or bi-dimensional, space is a geometric model of the planar projection of the physical universe in which we live.
    • Two dimensional, or bi-dimensional, space is a geometric model of the planar projection of the physical universe in which we live.
    • The two dimensions are commonly called length and width.
    • In art composition, drawing is a form of visual art that makes use of any number of drawing instruments to mark a two-dimensional medium (meaning that the object does not have depth).
    • Discuss two-dimensional space in art and the physical properties on which it is based

  • Constant Acceleration

    • Analyzing two-dimensional projectile motion is done by breaking it into two motions: along the horizontal and vertical axes.
    • The motion of falling objects is a simple one-dimensional type of projectile motion in which there is no horizontal movement.
    • In two-dimensional projectile motion, such as that of a football or other thrown object, there is both a vertical and a horizontal component to the motion.
    • The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical.
    • We analyze two-dimensional projectile motion by breaking it into two independent one-dimensional motions along the vertical and horizontal axes.

  • Distortions of Space and Foreshortening

    • Distortion is used to create various representations of space in two-dimensional works of art.
    • However, it is more commonly referred to in terms of perspective, where it is employed to create realistic representations of space in two-dimensional works of art.
    • Perspective projection distortion is the inevitable misrepresentation of three-dimensional space when drawn or "projected" onto a two-dimensional surface.
    • It is impossible to accurately depict three-dimensional reality on a two-dimensional plane.
    • Giotto is one of the most notable pre-Renaissance artists to recognize distortion on two-dimensional planes.

  • Multi-dimensional scaling tools

    • Alternatively, multi-dimensional scaling could be used (non-metric for data that are inherently nominal or ordinal; metric for valued).
    • This map lets us see how "close" actors are, whether they "cluster" in multi-dimensional space, and how much variation there is along each dimension.
    • Figures 13.10 and 13.11 show the results of applying Tools>MDS>Non-Metric MDS to the raw adjacency matrix of the Knoke information network, and selecting a two-dimensional solution.
    • In using MDS, it is a good idea to look at a range of solutions with more dimensions, so you can assess the extent to which the distances are uni-dimensional.
    • Two-dimensional map of non-metric MDS of Knoke information adjacency

  • Volumes

    • Volume is the quantity of three-dimensional space enclosed by some closed boundary—for example, the space that a substance or shape occupies or contains.
    • Three dimensional mathematical shapes are also assigned volumes.
    • One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in three-dimensional space.
    • The volume of the cuboid with side lengths 4, 5, and 6 may be obtained in either of two ways.

  • Three-Dimensional Coordinate Systems

    • A three dimensional space has three geometric parameters: $x$, $y$, and $z$.
    • Also known as analytical geometry, this system is used to describe every point in three dimensional space in three parameters, each perpendicular to the other two at the origin.
    • The cylindrical system uses two linear parameters and one radial parameter:
    • This is a three dimensional space represented by a Cartesian coordinate system.
    • Identify the number of parameters necessary to express a point in the three-dimensional coordinate system

  • Cylinders and Quadric Surfaces

    • A quadric surface is any $D$-dimensional hypersurface in $(D+1)$-dimensional space defined as the locus of zeros of a quadratic polynomial.
    • The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.
    • In common use, a cylinder is taken to mean a finite section of a right circular cylinder, i.e. the cylinder with the generating lines perpendicular to the bases, with its ends closed to form two circular surfaces.
    • A quadric, or quadric surface, is any $D$-dimensional hypersurface in $(D+1)$-dimensional space defined as the locus of zeros of a quadratic polynomial.

  • Conformational Stereoisomers

    • Structural formulas show the manner in which the atoms of a molecule are bonded together (its constitution), but do not generally describe the three-dimensional shape of a molecule, unless special bonding notations (e.g. wedge and hatched lines) are used.
    • The importance of such three-dimensional descriptive formulas became clear in discussing configurational stereoisomerism, where the relative orientation of atoms in space is fixed by a molecule's bonding constitution (e.g. double-bonds and rings).
    • In this section we shall extend our three-dimensional view of molecular structure to include compounds that normally assume an array of equilibrating three-dimensional spatial orientations, which together characterize the same isolable compound.
    • Many conformations of hexane are possible and two are illustrated below.