FACTOID # 145: Three of the top ten countries for GDP per capita are island nations: Bermuda, Cayman Islands, and Iceland.
 
 Home   Encyclopedia   Statistics   Countries A-Z   Flags   Maps   Education   Forum   FAQ   About 
 
WHAT'S NEW
RECENT ARTICLES
More Recent Articles »
 

FACTS & STATISTICS    Simple view

  1. Select countries to view: (hold down Control key and click to select several)

     

     

    Compare:

     

     

  1. Select fact or statistic: (* = graphable)

     

     

     

  2. (OPTIONAL) Compare to statistic: (both need to be graphable)

     

     

     

  3. View result as:

     

       
(OR) SEARCH ALL encyclopedia, stats & forums:   

Encyclopedia > Linear perspective

Linear perspective is the art of representing three-dimensional constructions on a two-dimensional surface. It presupposes a fixed viewpoint and a desire to create an "objective" recording of one's visual experience - two conditions which have been the most dominant in the Western art of the past half-millennium. Great Museums in the World (Louvre, Metropolitan Museum, MoMA, Picasso …) CGFA: A Virtual Art Museum Very large website with good reproduction quality scans of thousands of paintings Goetia Fine Art - Surrealism Art History With biographies and Works of the Surrealist Masters Art-Atlas. ...


Once the observer assumes a single point of view, several conclusions follow logically. The first and most important is this: objects appear to get smaller as their distance from the observer increases. That this is not self-evident in art is apparent from even a casual perusal of the art of other cultures and eras - most frequently objects are drawn or painted a certain size for reasons that have nothing to do with their position in space. In medieval Last Judgement paintings, for example, the relative scale of the various figures is determined only by their sacred significance; the most important are the largest. The word culture comes from the Latin root colere (to inhabit, to cultivate, or to honor). ... Drawing is one way of making an image: it is the process of making marks on a surface by applying pressure from or moving a tool on the surface. ... The Mona Lisa is perhaps the best-known artistic painting in the Western world. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...


Once the diminishment of scale with distance is noted, it is an easy step to understanding why the space between parallel lines must also appear to diminish. A wall retreating from the observer will appear to get progressively shorter, and the top and bottom edges of the wall will thus appear to move closer together.


It was an enormous conceptual leap when artists concluded that these lines, if extended indefinitely, would appear to meet at a single point on the horizon. This idea, long since verified, was likely made from a theoretical analysis of the process of seeing rather than direct observation. Van Eyck, for example, was unable to create a consistent structure for the converging lines in paintings like London's The Arnolfini Portrait because he was not aware of the theoretical breakthrough just then occurring in Italy. For the television programme, see Horizon. ... Van Eyck is the name of a family of Flemish painters. ... Categories: Art stubs | Paintings ...


Below are descriptions of the three main varieties of perspective technique. Note that the only difference among these three varieties is the orientation of linear objects being viewed relative to the viewer. Additionally, none of these varieties exist if the viewer is observing a nonlinear scene (for example, a random (ie, not aligned in a three-dimensional Cartesian coordinate system) arrangement of spherical objects). Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

Contents

1-point perspective

If the viewpoint is pointing directly into a linear object like a building or a road, one would use one vanishing point, that is the principal focus. All lines perpendicular to the painting plate would vanish in the vanishing point.


More precisely, one-point perspective exists when the painting plate is parallel to a "Cartesian scene" --- a scene which is composed entirely of linear elements that intersect only at right angles. Therefore, all elements are either parallel to the painting plate (either horizontally or vertically) or perpendicular to it. All elements that are parallel to the painting plate are drawn as parallel lines. All elements that are perpendicular to the painting plate converge at a single point on the horizon.


2nd kind of vanishing points

If the lines have angles to the painting plate, they would vanish in the other vanishing points. There are lot of vanishing points homologous to different angles. But all vanishing points should be located in the same horizontal line with the focus.


In other words, two-point perspective is derived from one-point perspective by yawing the line of vision so that the line of vision will be at an acute angle away from the focus. Then the lines which used to be horizontal and parallel will now be concurrent, intersecting at the horizon. Interpreted according to projective geometry, the horizontal parallel lines of one-point perspective are actually concurrent, intersecting at the point at infinity [1:0:1]. When the head is turned by a slight angle, these lines no longer intersect at an ideal point, but at an affine point on the horizon, so they are no longer parallel. In a historical perspective on mathematics, the field of geometry that developed in the first half of the nineteenth century under the name projective geometry was a stepping stone from analytic geometry to algebraic geometry. ... The point at infinity, also called ideal point, is a point which when added to the real number line yields a closed curve called the real projective line, . Nota Bene: The real projective line is not equivalent to the extended real number line. ...


More precisely, two-point perspective exists when the painting plate is parallel to a "Cartesian scene" (a scene composed entirely of linear elements intersecting only at right angles) in one axis (usually the z-axis) but not parallel to the other two axes.


3rd kind of vanishing points

If the lines have angles from the painting plate up or down, one would use the other kind vanishing points. Those vanishing points must located in the same vertical line with the focus. Looking at the object from above or below, the horizontal line with the focus and all other 2nd VPs would left the horizon up or down.


Three-point perspective exists when the painting plate is viewing a "Cartesian scene" (a scene composed entirely of linear elements intersecting at right angles) and is not parallel to any of the scenes three axes. Elements that are parallel to each of the three axes will converge to three vanishing points respectively.

Perspective illustration from zh wiki File links The following pages link to this file: Linear perspective Categories: GFDL images ... Perspective illustration from zh wiki File links The following pages link to this file: Linear perspective Categories: GFDL images ...

See also

Curvilinear perspective is a way of drawing using five vanishing points. ... The Groom Bewitched, woodcut, c. ... Aerial perspective or atmospheric perspective is the effect on the appearance of an object by air between it and a viewer. ...

External links

  • Mathematics of Perspective Drawing (http://www.math.utah.edu/~treiberg/Perspect/Perspect.htm)
  • Drawing Comics - Perspective (http://www.scottmcdaniel.net/drawing/perspective/perspective.html)
  • 1-point perspective:
  • 2-point perspective:
    • Belvedere (http://www.cs.unc.edu/~davemc/Pic/Escher/Belvedere.jpg) by M. C. Escher
    • Dream (http://www.cs.unc.edu/~davemc/Pic/Escher/Dream.jpg) by M. C. Escher
  • 3-point perspective:

  Results from FactBites:
 
Perspective (graphical) - Wikipedia, the free encyclopedia (3974 words)
Perspective (from Latin perspicere, to see clearly) in the graphic arts, such as drawing, is an approximate representation on a flat surface (such as paper) of an image as it is perceived by the eye.
Perspectives consisting of many parallel lines are observed most often when drawing architecture (architecture frequently uses lines parallel to the x, y, and z axes).
Typically, mathematically constructed perspectives are "linear" in that the ratio at which more distant objects decrease in size is constant (ie, graphing the drawn size of a one-foot object versus the distant from viewer will form a straight line).
Perspective projection - Wikipedia, the free encyclopedia (239 words)
Perspective projection is a type of drawing, or rendering, that graphically approximates on a planar (two-dimensional) surface (e.g.
A perspective projection drawing must be made according to an established geometric protocol.
All perspectives on a planar surface have some degree of distortion, similar to the distortion created when portraying the earth's surface on a planar map.
  More results at FactBites »


 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your comments
Please enter the 5-letter protection code

Want to know more?
Search encyclopedia, statistics and forums:

 


Lesson Plans | Student Area | Student FAQ | Reviews | Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms.