Aspect ratio

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This article is about shapes. For the aspect ratio of images, film and video, see Aspect ratio (image).

The aspect ratio of a geometric shape is the ratio between its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side - the ratio of width to height,[1] when the rectangle is oriented as a "landscape".

The aspect ratio is expressed as two numbers separated by a colon (x:y). The values x and y do not represent actual width and height but, rather, the "relation" between width and height. As an example, 8:5, 16:10 and 1.6:1 are the same aspect ratio.

In objects of more than two dimensions, such as Hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.

Applications and uses[edit]

The term is most commonly used with reference to:

Aspect ratios of simple shapes[edit]

Rectangles[edit]

Main article: Aspect ratio (image)

For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. A square has the smallest possible aspect ratio of 1:1.

Examples:

Ellipses[edit]

For an ellipse, the aspect ratio denotes the ratio of the major axis to the minor axis. An aspect ratio of 1:1 is a circle.

Elps-slr.svg

Aspect ratios of general shapes[edit]

In geometry, there are several alternative definitions to aspect ratios of general compact sets in a d-dimensional space:[2]

  • The Diameter-Width Aspect Ratio (DWAR) of a compact set is the ratio of its diameter to its width. A circle has the minimal DWAR which is 1. A square has a DWAR of sqrt(2).
  • The Cube-Volume Aspect Ratio (CVAR) of a compact set is the d-th root of the ratio of the d-volume of the smallest enclosing axes-parallel d-cube, to the set's own d-volume. A square has the minimal CVAR which is 1. A circle has a CVAR of sqrt(2). An axis-parallel rectangle of width W and height H, where W>H, has a CVAR of sqrt(W^2/WH) = sqrt(W/H).

If the dimension d is fixed, then all reasonable definitions of aspect ratio are equivalent to within constant factors.

Notations[edit]

Aspect ratios are mathematically expressed as x:y (pronounced "x-to-y") and x×y (pronounced "x-by-y"), with the latter particularly used for pixel dimensions, such as 640×480.

Cinematographic aspect ratios are usually denoted as a (rounded) decimal multiple of width vs unit height, while photographic and videographic aspect ratios are usually defined and denoted by whole number ratios of width to height. In digital images there is a subtle distinction between the Display Aspect Ratio (the image as displayed) and the Storage Aspect Ratio (the ratio of pixel dimensions); see Distinctions.

See also[edit]

References[edit]

  1. ^ Rouse, Margaret (September 2005). "What is aspect ratio?". WhatIs?. TechTarget. Retrieved 3 February 2013. 
  2. ^ Smith, W. D.; Wormald, N. C. (1998). "Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)". p. 232. doi:10.1109/sfcs.1998.743449. ISBN 0-8186-9172-7.  |chapter= ignored (help) edit

External links[edit]