Isometric projection

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Isometric projection is a form of graphical projection, or more specifically, axonometric projection. It is a method for the visual representation of three-dimensional objects in two dimensions in which the angles between the projection of the x, y, and z axes are all the same, or 120°. For objects with surfaces that are substantially perpendicular to and/or parallel with one another, it corresponds to rotation of the object by +/- 45° about the vertical axis, followed by rotation of approximately +/- 35.264° [= arcsin(tan(30°))] about the horizontal axis starting from an orthographic projection relative to an object's face (a perpendicular view to a face of an object).

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Isometric projection can be visualized by considering the view of a cubical room from an upper corner, looking towards the opposite lower corner. The x-axis is diagonally down and right, the y-axis is diagonally down and left, and the z-axis is straight up. Depth is also shown by height on the image. Lines drawn along the axes are at 120° to one another. The term isometric comes from the Greek for "equal measure.", which reflects that the scale along each axis of the projection is the same (this is not true of some other forms of graphical projection). Isometric projection is one of the projections used in drafting engineering drawings.

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Isometric projection in video games and pixel art

In the fields of video games and pixel art, the isometric projection used may deviate slightly due to the limitations of raster graphics; without anti-aliasing, lines in the x and y axes would not follow a neat pattern when drawn 30° to the horizontal, and earlier computer graphics were also less capable of supporting more colors to effectively utilize anti-aliasing. Typically, a 2:1 pixel pattern ratio is used to simulate x and y axes lines, resulting in these axes following a 26.565° (arctan 0.5) angle to the horizontal instead. It should therefore be noted that this variation of isometric projection is more accurately described as a form of dimetric projection, since only two of the three angles between the axes are equal (116.565°, 116.565°, 126.87°). Many in video game and pixel art communities, however, continue to refer to this projection as "isometric perspective"; the term "3/4 perspective" is also commonly used.

Limits of isometric projection

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A problem with isometric projection is that because the lines representing each dimension are parallel on the page, objects do not become larger or smaller as they extend closer to the viewer. While advantageous for architectural drawings and sprite based video games, this can easily result in situations where depth and altitude are impossible to gauge, as is shown in the illustration to the right. Most contemporary video games have avoided this situation by dropping isometric perspective in favor for 3D rendering with vanishing points. Some of the famous "impossible architecture" works of M.C. Escher exploit this isometric limitation. Waterfall (1961), is a good example, in which the building is isometric, but the faded background is not.

Notable examples of "isometric" computer and video games

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External links

fr:Perspective isométrique fi:Isometrinen projektio