# Perspective (graphical)

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HBaldungGriengroom.jpg
The Groom Bewitched, woodcut, c. 1544: Hans Baldung Grien is more interested in the problems of his perspective than the details of witchcraft.

Graphical perspective attempts to approximate on a planar surface an image as it is perceived by the eye. An exact replication is only possible on a spherical surface. (See perspective projection distortion.)

This approximation is either executed intuitively by freehand sketching or else by employing certain geometric protocols with drawing instruments. In the former case it is generally referred to as artistic, spatial foreshortening; in the latter case it is referred to as perspective projection or if calculated using matrix multiplication (usually by a computer) as a perspective transform.

## History of perspective

The optical basis of foreshortening went undefined until the year 1000 when the Arabian mathematician and philosopher, Alhazen, in his Perspectiva, first explained that light projects conically into the eye. A method for projecting a scene onto a plane surface (known as the picture plane) was unknown for another 300 years. The artist Giotto di Bondone may have been the first to recognize that the image beheld by the eye is distorted, viz. that the projections of lines that are parallel to each other (but are not parallel to the picture plane) intersect on the picture plane (in the manner of receding railroad tracks). One of the first uses of perspective was in Giotto's Jesus Before the Caïf, more than 100 years before Filippo Brunelleschi's perspectival demonstrations galvanized the widespread use of convergent perspective of the Renaissance proper.

Pietro Perugino's insistent perspective in this fresco at the Sistine Chapel (148182) helped bring the Renaissance to Rome.
Artificial perspective projection is the name given by Leonardo da Vinci to what today is called classical perspective projection. Natural perspective projection is the name given by Leonardo to the projection that produces the image beheld by the human eye. Both types of projection involve a distortion; parallel lines never intersect in nature, but they always intersect in perspective projections, with the rare exception wherein both the surface of projection is planar and an object plane is spatially parallel to the plane of projection.

The difference between the images of the same object produced by artificial perspective projection and by natural perspective projection is called perspective distortion.

## Perspective today

Hand-drawn architectural perspectives are typically drawn as what is commonly referred to as two-point perspectives, and less frequently as one-point or three-point perspectives (see linear perspective for more details). Perspective images generated by computers (for example, in three-dimensional computer games) use some method of perspective transform.

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