# Alberti's Perspective Construction

**Feature Column Archive**

## 4. The backwards construction

In *Della Pittura* Alberti criticizes a rival construction
because *it does not locate the position of the eye*. In
fact, if the pavement construction has been done properly, it
can be run backwards to locate the ideal viewing position for
the picture: the point in space from which the illusion should
be most perfect. The easiest way to show how this works is by
an extension of our original checkerboard construction. This
image may be JAVA animated by clicking on its surface.

If the diagonal through `B` is extended beyond the image `X`
of the far left corner of the checkerboard, it meets the horizon in
the point `OO`. (Any one of the parallel diagonals will pass
through `OO`). Arguing with similar triangles, we can show
that the distance from `OO` to `C` is equal to
the distance from `O'` to `C'` and is therefore
equal to the distance from the picture of the eye used in the
construction.

The argument runs as follows: Equating ratos of
corresponding sides in the similar triangles
`H' C' O'` and `H' B A` gives

`|H' C'| / |B H'| = |O' C'| / |A B|`.
In the similar triangles
`X C OO`
and `X A B` the ratios of the altitudes
must be the same as the ratio of the bases.
This gives

`|H' C'| / |B H'|` = `|OO C| / |A B|`.
It follows that `|OO C| = |O'C'|`.