The perspective image of an infinite checkerboard. It can be constructed starting from any triangle , where and
form the near corner of the floor, and is the horizon (left figure). If is the corner tile, the lines and must be parallel to and
respectively. This means that in the drawing they will meet and at the horizon, i.e., at point and point respectively (right figure). This property, of course, extends
to the two bunches of perpendicular lines forming the grid.

The adjacent tile
(left figure) can then be determined by the following conditions:

1. The new vertices
and lie on lines and respectively.

2. The diagonal
meets the parallel line
at the horizon .

3. The line
passes through .

Similarly, the corner-neighbor of (right figure) can be easily constructed requiring
that:

1. Point
lie on .

2. Point
lie on the common diagonal
of the two tiles.

3. Line
pass through .

Iterating the above procedures will yield the complete picture. This construction shows how naturally projective geometry arises
from perspective design, since and can be interpreted as two coordinate axes in the real
projective plane with
and their points
at infinity, joined by the line at infinity .

The Möbius net is the result of a projective transformation of the two-dimensional lattice. Unlike in affine geometry, the length proportions along the two perpendicular
directions are not preserved, whereas the cross ratio, which is invariant by central
projection, is. The "horizontal" sides of the projected tiles have different
lengths, but are related by the central projections from (left figure) and (right figure), so that