This applet allows the point `O`, the position of the eye,
to be moved up and down, as well as towards and away from the frame.

The checkerboard is horizontal and abuts the edge of the
(vertical) frame. A point `O'` is drawn in the picture-plane (to the right in
this illustration),
on a level with
the vanishing-point C, and such that the horizontal distance `O'C'`
to
the frame is equal to
the distance `OC` from the eye to C.
Let `M` be the point where the far edge of the checkerboard
intersects the vertical plane through `O` and `C`.
The line of sight `OM` cuts the picture plane at `H`.
To construct the image of the far edge of the checkerboard, it
is enough to know the height of `H`. Since the checkerboard
is square, the figure `O'C'H'AP'` is congruent to the
figure `OCHMP`: the height of `H` is the same as the
height of `H'` which is the intersection of `O'A`
with the right-hand edge of the frame.

In this way the three-dimensional (blue) construction collapses
into the 2-dimensional (red) one, and the perspective problem
admits an elementary geometric solution.

This is produced with **JavaSketchpad**, a World-Wide-Web component of *The Geometer's Sketchpad.* Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).

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