When artists and mathematicians were looking for quick methods for creating anamorphoses, they were not concerned with perspective correctness. Their audience was not exposed to the wealth of images that we are today, so any image that produced a magical effect was suitable.
The use of stretching
If a grid is stretched, the spacing remains equal. See foreshortening to see how a grid behaves in a true perspective way. But in many cases this does not matter. It is very easy to see what the original image should be. This is the way road markings are made anamorphic.
Samuel Marolois used this method to draw an image of a dog in 1614 which was by then “the old-fashioned anamorphic method”. It does not matter which side of the screen you view from to restore the image. Neither works perfectly, because the stretching is not true anamorphosis. Note how he used a grid to help him create the drawing and how the grid is rectangular and equally spaced in the anamorphic version.
Words can be stretched very easily using graphics programs. Vector programs like Corel Draw or Adobe Illustrator allow you to do this very easily. If you use a pixel paint program, then resize the image. You need to stretch at least 1000% to get words that are impossible to read without looking from the end. They work better if you stretch along the vertical axis of the words, as here. (Turn your head and look along the screen.)
There is a puzzle image for you to print out and view on the downloads post.
Giacomo Barrozzi da Vignola wrote a book on perspective published in Rome in 1583 which include some perspective tricks. One of them was to take a picture and cut it into a set of strips. Pasting this onto a set of triangular cross-sectioned blocks of wood allowed the image to be recreated when viewed in a mirror.
This is not a perspective anamorphosis, but because the image is only cut and not stretched, it appears as good as new when viewed from the correct position. You do not have to use a mirror, but Vignola has used one to add to the magic. If you were to look and see the image in the mirror, you would only see the blank sides of the blocks and it would not be clear where the picture came from.
Making your own Vignola anamorphosis
Take a picture and cut it into a series of equal strips say an inch or 2.5 cm wide. Mark a series of lines on another piece of paper as if you were going to cut out the same width strips. Stick the strips of the cut-out picture in every other position. Fold up the paper along the edges of the strips to make a concertina. With the paper pushed together so that it looks like Vignola’s, look at the image in a mirror as he does or look at it obliquely.
There is an image of the Alice in Wonderland tea party for you to print out and fold on the downloads post.