Plane Anamorphosis

Creating an anamorphic picture on a plane is very similar to drawing normally in perspective. The only difference is that the picture plane (the window in the description of perspective) is not perpendicular to the artist’s line of site.

This is how Jean Francois Niceron (who wrote the most comprehensive books on how to draw anamorphic pictures in the seventeenth century) showed how to create a plane anamorphosis.

The two pictures in the centre are the images to be made anamorphic using the grid method. You need to look from the right side of the picture to see them restored.

The geometry of the grid is as follows:


You should be able to see similarities in the construction for a perspective grid described in the explanation of perspective. You should also be able to relate to Niceron’s picture above. The anamorphic effect is to look at the image on the picture plane and have it appear to be a square grid, as if the square grid were placed in the position AB.

The original grid is shown at the bottom left. The blue and red lines at the bottom of the diagram are a plan view (looking from above) to explain the geometry. In this plan view the eye views the grid (which is seen as a red line), and the vertical lines of the grid are projected on the picture plane, which is the blue line through B and N. The line through the centre of the red line from E is perpendicular to AB, and EN is also perpendicular to this line.

To create the anamorphic grid. This description relates the plan and the view on the picture. In practice you only have to draw the lines Niceron used, so a shortened version is described below:

1. Choose a point D above N. Construct NC, so that CD equals EN.
2. Draw perpendiculars above the projected ends of the grid, that is B and W, and then for each projection from the blue line WN.
3. Join C to where the perpendicular line corresponding to the central line of the grid meets the horizontal blue line through D.
4. Extend this line to find point T and find R the point symmetrically above the blue horizontal line through D.
5. The line drawn in step 5 also finds the position of point S, and point U is found symmetrically.
6. RSTU form the outside of the grid and the vertical perpendiculars locate one set of the lines of the grid.
7. To find the equivalent of the horizontal set, join D to where the line CST meets each of the vertical lines.

To see the grid in the correct perspective, look from the right at a point E which is in front of the plane of the image. Niceron and others did not bother with this, but only used a simplified construction.

1. Choose a point D with a horizontal line through it.
2. Choose C above the point D at a distance equal to the distance in front of the paper from which to view the completed image.
3. Draw a line RT perpendicular to the blue horizontal line, so that R and T are symmetrically placed.
4. Join C and T and D to R and T. CT cuts DR at S and U can be found symmetrically from the position of S, or alternatively by erecting a perpendicular to the blue line from S.
5. Divide RT into equal divisions to match the number of points in the vertical direction in the grid.
6. Join these points to D to give the equivalent of the horizontal set of lines of the grid.
7. To find the vertical set, draw vertical lines (perpendicular to the horizontal blue line) where the line CST meets each of the lines.

Comparison with a perspective foreshortening

In a normal perspective picture the foreshortening means that the lines of the grid appear closer together the farther away the lines of the grid are to the viewer. In a plane anamorphic grid, the lines are equally spaced on the real grid but appear closer together on the part of the image nearest to the viewing point.

The shape of the image is always like this:

This means if you have an image like the portrait of Edward VI by William Scrots which is in the National Portrait Gallery in London, and you see the widest and most stretched part at the left, then you must look from the right.

In fact if you look closely at the frame on the right of the picture, then you can see a gap through which you need to look to see the portrait restored. An almost complete photographic restoration looks like this:


Many books show this incorrectly restored version. The only one I know that has it correct, is John North’s “The Ambassador’s Secret”. The following is a restoration with good circles.

 

 

 

 

 

 

 

See the post on restoring anamorphic images by computer, on how NOT to restore the image by stretching.

The Passing Through Project

The artists Colin Wilbourn and Karl Fisher have created some public anamorphic art in the north east of England. The Passing Through sculpture (1997) is at St Peter’s Riverside in Sunderland. This is a plane anamorphosis. When you walk past it, the sculpture looks like an odd shape on the wall.


Go away from it, and the image starts to appear the way the artist originally saw it.


In the above view, at the bottom right hand corner you can see a seat. Sit on the seat and you can see that the true image is a door:

Holbein’s The Ambassadors

Perhaps the most famous painting with a hidden plane anamorphic object in it is the painting called The Ambassadors by Hans Holbein in the National Gallery in London.


For those who do know how to look at the painting, it has been described as all manner of puzzling objects from a banana to some sort of fish. If you look from the right hand edge of the painting, then you see it is a skull.

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4 responses to “Plane Anamorphosis

  1. I cannot thank you enough for this invaluable information on creating anamorphic drawings on paper (or on any plane, I suppose!).

    You have a definite knack for making the complex simple (as simple as I can imagine explaining anamorphics can be, and absolutely the best instructions I have found on the web thus far).

    There IS one thing I would like to make sure I understood correctly: When figuring out the distance between points D and C, you use the measurement equal to the length of the side of paper the anamorphic will be viewed from?
    For example, if I draw an anamorphic drawing vertically on 8″x10″ paper (and view the drawing from the 8″ bottom edge of the paper), then the distance from point C to D is 8″? If you wouldn’t mind, you can email me the answer at
    jaibhakti at aol dot com

    Thank you SO much for putting so much hard work into your website. I have bookmarked your site! 🙂

    Happy New Year!

  2. okay…I waited a day and then re-read the instructions again about 10 times and I realized that when you said the red line “A-B” was a ‘plan’ view and overhead view, that you literally meant that the red line represented the top edge of the original square graph. So, in essence, we could pretend that point E is Durher sitting at his table and line A-B would be the bird’s eye view of the top edge of his graphed/grid window. And then somewhere around B-W is where his nude female model would be posing (in his famous woodcut, which I believe is on your perspective page) although, of course, she would be posing in straight alignment to Duhrer’s eye, not diagonally, as line B-W is shown in the anamorphicized grid (is that a word? haha).

    I think I’ve got the correct understanding now. I am going to try this and then report back.

    Thanks again for the fantastic info (and please excuse my lack of geometric terminology).

  3. Does the gridded drawing you are putting into anamorphic perspective have to be a square with the this particular process?

    • No it doesn’t. However, for non square grids you have to obey the way the geometry works so that intersections of lines remain intersections.
      For a non-square grid the diagonals will not necessarily go through corners of the squares of the grid.
      So the best way to work with a non square grid is to identify a square as part of your grid and then add a extra strip to it.
      So say you have a five by 4 grid, Work on part of it as a 4 by 4 and then extend it.

      I will see if I can find some time to add a post on this as it is easier to draw than describe

      John S

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