Catoptical and Anaoptical Anamorphosis

As seen in the previous posts, some mediums of anamorphic images was on paper or on canvas. These are not the only two ways to represent an anamorphic image, there are also catoptical and anaoptical.

Catoptical

Catoptical is when an observer looks down on the image. The two most common forms are done by using mirrors in the shapes of cones and cylinders. There is also pyramidal anamorphosis where the mirror is a pyramid shape but this is much rarer and I could not find much information beyond this picture:

http://latander.livejournal.com/216413.html

The origins of cones and cylinders are obscure but Niceron and DuBreuil discuss these in books dating back to the 1600s.

Cone anamorphosis is prepared by geometric means. One must take an image and encapsulate it in a circular grid, once this is done the grid and image must be inverted.

This image looks correct when a conical mirror is placed in the center and is observed from above. Here is a modern example where it’s very easy to see how the image looks with and without the mirror.

http://www.anamorphosis.com/gallery.html

Another type of catoptical is called cylindrical anamorphosis. This is where a cylindrical mirror is placed on top of an image that has been distorted in a certain manner.

Philip Hickin has an algebraic equation to create this:

If someone wishes to try this, here is his explanation from his article, “Anamorphosis” from The Mathematical Gazette (1992).

“x and y are the image coordinates, and r and θ are the polar coordinates of the distorted drawing. The constant a is for scaling, while b is a constant to take the line y = 0 beyond the viewing cylinder’s diameter, and k determines how far the picture will wrap round the cylinder.”

This cylindrical image is of Charles I and is unique in one way. There is a skull that can be hidden under the mirror, once the mirror is removed the skull is visible and it becomes a memento mori which means, more or less, remember your mortality. It’s a thought that dates back to antiquity to remind people that there is more to life than material things.

Charles I (Post 1649)

Jurgis Baltrusaitis. Anamorphic Art, p.107

Anoptical

Anoptical is observed when the viewer looks up at an image. This has been best executed on ceilings and has been considered illusionism and tromp-l’oeil but it is executed in the same manner as anamorphic images so, from my research thus far, it seems it is labeled whatever an author feels like labeling it. Many Baroque churches used this to create a new look on ceilings to make them appear taller or even imitate sculptural details. One ceiling done well in particular is the ceiling of the corridor to the apartments of Saint Ignatius in Il Gesù painted by Andrea Pozzo from 1682.

Corridor to the apartments of Saint Ignatius, Il Gesù

Fred Leeman. Hidden Images. Games of Perception, Anamorphic Art, Illusion: From the Renaissance to the Present., p.38

The ceiling is actually curved but the anamorphic painting makes it appear flat and highly ornamented.

Color of corridor to Saint Ignatius apartments

Leeman, p.80.

Here you can see how the correct perspective changes the way the corridor looks.

With these different types, you can see how anamorphism took on many different directions but all accomplished the same thing.