Art, Math and Science at first seem like very different subjects, but they are related in variety of ways. Experience the relationship between math and art by creating mind boggling anamorphic illusion art.
Materials & Tools:
For small scale anamorphic art
- Simple 3D object (Cube or Pyramid works well)
- Anamorphic Projection Stand (or a stand with a viewfinder)
For large scale anamorphic art:
- Cardboard boxes
- A Pole with a stable base and a viewfinder
- Blue Painter’s Tape or Colorful Duct Tape
Basic Principles Behind Anamorphic Illusion Art
The light rays from each point on the object travel in straight lines to enter the viewer’s eye. If we extend these lines and plot points at where lines intersects with another surface, the resulting image is a central projection of the original object.
If the projection surface is perpendicular to the viewer’s line of sight, the projected image will look like an ordinary perspective drawing.
If the projection surface is not perpendicular to the viewer’s line of sight, then the projected image is an anamorphic projection of the original object.
Looking from the point of projection, the morphed image loses its distortion and becomes a misleading frame of reference for a viewer to judge the distance.
The stick figures in our sample picture look like they are standing at the same depth of field viewed from a particular point. In reality the person on the left is standing much closer to the viewer thus looks much bigger. View with a camera or with one eye closed to get the full effect of this illusion.
How to Create Anamorphic Images
There are a number of ways to create anamorphic images. Here, we are using a string stretched from a stationary viewfinder to points on a object. Stretched string simulate the light rays traveling from points on an object to the viewer’s eye.
For small scale anamorphic art:
Relying on projective geometry, anamorphic images can be created using a central projection to map points from a 3D object to their corresponding locations in a 2D anamorphic projection. One tool that can help create these images is an Anamorphic Projection Stand.
- Be sure the projection stand is affixed firmly to the desktop. It is imperative that the center of projection does not move as you map points from the 3D object to the page where you’ll draw the anamorphic projection. It is equally important that the 3D object you are projecting remains in the same location; it can be moved only if it is returned to its exact original location-‐ be sure to begin by marking the points on the base of the 3D object so that its original location is marked.
- In the viewfinder, the center of the eye hole-‐ where the projection string originates-‐ is the center of projection. The string is the projection line. Using the string to map points from the 3D object to the desktop, you’ll draw the 3D image on the desktop exactly as it appears to you when you look through the eye hole. In other words, if an edge is visible to you through the eyehole, then it will also appear in the drawn anamorphic projection; if an edge is not visible through the eyehole, then it will not be drawn (eg if it is on the back side of the 3D object and thus occluded). To project a point, pull the string taut so that it just barely makes contact with the 3D object and extends down to the desktop. Mark the point on the desktop where the string makes contact-‐ this is the projected image of the point on the 3D object. You may want to mark the points: for example, call the point on the 3D object A and its corresponding projection A’ (called “A prime”). Continue mapping points until you have enough to reconstruct the projected image.
- Connect the projected points to form the projected image. If two points on the 3D object are connected by an edge, then the two corresponding projected points will be connected by an edge in the projection. That is, if AB is a line on the 3D image, then A’B’ will be a line in the projected image.
- Now remove the string from the eye hole and view the projected image-‐ it should appear 3D. But it will only appear 3D when viewed from that exact location, the center of projection. Take a photo through the eye hole to make the 3 dimensionality of the image even more convincing. Adding color and shading to the image may also increase the appearance of 3D. To view the image without the projection stand, note the height of the center of projection (this is etched on the projection stands you used in the workshop), and also the distance between the 3D object and the center of projection.
Q: What can I use if I do not have a Anamorphic Projection Stand?:
A: You can build a substitute Anamorphic Projection Stand with a ruler, a box and a binder clip. Tape the ruler to the box and add weight to the box if the stand is not stable.
Q: What do I do if the object blocks the path of the string?
A: If the string can not be extended from a certain point of the object to the paper, mark the base of the object and pivot the object to clear the path of the string. Make sure to return the object to its original position after mapping the point.
For large scale anamorphic art:
Build a large Anamorphic Projection Stand with a pole and a heavy base. Following the instructions to create the small anamorphic projection, plot projection points on the ground and connect them to form an image. Use colorful tapes to outline the image, use chalk to fill each side of object with different color.
Position the camera at the center of projection (the location of the viewfinder) to take the picture.
- The entire system must remain static, with the exception of the projection line (the yarn), while creating the projection
- Anamorphic images will only appear 3D when viewed precisely from the center of projection
- For more information please visit: http://informalmathematics.org/projective-geometry-and-anamorphic-projection/
For more information on creating an Anamorphic Projection Stand, please contact Bohdan Rhodehamel at firstname.lastname@example.org