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Projective Geometry and Anamorphic Projection – InforMath

Projective Geometry and Anamorphic Projection

Anamorphosis has been present in art for centuries; the anamorphic skull in Hans Holbein’s The Ambassadors is a well known example. More recently, fleeting 3D sidewalk art has sprung up across the globe, capturing the imaginations of passersby who can’t help but stop and snap a photo of a friend seemingly teetering on the edge of oblivion or about to be swallowed by a shark.

One method of creating anamorphic images relies on projective geometry, specifically a central projection, to map points from a 3D object to their corresponding locations in the 2D anamorphic projection. The Anamorphic Projection Stand (APS) is a simple tool we created for making small scale, desktop anamorphic projections. The APS consists of a stand, a view finder, and a projection line. The projection line extends from the center of the eye hole in the view finder; the center of the eye hole serves as the center of projection. The projection line, in this case a piece of yarn, creates a physical mapping that extends from the center of projection, through a given point on the 3D object, then back down to the table where the projected point lives. By carefully and strategically mapping points from the 3D object down to the table top one can construct an anamorphic image of the 3D object.

center_vertex_proj point

20150627_073425

 

the pic through the view finder

A few important considerations:

The entire system must remain static, with the exception of the projection line, while creating the projection. That is, the center of projection must remain in the same place for each projection, as well as the 3D object. The 3D object can be moved only if it is returned to its exact same position for the next projection (be sure to the mark points on the base of the object).

Anamorphic images will only appear 3D when viewed precisely from the center of projection (note the boy looking through the view finder above). This doesn’t mean you must look through the eye hole to get the 3D view, just make sure you take note of the height of the center of projection, and the distance from the 3D object to the center of projection.

 

Written by Bohdan Rhodehamel
Contact Bohdan at bohdanr561@yahoo.com

2 Comments
  1. Amanda 2 years ago

    I am a teacher and want to try this with my class. How can I do this?

  2. Profile photo of Bohdan Rhodehamel
    Bohdan Rhodehamel 2 years ago

    Hi Amanda,

    One option is to make your own stands. This, of course, requires that you have access to a laser cutter to cut the acrylic pieces.

    However, you don’t need the stands to create the projections. Essentially what you need is a strong stand and a piece of string. You want the stand to be firmly affixed to the surface it is on so that your central point of projection does not move when you are making each projection.

    Consider the scale you want too. If it is on a desktop, then you might use, for example, a one gallon milk jug (filled with water) with a string tied to its handle. If you have a lot more room, say you have an outdoor basketball court, then you might use a larger piece of rope tied to one of the poles. Sidewalk chalk would work nicely for drawing.

    Hope this gives you some ideas. Let us know if you have other questions.

    Cheers,

    Bohdan

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