Undergraduate Research Projects - The Anamorphic Art Project

Anamorphic art is the process of image distortion so that when viewing the distorted image from a specific vantage point or through a lens or curved mirror the image appears normally. Students working in this area have produced formulas and algorithms for viewing images in mirrored cylinders, spheres, and general convex level surfaces.

This is another area in which you can either concentrate on just the mathematics or do software development or both. Along the mathematical side you can work on generalizing previous results, examine other types of Anamorphic Art, such as vantage point and lens, or go into the study of optical illusions. This project would also be good for secondary education majors and can provide numerous enrichment activities that can keep the student's attention as well as show them some of the nifty things that mathematics can do.

Background Needed for Mathematical Research

• Vector Calculus and analytic geometry.

Background Needed for Program Development

• Any programming language that has support for graphics applications and graphical user interfaces. Such as Java and Swing or C++ and Qt.
• Knowing how to implement graphics in the chosen language. For example, Java 2D, JOGL and/or OpenGL.

Mathematical Research Possibilities

• Extending the results and algorithms to parametrically defined surfaces.
• Vantage point explorations.
• Manipulating the surface the image is painted on.
• Explore the mathematics behind optical illusions.
• Develop middle and high school explorations on the mathematics behind anamorphic art and/or optical illusions.

Further Program Development

• Develop programs for producing the distorted images for vantage point anamorphic art.
• Develop programs for producing the distorted images for reflection anamorphic art off of polyhedron, level surfaces and parametrically defined surfaces.
• Develop POV-Ray scripts to emulate the reflection when using surfaces that are difficult to physically model.

Software

• Cylinder Reflection Generator
• Cylinder Reflection Generator Multi-Image Edition
• Cylinder Reflection Generator in Mathematica
• Image Printer