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Geometric Photo Manipulation

Tom Farmer

Figure 1

Tom Farmer is Associate Professor of Mathematics at Miami University.

I present here a way that students of calculus and linear algebra can use both artistic and mathematical abilities to transform ordinary photographs into interesting pictures having mathematical content. As a quick illustration, Figure 1 shows copies of an input photo tracing the path of a helix and viewed as if they were pasted onto an invisible cylinder. Similarly, almost any three dimensional object that you can imagine -- if you can describe it by mathematical formulas -- might be "colored" using a given photo. This idea is timely, not only because computer graphics is a rapid growth area that is notable for its uses of mathematics, but also because we now have easy access to digital photographic images via digital cameras and scanners.

Published October, 2002
© 2002, Thomas A. Farmer


Tom Farmer, "Geometric Photo Manipulation," Convergence (October 2005)