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Geometric Photo Manipulation - Examples

Tom Farmer

Generating pictures such as the ones in this article may require a little mathematics as well as a considerable amount of experimentation. For example, Figure 1 involves, among other things, expressing an arc of a helix in parametric form with arc length as the parameter. Parameterizations using some other parameter would be apt to deform the pictures or leave gaps. Figure 4 below requires that same type of parameterization for the circles that generate a torus; it is also an application of the tangent, normal, and binormal vectors of a parametric curve.

Figure 4

A picture like the one in Figure 5 can be a fun way to clarify a three-dimensional object. In this case we are able to visualize the shape of the solid obtained as the intersection of two cylinders arising from two input images.

Figure 5

There is no end to the possible examples, and many are apt to lead to challenges that can pique students' interest in mathematical topics.


Journal of Online Mathematics and its Applications