Isometries with DPGraph

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DPGraph is a 3D (and more) graphing program that is most useful for graphing surfaces.  We, however, have had some success in using it to program animations of transformations, as well. 

 

You must have a copy of DPGraph or the viewer to view our files.  Click here to go to the DPGraph website and download the viewer.

 

Our first assignment was to rotate a 3D object about an arbitrary line.  It was a little hard to grasp isometries in R^3 at first, so we utilized DPGraph’s somewhat artificial 2D capabilities to create a rotation about a point in 2D and then extended it to R^3 quite naturally.  Rotations are extremely easy to do in DPGraph because the program’s animation feature is based upon the trigonometric functions used to produce the rotation.  DPGraph’s scrollbar feature also came in handy for including all possible points of rotation. 

 

Our first (2D) attempt can be viewed here.   Click on the scrollbar menu to move the intersecting lines.  The A scrollbar moves the X variable and the B scrollbar moves the Y variable.

 

We were easily able to extend it to R^3, with just a few adjustments.  Click here to see a rotation about the intersection of two planes.  The scrollbar can be used to move the planes, just as in the previous example.