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# CSPlotter

A Mathematica package for visualizing contact structures in R3.

To use CSPlotter you need to download the file CSPlotter.m and put it in your current working directory in Mathematica. (You may also view the code here.) From the Mathematica prompt, you can then load it by typing
 ```<
If this generates an error, Mathematica can not find the file CSPLotter.m. The command Directory[] shows what directory Mathematica is currently in, and you can use SetDirectory["/user/mydir"] to change this directory.

Once you have loaded CSPlotter.m, it will provide the command contactelement(pos, v, s) that produces a small tile at pos, normal to v, and of size s. Since at each point in R3 a contact structure is a two dimensional subspace of the tangent space, such tiles can be used to visualize a contact structure in R3 at one point. (The tile shows the orientation of the vector subspace.) By plotting many such tiles, one can visualize the whole contact structure. For example, the standard contact structure ker dz-x dy is visualized using the commands:
 ```xmin = -3.5; xmax = 3.5; dx = (xmax - xmin)/14; ymin = -3.5; ymax = 3.5; dy = (ymax - ymin)/16; size = dy; normal[x_, y_, z_] = {0, -x, -1}; Table[contactelement[{x, y, 0}, normal[x, y, 0], size], {x, xmin, xmax, dx}, {y, ymin, ymax, dy}]; out = Show[%, coords[xmax + 1, ymax + 1, 3.4], Boxed -> False] ```
This gives the following picture:

Since the contact structure does not depend on z, the structure is only plotted for z=0. In this picture it is clearly seen that at x=0, the tiles are normal to z, and as x becomes non-zero the tiles rotate around the x-axis. The command coords is also provided by CSPlotter. It produces the coordinate axes of variable lengths. For more information on the commands, see the CSPlotter.m source file.

CSPlotter has been tested with Mathematica 5.0.1.0.

## More examples

• Standard structures [.nb]
• Alternative representation of the standard structures [.nb]
• Zoom in of the alternative representation [.nb]