© Steffen Weber, March 1999
This applet calculates Fourier transforms (FT) of a given pointset. The pointset is generated by the plane space groups (see Project 22). You may transform all points or only one unit cell. Before calculating the FT all points which are identical (because they are on symmetry centers) are identified, so that any position gives only one point contributing to the FT. The cell dimensions may also be varied interactively using the sliders. The zoom slider has no effect on the transform. Change the cell width, cell height or cell angle if you want to scale/modify the FT. All "atoms" are used as point scatterers with unit scattering power (independent of the color you choose). The FT is calculated as a 100x100, 200x200 or 300x300 pixel image for a Fourier space region x*,y* = [-0.5, 0.5] . 5x5 unit cells are always used. If the number of atoms exceeds 2000 only 3x3 cells are used. If the calculation takes too long choose a simple plane group like p1 or remove some atoms from the unit cell.
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The black window represents one cartesian unit cell (unit cell editor). The grid indicates the unit cell coordinates x,y=[0,1]. You may first click at the color chooser to select an "atom" color. Then click on the unit cell area. You may add other atoms by just clicking on other empty areas within the unit cell editor. If you click at an already present atom you may drag it around. If you double click at an atom it will be removed from the cell. Then you have the choice to select a plane space group using the radio buttons on the right side. To calculate the FT click "Fourier transform".
Drag/click with left mouse button for "atom" color "p" and with the right mouse button for the background color "b". The background color is only applied in the pattern and not in the unit cell editor! Both colors are indicated in the little boxes on the right side of the color chooser area.