SHAPE is a program to calculate and display the morphology and symmetry of single crystals, twins and epitaxial and other intergrowths. Some of the basic mathematical aspects of the program were described in a paper in The American Mineralogist (1980, V.65, p.465). However, many important improvements have been made since then in the capabilities and speed of the program.
To draw an individual crystal, it is necessary to enter only the crystal class, the unit cell parameters, and the indices and central distance for one face of each form. The crystal drawing can be rotated, translated and rescaled, and crystal axes can be added at will.
The central distances, which determine the prominence (area) of each form, may be derived from the unit cell and space group, using the Donnay-Harker morphological "law".
The crystal can be displayed in an orthographic projection rotated in a standard way (virtually identical to clinographic projection), or in a "straight-on" orthographic projection, and the view of the crystal can be combined with a stereonet showing the poles to the faces and the crystal axes. The mouse cursor can be used to index any of the visible faces. Any of the faces can be filled in with color (if a color display is used) or dot shading patterns. The entire crystal can be shaded, in color or black-and-white. Stereopairs of the image may be drawn, either as separate images or as superimposed anaglyphs (two-color).
The 3D Drawing Modes, which use OpenGL or Direct3D system software, allow a number of special effects, such as transparent faces. In these modes, the symmetry elements (rotation axes and mirror planes) may be shown.
Stereo output through quad-buffered OpenGL (or Direct3D on Windows) is available for appropriate hardware (suitable graphics cards, monitors, projectors and/or eyewear).
The central distance, and therefore the size, of each face may be adjusted on-screen by clicking with the mouse.
After having generated a single crystal, and even after having rotated it, the crystal may be twinned in any of several ways. Almost any kind of twin is possible, including many kinds of multi-crystal aggregates. Also, epitaxial intergrowths may be drawn, again including multi-crystal aggregates. All inter-crystal edges and corners may be drawn, and all unwanted lines may be removed from these plots, producing an absolutely perfect final version.
Sections of crystals may be drawn for any orientation and at any level. Growth zoning may be modeled in section, using non-linear growth rates and/or different start and end times for multiple crystals. Also, non-crystallographic symmetry can be used to draw quasi-crystals.
Hard copies of the drawings can be made in several ways. The screen image can be reproduced with dot-matrix or laser printers - actually, with the high-resolution modes of these printers, the resolution of the image is much improved over the screen. Plots can also be made with most pen plotters. Finally, if neither a pen plotter nor a suitable dot-matrix printer is available, the coordinates of the corners and other information can be listed and the drawing can be made by hand.
Running the program is not difficult the input is interactive and usually simple. However, a knowledge of elementary crystallography is assumed. Some examples, the first one in the form of a tutorial, are given after the instructions.