Representation of a sphere family

Spheres are characterized by their centers and radii; namely by four DOUBLE parameters. Other information may also be associated with them, for example the orientation of their poles and Greenwich meridians, whose specification can be accomplished by additional parameters. If Euler angles are used, three additional parameters are required, for a total of seven.

Beyond that, any amount of additional information may be considered, such as tags, identifying subgroupings to which they belong, associated chemical information when they represents atoms within a molecule, and so on. Foreseeing such an application, let us refer to the whole family as a molecule, individual spheres as atoms. Subgroupings could be called radicals, if needed.

The basic operations to be performed on a sphere family, other than drawing its pictorial representation, consist in altering one or more of the parameters. In particular, the individual atoms, complete with orientation, can be placed in the molecule and if need be, adjusted.

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The molecule as a whole can be translated or rotated, without affecting the orientation of the atoms.

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the entire molecule can be scaled; to fit it onto a page, or to change the style of representation -- say from van der Waals radii to positions of the nuclei.

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changing the orientation of the atoms without moving their centers. This could be done to identify individual atoms, for example.

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altering any combination of parameters for an individual atom.

To accomplish these transformations, we define several operations from the realm of matrix or vector algebra; in particular, we give a certain prominence to some frequently used combinations of operations.