“QUADRIL: A computer language for the description of quadric-surface bodies” by Levin

Most man-made objects can be closely approximated by bodies whose surfaces are composed of portions of second-order (quadric) surfaces. These surfaces include elliptic, hyperbolic, and parabolic cylinders, as well as quadric cones, paraboloids, hyperboloids, ellipsoids, and pairs of planes. Simple planes (first-order surfaces) may be included as degenerate quadric surfaces. Because these quadric-surface bodies are so useful for modelling man-made objects, it is important that any Computer-Aided Design (CAD) system be able to work with such bodies. The “QUADRIL” language described here was designed to accept descriptions of quadric-surface bodies in character-string form. QUADRIL has a mixture of English-like and algebraic syntax. It may be used to specify quadric-surface bodies and then to display them on various media. QUADRIL will accept descriptions of quadric-surface bodies either as “volumetric” combinations of basic bodies, or as boolean functions of bounding surfaces. English-like syntax is used for specifying what surfaces and basic bodies are used, while algebraic syntax is used to transform the canonical forms of the surfaces or bodies into the shape, position, and orientation that the user desires. Volumetric combination of bodies involves the operations of union (+), intersection (*), and subtraction (-). Boolean specification of volumes is in terms of a boolean tree with the bounding surfaces as leaf nodes. The tree is expressed as a character string. QUADRIL permits using user-created “STRUCTURES” as component bodies (“OBJECTS”) in greater STRUCTURES. The display of the quadric-surface bodies may also be specified in QUADRIL. The user is considered fixed in space, while the body is transformed to give the desired view.

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