Glossary

Boundary-conforming subdivision.
The schemata of this type of spatial subdivision include meshes and binary space partition trees (BSP trees). The elements of the meshes, which define the boundaries of the object, are polyhedra. BSP trees work by recursively subdividing space. Each interior node separates space into two disjointed point sets. The leaves of the tree are labelled 'in' or 'out'. The union of all the 'in' cells model the object (Hoffman & Rossignac 1996, 5).
Boundary-approximating subdivision.
These schemata work either by grids or octrees. Grid schemata subdivide space in conformance with a grid system. The elements of the grid are typically hexahedra. Octree schemata recursively divide a cube into eight further cubes. Each cube is either black (if it is inside the object), white (outside the object), or grey (on the boundary). Grey cubes are sub-divided. (Hoffman & Rossignac 1996, 5).
B-rep
Boundary-representation model. A solid model which deals with an object by describing its physical boundaries.
Computer-Aided Design. The use of computers to help in design work, for example by architects. The emphasis is on visual information. The term is also used by some people to refer to Computer-Aided Drafting, and is related to CADD - Computer-Aided Drafting and Design.
CAE
Computer-Aided Engineering. The use of computers to help in the design of a product with regard to its physical properties.
CSG
Constructive Solid Geometry. A solid modeller which deals with an object by treating it as the product of a series of boolean operations (such as unions and subtractions) performed on a range of primitives (such as spheres and boxes).
CPU
Central Processing Unit. The unit in a computer which controls its overall operation and carries out arithmetic-logical operations.
GUI
Graphical User Interface. The human eye is better able to work with a visual representation of an object than with a string of co-ordinates (or similar method), and so GUI are used.
CGAL
Computer Graphics Animation Language. A surface modeller developed by Peter Comninos at Teesside Polytechnic, primarily for graphical animation. It was run by Chapman (1990) on an Apollo Domain 4000 workstation to produce a model of the Hoffman limekiln.
ER
Entity Relationship model. The ER model describes data as entities, attributes and relationships. That is to say, 'things', how they can be described in themselves, and how they relate to one another.
exact arithmetic.
Arithmetic carried out with numbers which are exact, rather than approximations, as is the case with floating-point numbers. The results are precise, rather than approximations.
floating point arithmetic.
Calculations involving floating point arithmetic. In addition to the inaccuracies involved in storing floating point numbers, calculations with them are also problematic when two mantissas with very different exponents are used. The results of the arithetic are not exact.
Floating Point Numbers.
These are used when the number is expected to be very large or small. The number is represented as a mantissa (or 'integer') plus an exponent (or 'characteristic'). For instance, 4,900,000 may be written as 0.49 x 10 7, where 0.49 is the mantissa nd 7 is the value of the exponent. Problems arise when one attempts to store a number such as 4,900,001, as the number is still recorded as 0.49 x 10 7 .
GIS
Geographic Information Systems. These are designed to store, analyse and display spatial data which exist along a single surface. They are used for working with map data.
incidence tests.
Testing whether something is the case, such as whether an object is in a particular point in space.
NURBS
Non-uniform rational B-splines. The representation of any curve requires an algorithmic expression. Some algorithms allow a curve to be expressed precisely, so that any point along it can be known. Other algorithms provide ways in which the curve can be mathematically approximated, and these have been the commonest in use; the approximation becomes greater as the curve becomes more complicated. NURBS are of the former type, and so are more accurate in their recording of the position of the curve. (A spline is originally a flexible ruler used in draughting to produce curved lines).
spatial-subdivision.
Used in solid modelling as a way of representing a solid. The space is decomposed into cells. Each cell has a simple topological structure, and also often a simple geometric structure. There are two forms of spatial subdivision: boundary conforming and boundary approximating. (Hoffman & Rossignac 1996, 5)
vector-computations.
Computations involving vectors. Vectors are mathematical entities which possess both value and direction, as opposed to scalars, which possess simply value.
WINSOM
Winchester Solid Modeller. A CSG solid modeller developed by IBM's Scientific Centre at Winchester (Burridge et al 1989).