Unbounded Half-spaces:

This defined a rectangular cube, centred on the region, whose boundary is the six planes whose equations are specified below.

y = - 4 and y = 4

 x = - 4 and x = 4

z = - 1 and z = 1

                 Figure: Rectangular Cube

Figure illustrated the various half-spaces along with their local coordinate systems and the limits on their configuration parameters. The solid S illustrated in Figure (a) is represented by utilizing half-spaces in Figure. It needs nine half-space (eight planes & one cylinder) H₁ to H₀. The half-space H₇ and H₈ that model the front and back faces of the model are not illustrated in the figure.

Half spaces are lower level primitives and any complicated object may be modelled as half-spaces combined by the set of operations. One form of CSG may be based on unbounded half-spaces.

The major advantage of half-spaces is its conciseness in representing objects compared to other schemes such like CSG. Though, this representation may lead to unbounded solid models resulting in missing faces and abnormal shaded images. Modelling by half-spaces is also cumbersome for designers. This is useful only for research purposes.