Computer Aided Engineering Design

SOLID MODELING 253

real projective plane or a cross cap which, again, cannot be constructed in three-dimensions without
self intersection. Another way to model a projective plane is to connect each point on the rim of a
hemisphere to a corresponding point on the opposite side with a twist. The third way is to attach a disc
to a Möbius strip making it a closed surface without boundaries.

(a) Instructions for building a torus

(b) Instructions for building a Möbius strip

(c) Instructions for building a Klein bottle, the usual projection and that

generated by revolving a figure ‘8’

(d) Instructions for building a Real Projective plane or a cross-cap (rightmost figure) from a

rectangular paper

Figure 8.9 Some basic surfaces.