Selected Bibliography Architecture - Form Space and Order | Page 57

SU R FACES

In the transition from the shapes of planes to the forms of
volumes is situated the realm of surfaces. Surface first refers
to any figure having only two dimensions, such as a flat plane.
The term, however, can also allude to a curved two-dimensional
locus of points defining the boundary of a three-dimensional
solid. There is a special class of the latter that can be generated
from the geometric family of curves and straight lines. This
class of curved surfaces include the following:
• Cylindrical surfaces are generated by sliding a straight line
along a plane curve, or vice versa. Depending on the curve,
a cylindrical surface may be circular, elliptic, or parabolic.
Because of its straight line geometry, a cylindrical surface
can be regarded as being either a translational or a ruled
surface.
• Translational surfaces are generated by sliding a plane curve
along a straight line or over another plane curve.

• Ruled surfaces are generated by the motion of a straight
line. Because of its straight line geometry, a ruled surface is
generally easier to form and construct than a rotational or
translational surface.

• Rotational surfaces are generated by rotating a plane curve
about an axis.

• Paraboloids are surfaces all of whose intersections by planes
are either parabolas and ellipses or parabolas and hyperbolas.
Parabolas are plane curves generated by a moving point
that remains equidistant from a fixed line and a fixed point
not on the line. Hyperbolas are plane curves formed by the
intersection of a right circular cone with a plane that cuts
both halves of the cone.
• Hyperbolic paraboloids are surfaces generated by sliding
a parabola with downward curvature along a parabola with
upward curvature, or by sliding a straight line segment with
its ends on two skew lines. It can thus be considered to be
both a translational and a ruled surface.

42 / A R C H I TE C TU R E : F O R M , S PA C E , & O R D E R