ARCH 221 Fundamentals of Architecture

point-line-surface-volume
The primary elements of form in the order of their growth:
- from the point to a one-dimensional line,
- from the line to a two- dimensional plane,
and
- from the plane to a three-dimensional volume.

Each element is first considered as a conceptual element, then as a visual element in the
vocabulary of architectural design.

As conceptual elements, the point, line, plane, and volume are not visible except to the mind’s
eye. While they do not actually exist, we nevertheless feel their presence. We can sense a
point at the meeting of two lines, a line marking the contour of a plane, a plane enclosing a
volume, and the volume of an object that occupies space.

When made visible to the eye on paper or in three-dimensional space, these elements become
form with characteristics of substance, shape, size, color, and texture. As we experience
these forms in our environment, we should be able to perceive in their structure the existence
of the primary elements of point, line, plane, and volume.
A point marks a position in space.

Conceptually, it has no length, width, or depth,

and is therefore static, centralized, and
directionless.

As the prime element in the vocabulary of form,

a point can serve to mark:
• the two ends of a line
• the intersection of two lines
• the meeting of lines at the corner of a plane or
volume
• the center of a field

Although a point theoretically has neither shape

nor form, it begins to make its presence felt
when placed within a visual field.

At the center of its environment, a point is

stable and at rest, organizing surrounding
elements about itself and dominating its field.

When the point is moved off-center, however,

its field becomes more aggressive and begins
to compete for visual supremacy. Visual tension
is created between the point and its field.
Point
 indicates a position in space.

A point extended becomes a with properties of:

 length
 direction
 position

A line extended becomes a with properties of:

 length and width
 shape
 surface
 orientation
 position

A plane extended becomes a with properties of:

 length, width, and depth
 form and space
 surface
 orientation
 position
 the point

• sphere: Cenotaph for Sir Isaac Newton,

Project, 1784, Étienne-Louis Bouleé

Piazza del Campidoglio, Rome, c. 1544, Michelangelo

Buonarroti.
The equestrian statue of Marcus Aurelius marks the
center of this urban space.

 cylinder:
Baptistery at Pisa,Italy,
1153–1265,  circle: Tholos of Polycleitos,Epidauros, Greece, c. 350 B.C.
Dioti Salvi
the point

Mont St. Michel, France, 13th

century and later.

The pyramidal composition

culminates in a spire that serves to
establish this fortified monastery as
a specific place in the landscape
 two points
Two points describe a line that connects
them. Although the points give this line
finite length, the line can also be
considered a segment of an infinitely
longer path.

Two points further suggest an axis

perpendicular to the line they describe
and about which they are symmetrical.
Because this axis may be infinite in
length, it can be at times more dominant
than the described line.

In both cases, however, the described

line and the perpendicular axis are
optically more dominant than the
infinite number of lines that may pass
through each of the individual points.
the line
the line

A point extended becomes a line.

Conceptually, a line has length, but no width or depth.
Whereas a point is by nature static, a line, in describing the path of a point in motion, is
capable of visually expressing direction, movement, and growth.

A line can serve to:

• join, link, support, surround, or intersect other visual elements
• describe the edges of and give shape to planes
• articulate the surfaces of planes
the line

At a smaller scale, lines articulate the edges

and surfaces of planes and volumes. These
lines can be expressed by joints within or
between building materials, by frames
around window or door openings, or by a
structural grid of columns and beams. How
these linear elements affect the texture of a
surface will depend on their visual weight,
spacing, and direction.

Town Hall, Säynätsalo, Finland, 1950–52, Alvar Aalto

the line

Seagram Building, New York City,

1956–58, Mies van Der Rohe and
Philip Johnson
the linear elements
Two parallel lines have the ability to
visually describe a plane. A
transparent spatial membrane can be
stretched between them to
acknowledge their visual relationship.
The closer these lines are to each
other, the stronger will be the sense of
plane they convey.

A series of parallel lines, through their repetitiveness, reinforces

our perception of the plane they describe. As these lines extend
themselves along the plane they describe, the implied plane
becomes real and the original voids between the lines revert to
being mere interruptions of the planar surface.

The diagrams illustrate the transformation of a row of round

columns, initially supporting a portion of a wall, then evolving into
square piers which are an integral part of the wall plane, and finally
becoming pilasters—remnants of the original columns occurring as
a relief along the surface of the wall.
the linear elements

Altes Museum, Berlin, 1823–30,

Karl Friedrich von Schinkel

A row of columns supporting an entablature—a colonnade—is

often used to define the public face or facade of a building,
especially one that fronts on a major civic space.

A colonnaded facade can be penetrated easily for entry, offers a

degree of shelter from the elements, and forms a semi-transparent
screen that unifies individual building forms behind it.
the linear elements
The linear members of trellises and pergolas can
provide a moderate degree of definition and
enclosure for outdoor spaces while allowing filtered
sunlight and breezes to penetrate.

Trellised Courtyard, Georgia O’Keefe Residence, Abiquiu, northwest of

Sante Fe, New Mexico

St. Philibert, Tournus, France, 950–1120.

This view of the nave shows how rows of

columns can provide a rhythmic measure
of space.
Shape is the primary identifying characteristic
of a plane. It is determined by the contour of
the line forming the edges of a plane.
Because our perception of shape can be
distorted by perspective foreshortening, we
see the true shape of a plane only when we
view it frontally.

The supplementary properties of a plane—its

surface color, pattern, and texture—affect
its visual weight and stability.

In the composition of a visual construction, a

plane serves to define the limits or boundaries
of a volume. If architecture as a visual art
deals specifically with the formation of three-
dimensional volumes of mass and space, then
the plane should be regarded as a key
element in the vocabulary of architectural
design.
the plane

A line extended in a direction other than its

intrinsic direction becomes a plane.

Conceptually, a plane has length and width,

but no depth.
the plane
Planes in architecture define three- In architectural design, we manipulate three generic
dimensional volumes of mass and types of planes:
space.
Base Plane
The properties of each plane—size, The base plane can be either the ground plane that
shape, color, texture —as well as serves as the physical foundation and visual base for
their spatial relationship to one building forms, or the floor plane that forms the lower
another ultimately determine the enclosing surface of a room upon which we walk.
visual attributes of the form they
define and the qualities of the space Overhead Plane
they enclose. The overhead plane can be either the roof plane that
spans and shelters the interior spaces of a building
from the climatic elements, or the ceiling plane that
forms the upper enclosing surface of a room.

Wall Plane
The wall plane, because of its vertical orientation, is
active in our normal field of vision and vital to the
shaping and enclosure of architectural space.
base plane
Three terraces approached by ramps rise toward the base of
the cliffs where the chief sanctuary is cut deep into the rock.

Mortuary Temple of Queen Hatshepsut, Dêr el-Bahari, Thebes, 1511–1480 B.C., Senmut.
base plane
Like the ground plane, the form of a floor
plane can be stepped or terraced to
break the scale of a space down to
human dimensions and create platforms
for sitting, viewing, or performing. It can
be elevated to define a sacred or
honorific place. It can be rendered as a
neutral ground against which other
elements in a space are seen as figures.

The floor plane is the horizontal element

that sustains the force of gravity as we
move around and place objects for our
use on it. It may be a durable covering of
the ground plane or a more artificial,
elevated plane spanning the space While the pragmatic, supportive nature of the
between its supports. In either case, the floor plane limits the extent to which it can be
texture and density of the flooring manipulated, it is nonetheless an important
material influences both the acoustical element of architectural design. Its shape, color,
quality of a space and how we feel as we and pattern determine to what degree it defines
walk across its surface. spatial boundaries or serves as a unifying
element for the different parts of a space.
 Exterior wall planes
wall plane isolate a portion of space
to create a controlled
interior environment.
Their construction
provides both privacy
and protection from the
climatic elements for the
interior spaces of a
building, while openings
within or between their
boundaries reestablish a
connection with the
exterior environment.
As exterior walls mold
interior space, they
simultaneously shape
exterior space and
describe the form,
massing, and image of a
building in space.
wall plane

As a design element, the plane of an exterior

wall can be articulated as the front or primary
facade of a building. In urban situations, these
facades serve as walls that define courtyards,
streets, and such public gathering places as
squares and marketplaces.
wall plane Country House in Brick, Project, 1923, Mies van der Rohe

In the project, freestanding brick bearing walls,

together with L-shaped and T-shaped configurations
of planes, create an interlocking series of spaces.
 overhead plane
The roof plane is the essential sheltering
element that protects the interior of a building
from the climatic elements. The form and
geometry of its structure is established by the
manner in which it spans across space to bear
on its supports and slopes to shed rain and
melting snow. As a design element, the roof
plane is significant because of the impact it
can have on the form and silhouette of a
building within its setting.

The roof plane can be hidden from view by the

exterior walls of a building or merge with the
walls to emphasize the volume of the building
Robie House, Chicago,1909, Frank Lloyd Wright. mass. It can be expressed as a single
sheltering form that encompasses a variety of
The low sloping roof planes and broad spaces beneath its canopy, or comprise a
overhangs are characteristic of the Prairie number of hats that articulate a series of
School of Architecture. spaces within a single building.
 overhead plane

A roof plane can extend outward to form overhangs that shield door and window openings from
sun or rain, or continue downward further still to relate itself more closely to the ground plane. In
warm climates, it can be elevated to allow cooling breezes to flow across and through the interior
spaces of a building.

With the skylights placed on

hexagonal roofs, Sedat Hakkı Eldem
brought a modern interpretation to
providing natural light from the roof in
architecture.
Atatürk Library, Istanbul,1939, Sedad Hakkı Eldem.
the plane
The overall form of a building
can be endowed with a
distinctly planar quality by
carefully introducing
openings that expose the
edges of vertical and
horizontal planes. These
planes can be further
differentiated and
accentuated by changes in
color, texture, or material.

Fallingwater (Kaufmann House), near Ohiopyle, Pennsylvania ,1936–37, Frank Lloyd Wright.

Reinforced concrete slabs express the horizontality of the floor

and roof planes as they cantilever outward from a central vertical
core.
https://vimeo.com/149398808
the volume
A plane extended in a direction other than its
intrinsic direction becomes a volume.
Conceptually, a volume has three dimensions:
length, width, and depth.

All volumes can be analyzed and understood

to consist of:

• points or vertices where several planes

come together

• lines or edges where two planes meet

 planes or surfaces that define the limits or
boundaries of a volume
the volume

Form is the primary identifying

characteristic of a volume. It is
established by the shapes and
interrelationships of the planes
that describe the boundaries of
the volume.

As the three-dimensional element in the vocabulary of architectural design, a volume can be

either a solid— space displaced by mass—or a void—space contained or enclosed by planes.
the volume
Building forms that stand as objects in the
landscape can be read as occupying volumes
in space.

The building stands in landscape as

crystallized entity.