5
Paraline Drawings
Paraline drawings include a subset of orthographic projections
known as axonometric projectionsÑthe isometric, dimetric, and
trimetricÑas well as the entire class of oblique projections. Each
type offers a slightly different viewpoint and emphasizes different
aspects of the drawn subject. As a family, however, they combine
the measured precision and scalability of multiview drawings and
the pictorial nature of linear perspective. Because of their pictorial
quality and relative ease of construction, paraline drawings are
appropriate for visualizing an emerging idea in three dimensions
early in the design process. They are capable of fusing plan,
elevation, and section into a single view and illustrating threedimensional
patterns and compositions of space. Portions of a
paraline drawing can be cut away or made transparent to see inside
and through things, or expanded to illustrate the spatial
relationships between the parts of a whole. At times, they can even
serve as a reasonable substitute for a birdÕs-eye perspective.
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PARALINE DRAWINGS
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Paraline drawings communicate the three-dimensional
nature of an object or spatial relationship in a single image.
Hence, they are also called single-view drawings to
distinguish them from the multiple and related views of
plans, sections, and elevations. They can be distinguished
from the other type of single-view drawing, linear
perspective, by the following pictorial effects.
¥ Parallel lines, regardless of their orientation in the
subject, remain parallel in the drawn view; they do not
converge to vanishing points as in linear perspective.
¥ Any linear measurement parallel to one of the three
major axesÑalong axial linesÑcan be made and drawn
to a consistent scale. Axial lines naturally form a
rectangular grid of coordinates that we can use to find
any point in three-dimensional space.
¥ Nonaxial lines refer to those lines that are not parallel to
any of the three principal axes. We cannot measure
dimensions along these nonaxial lines, nor can we draw
them to scale. To draw nonaxial lines, we must first
locate their end points using axial measurements and
then connect these points. Once we establish one
nonaxial line, however, we can draw any line parallel to
that line, since parallel lines in the subject remain parallel
in the drawing.
¥ Paraline drawings present either an aerial view looking
down on an object or scene, or a wormÕs-eye view looking
upward. They lack the eye-level view and picturesque
quality of linear perspectives. They represent what we
know rather than how we see, depicting an objective
reality that corresponds more closely to the picture in
the mindÕs eye than to the retinal image of linear
perspective.
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TYPES OF PARALINE DRAWINGS
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There are several types of paraline drawings, each named after the
method of projection that is used to develop them. Two of the most
common in architectural drawing are discussed in this chapter:
isometric and oblique drawings.
In both isometric and oblique drawings:
¥ All parallel lines in the subject remain parallel in the drawing.
¥ All lines parallel to the principal X-Y-Z- axes can be measured and
drawn to scale.
The images that emerge from oblique projections are distinct from
isometric views that develop from orthographic projection. The ease
with which we can construct an oblique drawing has a powerful
appeal. If we orient a principal face of the subject parallel to the
picture plane, its shape remains true and we can draw it more easily.
Thus, oblique views are especially convenient for representing an
object that has a curvilinear, irregular, or complicated face.
Plan Obliques
¥ The principal set of horizontal planes oriented parallel to the
picture plane is emphasized and can be represented in true size,
shape, and proportion.
¥ Plan views can be utilized as base drawingsÑa definite
advantage when drawing horizontal planes with circular or
complex shapes.
¥ Plan obliques have a higher angle of view than isometric drawings.
Isometric Drawings
¥ All three principal sets of planes share equal emphasis.
¥ The angle of view is slightly lower than that of plan obliques.
¥ Plans and elevations cannot be used as base drawings.
Elevation Obliques
¥ The principal set of vertical planes oriented parallel to the picture
plane is emphasized and can be represented in true size, shape,
and proportion. The other vertical set and the principal horizontal
set of planes are both foreshortened.
¥ An elevation can be used as a base drawing. This view should be of
the longest, the most significant, or the most complex face of the
object or building.
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ISOMETRIC DRAWINGS
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Isometric drawings establish a lower angle of view
than plan obliques and give equal emphasis to the
three principal sets of planes. They preserve the
relative proportions of a subject or scene and are not
subject to the distortion inherent in oblique views.
¥ To construct an isometric drawing, first establish
the direction of the three principal axes. Because
they are 120¡ apart on the picture plane, if we draw
one axis vertically, the other two axes make a 30¡
angle with a horizontal on the drawing surface.
¥ Then lay out the true lengths of all lines parallel to
the three principal axes and draw them to the same
scale.
¥ Isometric drawings of forms based on the square
can create an optical illusion and be subject to
multiple interpretations. This ambiguity results
from the alignment of lines in the foreground with
those in the background. In such cases, a plan
oblique might be a better choice.
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PLAN OBLIQUES
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Plan obliques present a higher angle of view than
isometric drawings and emphasize the set of
horizontal planes by revealing their true size, shape,
and proportions.
¥ To construct a plan oblique, begin with a plan drawing and rotate
it to the desired angle relative to a horizontal on the drawing
sheet or board.
¥ When drafting a plan oblique, the triangles encourage the use of
45¡-45¡ and 30¡-60¡ angles in establishing the orientation of
the principal horizontal planes.
¥ Note that we can emphasize one of the sets of vertical planes
over the other or show them to be of equal importance by varying
this angle.
¥ In a 45¡-45¡ plan oblique, both principal sets of vertical planes
receive equal emphasis.
¥ In a 30¡-60¡ plan oblique, one principal set of vertical planes
receives more emphasis than the other.
¥ From the rotated plan view, we project the vertical edges and
planes of the subject.
¥ We usually lay out and draw these vertical dimensions to their
true lengths.
¥ To offset the appearance of distortion, we may reduce the
vertical dimensions to 1/2, 2/3, or 3/4 of their true lengths.
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ELEVATION OBLIQUES
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Elevation obliques orient a principal vertical face or set of
vertical planes parallel to the picture plane and therefore
reveal their true sizes, shapes, and proportions.
¥ To construct an elevation oblique, we begin with an elevation
view of the principal face of the subject. This should be the
longest, the most significant, or the most complex face of
the subject.
¥ From significant points in the elevation view, we then
project the receding lines back at the desired angle into the
depth of the drawing.
¥ In drafting with triangles, we typically use 45¡, 30¡, or 60¡
angles for the receding lines. In sketching, we need not be as
precise, but once we establish an angle for the receding
lines, we should apply it consistently.
¥ Remember that the angle we use for the receding lines
alters the apparent size and shape of the receding planes.
By varying the angle, the horizontal and vertical sets of
receding planes can receive different degrees of emphasis.
In all cases, the primary emphasis remains on the vertical
faces parallel to the picture plane.
receding lines to 1/2, 2/3, or 3/4 of their true lengths.
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CONSTRUCTING PARALINE DRAWINGS
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There are three basic approaches to constructing the entire
class of paraline drawings. When constructing and
presenting a paraline drawing, keep in mind that paraline
views are easiest to understand if vertical lines in space are
also oriented vertically on the drawing surface.
¥ The first is a subtractive approach appropriate for
relatively simple forms. It involves constructing a paraline
view of a transparent rectangular box that encompasses
the entire volume of the subject, and then working in a
subtractive manner to remove material and reveal the
form.
¥ A second approach, appropriate for a composition of
discrete forms, reverses the procedure of the subtractive
approach. It requires drawing a paraline view of the parent
form first, and then adding the subordinate forms.
¥ The third approach is appropriate for irregularly shaped
forms. It begins with a paraline view of a horizontal plane
of the subject or the profile of a vertical section cut. We
can then extrude the shape vertically or extend it back
into the depth of the drawing.
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CIRCLES & FREE-FORM SHAPES
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Any circles oblique to the picture plane appear as ellipses.
To draw such a circle in a paraline drawing, we must first draw
a paraline view of the square that circumscribes the circle.
Then we can use either of two approaches to drawing the
circle within the square.
¥ The first is an approximate method. By dividing the
square into quadrants and drawing diagonals from each
corner to quarter points along the sides of the square, we
can establish eight points along the circumference of the
circle.
¥ The four-center method uses two sets of radii and a
compass or circle template.
¥ From the midpoints of the sides of the square in the
paraline view, we extend perpendiculars until they intersect.
¥ With the four points of intersection as centers and with
radii r1 and r2, we describe two sets of arcs in equal pairs
between the origin points of the perpendiculars.
¥ It is often more convenient to draw a plan oblique rather
than an isometric of a circular or free-form plan because
the plan itself can be used as the base drawing and the
horizontal shapes remain true.
We can use a grid to transfer curvilinear or free-form shapes
from an orthographic view to the paraline view.
¥ First, we construct a grid over a plan or elevation view of
the shape. This grid may either be uniform or correspond
to critical points in the shape. The more complex the shape,
the finer the grid divisions should be.
¥ Then we construct the same grid in the paraline view.
¥ Next, we locate the points of intersection between the grid
and the free-form shape and plot these coordinates in the
paraline view.
¥ Finally, we connect the transferred points in the paraline
view.
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SPATIAL DEPTH CUES
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We can enhance the perceived depth of a paraline drawing
by utilizing a hierarchy of line weights to distinguish
between spatial edges, planar corners, and surface lines.
¥ Spatial edges are the boundaries of a form separated from
the background by some intervening space.
¥ Planar corners are the intersections of two or more planes
that are visible to the eye.
¥ Surface lines are lines that represent an abrupt contrast
in color, tonal value, or material; they do not represent a
change in form.
¥ 3D-modeling programs treat lines as the continuous edges
of polygons. It may therefore be difficult to define this
hierarchy of line weights without first transferring the
graphic image to a two-dimensional environment.
¥ To separate planes in space, to clarify their different
orientations, and especially to distinguish between the
horizontal and the vertical, we can use contrasting
textures and patterns.
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USES OF PARALINE DRAWINGS
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Even though a paraline drawing always presents either
an aerial view or a wormÕs-eye view of a subject, we can
construct a paraline view in any of several ways to
reveal more than the exterior form and configuration
of a design. These techniques allow us to gain visual
access to the interior of a spatial composition or the
hidden portions of a complex construction. We
categorize these techniques into expanded views,
cutaway views, phantom views, and sequential views.
Expanded Views
To develop what we call an expanded or exploded
view, we merely shift portions of a paraline drawing to
new positions in space. The finished drawing appears
to be an explosion frozen at a point in time when the
relationships between the parts of the whole are
most clear.
¥ Expanded views are extremely useful in describing
the details, layering, or sequence of a construction
assembly. Remember that, as with other drawing
types, the larger the scale of a paraline drawing, the
more detail you have to show.
¥ At a larger scale, expanded views can effectively
illustrate vertical relationships in multistory
buildings as well as horizontal connections across
space.
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EXPANDED VIEWS
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¥ The displacement of the parts should be in the order
and direction in which they fit together.
¥ For axial compositions, the expansion occurs either
along the organizing axis or perpendicular to it.
¥ For rectangular compositions, the parts relocate along
or parallel to the principal X-, Y-, and Z-axes.
¥ Indicate the relationships of the parts, to each other
and to the whole, with dotted, dashed, or delicately
drawn lines.
¥ Any overlap between the expanded parts of the
drawing should not conceal significant information.
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CUTAWAY VIEWS
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A cutaway view is a drawing having an outer section or
layer removed to reveal an interior space or an internal
construction. This strategy can also effectively manifest
the relation of an interior to the exterior environment.
¥ The simplest method for creating a cutaway view is to
remove an outer or bounding layer of a composition or
construction.
¥ For example, removing a roof, ceiling, or wall allows us
to look down and see into an interior space. Removing
a floor permits a view up into a space.
¥ We can remove a larger section by slicing through the
heart of a composition. When a composition exhibits
bilateral symmetry, we can make this cut along the
central axis and indicate the footprint or plan view of
the part removed.
¥ In a similar fashion, we can create a cutaway view of a
radially symmetrical composition by slicing through
the center and removing a quadrant or similar pieshaped
portion.
¥ To reveal a more complex composition, the cut may
follow a three-dimensional route. In this case, the
trajectory of the cut should clarify the nature of the
overall form building as well as the organization and
arrangement of interior spaces.
¥ ...
Januszek66