With multiview orthographic projections
, up to six
pictures of an object are produced, with each projection plane
parallel to one of the coordinate axes of the object.
The views are positioned relative to each other according to either
of two schemes: first-angle
projection. In each, the appearances of views may be thought of as
onto planes that form a 6-sided box around
Quadrants in descriptive geometry
Gaspard Monge's four quadrants and two
Modern orthographic projection is derived from Gaspard Monge
's descriptive geometry. Monge
defined a reference system of two viewing planes, horizontal
("ground") and vertical V
two planes intersect to partition 3D space into 4 quadrants, which
- I: above H, in front of V
- II: above H, behind V
- III: below H, behind V
- IV: below H, in front of V
These quadrant labels are the same as used in 2D planar geometry,
as seen from infinitely far to the "left", taking H
to be the X
-axis and Y
The 3D object of interest is then placed into either quadrant
(equivalently, the position of the
intersection line between the two planes is shifted), obtaining
- and third-angle
are also mathematically
valid, but their use would result in one view "true" and the other
view "flipped" by 180° through its vertical centerline, which is
too confusing for technical drawings.
Monge's original formulation uses two planes only, and obtains the
top and front views only. The addition of a third plane to show a
(either left or right) is
a modern extension. The terminology of quadrant
is a mild
anachronism, as a modern orthographic projection with three views
corresponds more precisely to an octant of 3D space.
In first-angle projection
, the object is
conceptually located in quadrant I
, i.e. it
floats above and before
the viewing planes, the
planes are opaque
, and each view is
through the object onto the plane furthest
from it. (Mnemonic: an "actor on a stage".) Extending to the
6-sided box, each view of the object is projected in the direction
(sense) of sight of the object, onto the (opaque) interior walls of
the box; that is, each view of the object is drawn on the opposite
side of the box. A two-dimensional representation of the object is
then created by "unfolding" the box, to view all of the
walls. This produces two plan views
and four side view
Image:first angle projecting.png|Image of object in box, with views
of object projected in the direction of sight onto walls using
first-angle projection.Image:first angle unfolding.png|Similar
image showing the box unfolding from around the object.Image:first
angle unfolded.png|Image showing orthographic views located
relative to each other in accordance with first-angle
An example of a multiview orthographic
drawing from a US Patent (1913), showing two views of the same
Third angle projection is used.
In third-angle projection
, the object is
conceptually located in quadrant III, i.e. it lurks below
the viewing planes, the planes are
, and each view is
onto the plane closest to it. (Mnemonic: a
"shark in a tank", esp. that is sunken into the floor.) Using the
6-sided viewing box, each view of the object is projected opposite
to the direction (sense) of sight, onto the (transparent) exterior
walls of the box; that is, each view of the object is drawn on the
same side of the box. The box is then unfolded to view all of its
Here is the construction of third angle projections of the same
object as above. Note that the individual views are the same, just
Image:third angle projecting.pngImage:third angle
unfolding.pngImage:third angle unfolded.png
First-angle projection is as if the object were sitting
the paper and, fromthe "face" (front) view, it
is rolled to the right to show the left side or rolled up to show
its bottom. It is standard throughout Europe (excluding the UK) and
Asia. First-angle projection used to be common in the UK, and may
still be seen on historical design drawings, but has now fallen
into disuse in favour of third-angle projection.
Third-angle is as if the object were a box to be unfolded. If we
unfold the box so that the front view is in the center of the two
arms, then the top view is above it, the bottom view is below it,
the left view is to the left, and the right view is to the right.
It is standard in the United Kingdom (BS 8888:2006 specifies it as
the default projection system), USA, Canada and Australia.
Both first-angle and third-angle projections result in the same 6
views; the difference between them is the arrangement of these
views around the box.
A great deal of confusion has ensued in drafting rooms and
engineering departments when drawings are transferred from one
convention to another. On engineering drawings
, the projection
angle is denoted by an international symbol consisting of a
, respectively for
first-angle (FR) and third-angle (US):
Comparison of the first-angle and
third-angle projections used in France and the U.S.,
The 3D interpretation of the symbol can be deduced by envisioning a
solid truncated cone, standing upright with its large end on the
floor and the small end upward. The top view is therefore two
concentric circles ("donut"). In particular, the fact that the
inner circle is drawn with a solid line instead of dashed
disambiguates this view as the top view, not the bottom view.
- In first-angle projection, the "top" view is pushed
down to the floor, and the "front" view is pushed back to the rear
wall; the intersection line between these two planes is therefore
closest to the large end of the cone, hence the first-angle symbol
shows the cone with its large end open toward the donut.
- In third-angle projection, the "top" view is pulled up
to the ceiling, and the "front" view is pulled forward to the front
wall; the intersection line between the two planes is thus closest
to the small end of the cone, hence the third-angle symbol shows
the cone with its large end away from the donut.
Multiviews without rotation
Orthographic multiview projection is derived from the principles of
produce an image of a specified, imaginary object as viewed from
any direction of space. Orthographic projection is distinguished by
parallel projectors emanating from all points of the imaged object
and which intersect a plane of projection at right angles. Above, a
technique is described that obtains varying views by projecting
images after the object is rotated to a desired position.
Descriptive geometry customarily relies on obtaining various views
by imagining an object to be stationary, and changing the direction
of projection (viewing) in order to obtain the desired view.
See Figure 1
. Using the rotation technique above, note
that no orthographic view is available looking perpendicularly at
any of the inclined surfaces. Suppose a technician desired such a
view to, say, look through a hole to be drilled perpendicularly to
the surface. Such a view might be desired for calculating
clearances or for dimensioning purposes. To obtain this view
without multiple rotations requires the principles of Descriptive
Geometry. The steps below describe the use of these principles in
third angle projection.
Figures one through nine.
- Fig.1: Pictorial of imaginary object that the
technician wishes to image.
- Fig.2: The object is imagined behind a vertical plane
of projection. The angled corner of the plane of projection is
- Fig.3: Projectors emanate parallel from all points of
the object, perpendicular to the plane of projection.
- Fig.4: An image is created thereby.
- Fig.5: A second, horizontal plane of projection is
added, perpendicular to the first.
- Fig.6: Projectors emanate parallel from all points of
the object perpendicular to the second plane of projection.
- Fig.7: An image is created thereby.
- Fig.8: A third plane of projection is added,
perpendicular to the previous two.
- Fig.9: Projectors emanate parallel from all points of
the object perpendicular to the third plane of projection.
Figures ten through seventeen.
- Fig.10: An image is created thereby.
- Fig.11: A fourth plane of projection is added parallel
to the chosen inclined surface, and per force, perpendicular to the
first (Frontal) plane of projection.
- Fig.12: Projectors emanate parallel from all points of
the object perpendicularly from the inclined surface, and per
force, perpendicular to the fourth (Auxiliary) plane of
- Fig.13: An image is created thereby.
- Fig.14-16: The various planes of projection are
unfolded to be planar with the Frontal plane of projection.
- Fig.17: The final appearance of an orthographic
multiview projection and which includes an "Auxiliary view" showing the true shape of an
, or cross-section
, is a view of
a 3-dimensional object from the position of a plane through the
object. A floor plan
is a section viewed
from the top. In such views, the portion of the object in front of
the plane is omitted to reveal what lies beyond. In the case of a
floor plan, the roof and upper portion of the walls may be omitted.
or roof plans are
orthographic projections, but they are not sections as their
viewing plane is outside of the object.
A cross-section is a common method of depicting the internal
arrangement of a 3-dimensional object in two dimensions. It is
often used in technical drawing
and is traditionally crosshatched
style of crosshatching indicates the type of material the section
With computed axial
, computers construct cross-sections from x-ray
Image:Cross section.png|A 3-D view of a beverage-can stove
yellow.Image:Seal_mechanical_compression.png|A 2-D cross-sectional
view of a compression seal.
is a view of a 3-dimensional object
from the position of a horizontal plane beside an object. In other
words, an elevation is a side-view as viewed from the front, back,
left or right.
An elevation is a common method of depicting the external
configuration and detailing of a 3-dimensional object in two
dimensions. Building façades are shown as elevations in architectural drawings
and technical drawings
Elevations are the most common orthographic projection for
conveying the appearance of a building from the exterior. Perspectives
are also commonly used
for this purpose. A building elevation is typically labeled in
relation to the compass direction it faces; the direction from
which a person views it. E.g. the North Elevation of a building is
the side that most closely faces true north on the compass.
Interior elevations are used to show detailing such as millwork
and trim configurations.
In the building industry elevations are a non-perspective view of
the structure. These are drawn to scale so that measurements can be
taken for any aspect necessary. Drawing sets include front, rear
and both side elevations. The elevations specify the composition of
the different facades of the building, including ridge heights, the
positioning of the final fall of the land, exterior finishes, roof
pitches and other architectural details.
Image:Panthéon Soufflot - élevation
principale.png|Principal façade of the Panthéon,
Paris, by Jacques-Germain
is view of a 3-dimensional object from the
position of a horizontal plane through the object. In other words,
a plan is a section
from the top. In such views, the portion of the object in above the
plane is omitted to reveal what lies beyond. In the case of a
, the roof and upper portion of
the walls may be omitted.
Roof plans are orthographic projections, but they are not sections
as their viewing plane is outside of the object.
A plan is a common method of depicting the internal arrangement of
a 3-dimensional object in two dimensions. It is often used in
traditionally crosshatched. The style of crosshatching indicates
the type of material the section passes through.
An auxiliary view
is a view taken from an angle
that is not
one of the primary views. An auxiliary view is
a view at an angle used to give deeper insight into the actual
shape of the object.
Image:Auxiliary_Views_1.PNG|An auxiliary view next to three primary
views. This example image may be incomplete, as the box is missing
in the auxiliary view.Image:Auxiliary_Views_2.PNG|Another example
of an auxiliary view (rather than a primary view from an