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Design and Communication
Graphics
Axonometric Projection
Table of Contents
Introduction
Placing the Axonometric Plane
Exploring the Axonometric
Plane
Positioning the Axonometric
Plane
Isometric Projection
Deriving Orthographic Views
What is Axonometric Projection?
• Axonometric Projection is a parallel projection
technique used to create a pictorial drawing of
an object by projecting that object onto a plane
• The plane of projection is called the axonometric
plane
• When the projectors are drawn perpendicular to
the axonometric plane, axonometric projection
becomes a form of orthographic projection
• In axonometric projection, the spectator is
located at an infinite distance from the
axonometric plane
Parallel Projection onto a Plane
Placing the Axonometric Plane
• The axonometric plane is an oblique plane
which is inclined to the horizontal, vertical
and end vertical planes
• It extends to infinity
• It intersects the three planes of reference
to form a triangle
• This triangle is called the trace triangle
Placing the Axonometric Plane
Exploring the Axonometric Plane
the trace triangle
the axonometric plane
is infinite in size
the three planes of
reference
The Trace Triangle
The three
traces
form thebetween
sides ofthe
theaxonometric
trace triangleplane and the
lines of
intersection
The
axonometric
plane
represented
by of
this
triangle plane
planes
of reference
giveisthe
three traces
thetrace
axonometric
another vertical trace
the vertical trace
the horizontal trace
Viewing the Axonometric Plane
The viewing direction is
always at right angles to
the axonometric plane
Edge view of
Axonometric
Plane
Axonometric Plane
Viewing the Axonometric Plane
the trace triangle is seen as a true shape
and
the traces appear as true lengths
true lengths
true shape
X, Y and Z axes
Y
The X axis is the line of
intersection between the
vertical plane and the
horizontal plane
The Y axis is the line of
intersection between the
vertical plane and the end
vertical plane
The Z axis is the line of
intersection between the
end vertical plane and the
horizontal plane
Z
The origin is the point of
intersection of the 3 planes
X
X, Y and Z axes
The XY plane is the vertical plane
Y
The YZ plane is the end vertical plane
The XZ plane is the horizontal plane
The Y axis is always vertical
X
Z
The VP and EVP may be interchanged
The X and Z axes will be interchanged accordingly
Z
X
X, Y and Z axes
In axonometric projection the X, Y and Z axes
are projected onto the axonometric plane
Y
The vertices of the trace
triangle lie on the axes
Z
X
Positioning the Axonometric Plane
Changing distances D, D1 and D2 along
the axes determines the type of projection
Y
D2
There are 3 types of projection
 Isometric
 Dimetric
 Trimetric
Z
X
Positioning the Axonometric Plane
Y
Z
C°
NOTE
Changing these angles will
also determine different types
of Axonometric Planes.
X
Further Exploring the Axonometric Plane
Further Exploring the Axonometric Plane
When the planes of referenceEnd
areVertical
sectioned by the axonometricPlane
plane, 3 triangular lamina remain
Y
Vertical
Plane
•Vertical Plane
•Horizontal Plane
•End Vertical Plane
X
Z
Question:
What is known about these triangular
planes on the reference planes?
Horizontal
Plane
Further Exploring the Axonometric Plane
What is known about the remaining triangular sections of
the planes of reference?
the trace is seen as
a true length
the true angle at
the origin is 90o
triangular
plane on the
Vertical Plane
Note:
This applies to all 3
triangular sections
Isometric Projection
Types of Axonometric Projection
Axonometric projections are classified according to how
the 3 principal axes are inclined to the axonometric plane
There are 3 types of projection:
– Isometric Projection
– Dimetric Projection
– Trimetric Projection

In isometric projection, the 3 principal axes are
equally inclined to the axonometric plane

In dimetric projection, two of the axes are equally
inclined to the axonometric plane

In trimetric projection, all three axes are inclined at
different angles to the axonometric plane
Isometric Projection
Y
• all 3 distances are equal
D2
In Isometric Projection:
• all 3 angles between the
axes are equal
• the trace triangle is
equilateral
120°
Z
X
Isometric Projection
What is known about the triangular planes behind
the reference planes?
the trace is a
true length
Right-angled triangle
The triangle has 2
equal sides and is
therefore isosceles
Deriving the Orthographic Views
If this triangular plane is contained
on the vertical plane, an elevation
can be projected onto it
Vertical Plane
This triangular vertical
plane is inclined behind
the axonometric plane
and a true shape of the
triangle and elevation
cannot be seen
Question:
How can a True Shape of the
Triangle be located?
Elevation of a
block
Deriving the Orthographic Views
The triangular planes could be rotated about the traces
onto the axonometric plane.
Deriving the Orthographic Views
What would the problem be with projecting this
view onto the Axonometric Plane?
If the block is projected back
onto the axonometric plane
in this position it will be
drawn upside-down
The position of the
developed planes will need
to change to view the block
from the front
Deriving the Orthographic Views
If the planes are rotated (hinged) in the other direction a front
view could obtained
Deriving the Orthographic Views
A true shape of each of the
reference planes may be located
The orthographic views may
be drawn on them
Horizontal
Plane
Setting up the Orthographic Views
What size is this Axonometric Plane?
Step 1: Draw the axes
Y
In isometric projection the axes are
inclined at 30° to the horizontal in order
to produce the 120° angle between them
Step 2: Construct the axonometric
plane
O
The size of the axonometric
plane does not matter
Size of Plane
Z
X
Setting up the Orthographic Views
Step 3: Rotate the triangular vertical plane to see true shape
The triangle is rotated about the vertical trace; therefore
the lines of rabatment are perpendicular to this trace
Y
Y
A semi-circle
is constructed
to locate the
90° angle
O
O
Z
X
X
Setting up the Orthographic Views
What is known about this triangle?
Y
Section of
vertical plane
90° angle
Y
Isosceles triangle
O
45° angle
O
Z
X
X
Worksheet 1 – Setting up Views
A set of isometric axes is given. The horizontal trace AB of the
axonometric plane ABC is also shown.
(i)
Determine the traces of the axonometric plane ABC.
(ii)
Develop each of the reference planes.
(iii)
Index all views.
Worksheet 1 – Setting up Views
Y
Y
Y
O
O
X
Z
O
Z
X
O
Z
Horizontal Plane
x
Worksheet 2 – Child’s Playhouse
A child’s playhouse is shown in the
photograph across. The elevation and end
elevation of the house is also included.
Draw the isometric projection of the house
having axes inclined as shown.
40
50
120°
20
20
20
END ELEVATION
15
25
10
ELEVATION
20
10
Worksheet 2 – Child’s Playhouse
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Worksheet 2 – Child’s Playhouse
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Worksheet 2 – Child’s Playhouse
Worksheet 3 – Litter Bin
10
25
10
Shown in the photograph is a litter bin, also
included is the Elevation and Plan of the
litter bin.
10
70
120°
ELEVATION
60
Draw the isometric projection of the bin
having axes inclined as shown.
65
PLAN
Worksheet 3 – Litter Bin
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Worksheet 3 – Litter Bin
Dimetric Projection
Dimetric Projection
What if the viewing position is changed?
Dimetric Projection
The viewing position of the
planes has been lowered
The apparent angles between the
reference planes have changed
Y
The Y axis has remained vertical
and
The apparent angles between the
Y axis and the X and Z axes have
reduced
Z
Two of the angles have remained
equalThis is Dimetric Projection
X
Dimetric Projection
The viewing position may be lowered or raised. The position of the
axonometric plane will rotate so that it remains perpendicular to the viewing
direction
Dimetric Projection
Y
As the plane rotates the
traces of the
axonometric plane
change, producing an
isosceles triangle
Equal
Two of the apparent
angles between the
axes remain equal at
all times
X
Traces
Equal
Z
Dimetric Projection
Observing the Traces of
Axonometric Planes
Y
If the Y axis is extended to
intersect the trace, the angle
formed is 90°
In turn, if the X and Z axes
are extended the angle
formed is also 90°
Perpendicular
Why is this so?
X
Z
Perpendicular
Dimetric Projection
Dimetric Projection
Vertical Plane
The Z axis is the line of
intersection between two
reference planes
Y
The Z axis is perpendicular
to the Vertical Plane
Perpendicular
The Vertical Plane contains
the vertical trace of the
axonometric plane, therefore
the Z axis must be
perpendicular to this trace
Z axis
X
Z
Worksheet 4 - Dimetric Projection
As set of dimetric axes is given as well as the horizontal trace AB of the
axonometric plane ABC.
(i)
Determine the traces of the axonometric plane ABC
(ii)
Develop each of the reference planes.
(iii)
Index all views.
Worksheet 4
C
C
Y
C
O
O
B
B
O
A
X
O
A
B
Z
B
Worksheet 5 - Dimetric Projection
A photograph of a measuring tape is shown.
The elevation, plan and end elevation are
also given.
Draw the dimetric projection of the measuring
tape having axes inclined as shown.
Y
15
40
25
15
ELEVATION
35
END-ELEVATION
80
PLAN
25
X
Z
150°
Worksheet 5 - Dimetric Projection
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Worksheet 5 - Dimetric Projection
3
4
5
2
6
4
3
1
5
2
7
6
1
7
1
2
3
4
5
6
7
Worksheet 6 - Dimetric Projection
A photograph of an apartment intercom is
shown with the elevation, plan and end
elevation given.
Draw the dimetric projection of the intercom
having axes inclined as shown.
15
15
10
60
15
Y
Z
ELEVATION
35
140°
20
X
PLAN
Worksheet 6 - Dimetric Projection
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Worksheet 6 - Dimetric Projection
Y
4
5
3
6
2
7
5
4
1
3
8
12
2
9
11
6
7
10
1
8
12
9
11
X
10
Z
7
6,8
5,9
4,10
3,11
2,12
1
Trimetric Projection
Trimetric Projection
What if the viewing position is changed such that none of the
apparent angles are equal?
Trimetric Projection
Trimetric Projection
There are numerous positions
where the apparent angles
between the reference planes
appear unequal.
Y
The Y axis has remained vertical
and
The apparent angles between the
Y axis and the X and Z axes are
unequal.
In this case all three angle are
unequalThis is Trimetric Projection
Z
X
Trimetric Projection
As the viewing position is changed, the position of the axonometric plane
rotates perpendicular to the viewing position to produce a scalene trace triangle
Trimetric Projection
As the plane rotates the
traces of the
axonometric plane
change, producing an
scalene triangle
The apparent angles
between the reference
planes are all unequal.
Y
X
Z
Worksheet 7 - Trimetric Projection
As set of Trimetric Axes are given.
(i) Determine the traces of the Axonometric Plane ABC
(ii) Develop each of the Reference Planes.
(iii) Index all views.
Worksheet 7 - Trimetric Projection
C
C
Edge view of
End VP
Y
C
Edge View
of HP
Edge View
of HP
o
o
o
A
B
B
A
Z
X
o
Trace is constructed
perpendicular to Y-Axis
A
B
Edge view of VP
Worksheet 8 - Trimetric Projection
Y
15
X
10
ELEVATION
A photograph of a Disco Ball is shown with
the Elevation and Plan over.
Draw the trimetric projection of the Disco
Ball having axes inclined as shown.
PLAN
30
Z
Worksheet 8 - Trimetric Projection
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Worksheet 8 - Trimetric Projection
6,8
Centre of Sphere
7
5,9
4,10
Sphere is a sphere in
all views
3,11
1 2,12
6
5
7
4
8
3
9
2
10
1
12
11
Worksheet 9 - Trimetric Projection
35
Y
30
Shown is photograph of news reporters
microphone. The Elevation and Plan of the
microphone is shown over.
X
70
Z
ELEVATION
70
Draw the trimetric projection of the
Microphone having axes inclined as
shown.
70
PLAN
Worksheet 9 - Trimetric Projection
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Worksheet 9 - Trimetric Projection
1 2
12
3
4
5
11
10
6
9 8 7