The document discusses isometric drawings and projections, focusing on how to depict three-dimensional objects, particularly cubes, in a 2D format. It explains the technique of creating isometric drawings using box construction, emphasizing the importance of maintaining true dimensions and the angles of isometric lines. Additionally, it covers how to represent circles and ellipses in isometric views and includes a bibliography for further reference.

1. Isometric
drawings
(perspectives)
Working document
Linguistic review 29-09-07

2. Isometric projections
A cube shown with this type of
projection pivots 45º to show two
faces on the projection plane
instead of a single face.
It is then tilted frontward or
backward, allowing three faces to
be observed.

3. Isometric projections
A cube shown with this type of
projection pivots 45º to show two
faces on the projection plane
instead of a single face.
It is then tilted frontward or
backward, allowing three faces to
be observed.

4. Isometric projections
Three views of a cube in
multi-view orthogonal
projection.
Top view
Front view Right side view

5. Isometric projections
45º
We pivot the cube
45º to show two of
its faces.
Top view
Front view Right side view

6. The cube is lifted
and pivots around
point O.
Isometric projections
The cube turns
around point O until
the AB diagonal
becomes horizontal.
O
A
B

7. Isometric projections
This front view shows
the isometric
projection of the cube
in its new position.
True
dimensions
Because the cube is tilted,
most of the dimensions of its
isometric projection are about
80% of their true dimensions.

8. Isometric projections
This front view shows
the isometric
projection of the cube
in its new position.
True
dimensions
Because the cube is tilted,
most of the dimensions of its
isometric projection are about
80% of their true dimensions.

9. Isometric projections
All lines parallel to axes
1, 2 and 3 are isometric
lines.
2 3
1
120º
The isometric lines are
angled at 30º.
The lines not parallel to
axes 1, 2 and 3 are
non-isometric lines.
The sides of the cube and
all planes parallel to them
are isometric planes.
Axes 1, 2 and 3 form
120º angles between
one another.
The projection is isometric
(equal measures) because
the height of axis 1, the
length of axis 2 and the width
of axis 3 are all proportionally
reduced.
Characteristics of isometric projections
Characteristics of isometric projections

10. All lines parallel to axes
1, 2 and 3 are isometric
lines.
2 3
1
120º
The isometric lines are
angled at 30º.
The lines not parallel to
axes 1, 2 and 3 are
non-isometric lines.
The sides of the cube and
all planes parallel to them
are isometric planes.
Axes 1, 2 and 3 form
120º angles between
one another.
The projection is isometric
(equal measures) because
the height of axis 1, the length
of axis 2 and the width of axis
3 are all proportionally
reduced.
Characteristics of isometric projections
Characteristics of isometric projections
Isometric projections

11. Isometric drawing
20
20
50
10
8
14
28
35
We will illustrate the main stages of
isometric drawing of the object shown
above in multi-view.
We will use a method called box
construction.

12. 20
20
50
10
8
14
28
35
We will illustrate the main stages of
isometric drawing of the object shown
above in multi-view.
We will use a method called box
construction.
To create the box, use construction lines to
outline an isometric box as large as the
overall object to be drawn.
The vertical axis is equal to the real height.
The two other axes, drawn at 30° to
horizontal, correspond to the actual width
and length of the object.
Isometric drawing

13. 20
20
50
10
8
14
28
35
We will illustrate the main stages of
isometric drawing of the object shown
above in multi-view.
We will use a method called box
construction.
To create the box, use construction lines to
outline an isometric box as large as the
overall object to be drawn.
The vertical axis is equal to the real height.
The two other axes, drawn at 30° to
horizontal, correspond to the actual width
and length of the object.
Isometric drawing

14. Isometric drawing
The object is drawn by
removing volumes from the box.
A 30º- 60º set square is used to
trace the isometric lines.
The box is an isometric drawing
as large as the overall object to
be shown. Its lines are drawn
very faintly.
Measurements are reported on
the isometric axes, or on lines
parallel to these axes.

15. Isometric drawing
The object is drawn by
removing volumes from the box.
A 30º- 60º set square is used to
trace the isometric lines.
The box is an isometric drawing
as large as the overall object to
be shown. Its lines are drawn
very faintly.
Measurements are reported on
the isometric axes, or on lines
parallel to these axes.

16. Isometric drawing
STAGE 1 STAGE 2 STAGE 3
Sketch the box.
STAGES OF DRAWING IN ISOMETRIC PERSPECTIVE
Measure on the
axes and trace the
details in
construction lines.
Carry out the final
layout.

17. Isometric drawing
STAGE 1 STAGE 2 STAGE 3
Sketch the box.
STAGES OF DRAWING IN ISOMETRIC PERSPECTIVE
Measure on the
axes and trace the
details in
construction lines.
Carry out the final
layout.

18. Non-isometric (oblique) lines
and surfaces are not true to
size in isometric perspective.
Isometric drawing
How to draw non-isometric lines and surfaces
Dimensions of inclined lines and
surfaces are determined by using their
coordinates which must be located on
isometric lines.
A
B
D
C
C
D
A
B

19. Isometric drawing
Non-isometric (oblique) lines
and surfaces are not true to
size in isometric perspective.
How to draw non-isometric lines and surfaces
Dimensions of inclined lines and
surfaces are determined by using their
coordinates which must be located on
isometric lines.
A
B
D
C
C
D
A
B

20. Isometric drawing
Grids and isometric drawing
A grid which includes all three isometric
axes may be used to draw isometric
perspectives.

21. Isometric drawing
Grids and isometric drawing
A grid which includes all three isometric
axes may be used to draw isometric
perspectives.

22. Isometric drawing
Showing circles and arcs of circles in isometrics
Circles and arcs of circles on isometric
planes are shown in isometric projection
using ellipses within an isometric square.
The sides of the square are equal to the
diameter of the circle and each side of the
circle touches the square.
To draw a circle in isometric perspective
on the computer, use a modified circle
inserted into an isometric square.
To draw it as a sketch or with a compass,
draw four arcs of the circle in an isometric
square.

23. Isometric drawing
How to draw an ellipse composed of four arcs using a compass
1- Trace an isometric square.
2- Find the center of the square
using diagonals, then trace the
axis lines.

24. Isometric drawing
How to draw an ellipse composed of four arcs using a compass
1- Trace an isometric square.
2- Find the center of the square
using diagonals, then trace the
axis lines.
3- Finally, trace the median lines.

25. Isometric drawing
How to draw an ellipse composed of four arcs using a compass
3- Finally, trace the median lines.
The meeting point of the medians
shows the center of the four arcs of
the circle.
1- Trace an isometric square.
2- Find the center of the square
using diagonals, then trace the
axis lines.

26. Isometric drawing
ORTHOGRAPHIC MULTI-VIEW PROJECTION ISOMETRIC PROJECTION
«Construction box»
How to draw an object containing rounded parts

27. STIRLING, Norman. « Éléments de dessin industriel », Montréal, HRW,
1979, 372 p.
JENSEN, C.H. « Dessin industriel », Montréal, McGraw-Hill, 1972, 752 p.
GIESECKE, Frederick E., MITCHELL, Alva, SPENCER, Henry Cecil, HILL,
Ivan Leroy, GYGDON, John Thomas et NGUYEN, Dinh N. « Dessin
technique », Montréal, Éditions du Renouveau Pédagogique inc., 1982, 769
p
Bibliography