GL2:1
Engineering Communications GL2
Geometric modelling
Projection Systems
• Lecture presentations available on WWW:
http://www.mame.mu.oz.au/~mcg/EngCom
GL2:2
A graphic is a representation
on a 2-D surface of a 3-D scene
• An artist may attempt to
create a ‘realistic’ image.
• Note the use of
perspective.
• In fact, there are
distortions in this
picture, and it does not
create the same
projection on the retina
as a real scene would.
Meaning may be communicated
better by deliberate distortion
GL2:3
GL2:4
In engineering graphics:
• a variety of types of distorted images
are available to communicate meaning
• strict rules apply to the construction and
interpretation of these images
• a universal language of graphic
communication is thus achieved
GL2:5
2-D projection
View point
3-D object
Projection
rays
Perspective
projection
Projection plane
Engineering graphics are obtained by projection
from the 3-D object to the viewing surface (the
projection plane)
Types of
projection
• Perspective projection is
rarely used in manual
drawing
• Rather, we us a variety of
orthographic projections,
for which the projection
rays are parallel
GL2:6
GL2:7
View
point
at 
2-D projection
Parallel
projection
rays
3-D object
Projection plane
In orthographic projection, the projection
rays are parallel (view point at infinity)
Perspective projection is useful for
‘non technical’ communications
GL2:8
Perspective renderings for marketing, etc. are readily
obtained with computer-aided drawing (CAD) systems
Projection techniques
Bertoline, et al. Fig. 9.2
Orthogonal (multiview)
Oblique
Axonometric
Perspective
GL2:9
GL2:10
Categories of orthographic projection
Orthographic projection
( Parallel projectors)
Orthogonal
Axonometric
Oblique
Projectors
Normal to
projection plane
Normal to
projection plane
Inclined to
projection plane
Principal
plane of
object
Parallel to
projection plane
Inclined to
projection plane
Parallel to
projection plane
Third-angle orthogonal projection
Top view
GL2:11
Top horizontal plane
Glass projection box
First quadrant
Third quadrant
Left
side
view
Left profile plane
Front
vertical
plane
Front view
GL2:12
Third-angle orthogonal projection
horizontal plane
horizontal plane
depth
vertical
plane
depth
left
profile
plane
left
side
view
depth behind
vertical plane
depth behind
vertical plane
width
height below
horizontal plane
height
left profile plane
vertical plane
top
(plan
)
view
fron
t
view
GL2:13
Axonometric projection
• Lines of sight perpendicular to projection plane
• Principal axes all inclined to projection plane
TRIMETRIC
C
B
y
DIMETRIC
C
C
x
Example:
A=120º B=130º C=110º
x:y:z = 1 : 0.808 : 0.938
A
B
A
z
ISOMETRIC
z
y
B
x
Example:
A=C=131.5º B=97º
x : y : z = 0.5 : 1 : 1
A
y
z
x
Always:
A = B = C = 120º
x:y:z=1:1:1
GL2:14
Z
A
Isometric projection
isometric projection
B
projection plane
0.816

b
C
X
A = B = C = 120°
 = b = 30°
Y
Scale ratios = (2/3) = 0.816
X:Y:Z=1:1:1
For an isometric drawing, scale = FS on each axis
GL2:15
Oblique projection
Full scale

Scale = cot
Full scale
Principal object face parallel to projection plane
GL2:16
Varieties of oblique projection
Cavalier
Cabinet
General
Isometric sketch
GL2:17
width
Top view
height
Set square
T-square
Side view
Front view
GL2:18
Projections of a cube compared ...
Oblique
(Cabinet)
Full scale
Isometric
45º
Full scale
60º 30º
30º
semi-minor axis = (1/2)
semi-major axis = (3/2)
radius = 1
GL2:19
Introduction to
Cartesio
software
(download from
EngCom homepage)
GL2:20
Follow up
• Read Bertoline:
–§
–§
–§
–§
4.5: Introduction to Projections
8.1: Projection Theory
8.2: Multiview Projection Planes
8.3:Advantages of Multiview Drawings
• Do problems from Bertoline:
– Probs 4.2(6)(47), 4.3(2)(6)
• Check the EngCom web site