Addis Ababa University
Technology Faculty
Mechanical Engineering Department
Theory of Projection
By Beruk Fekadu
PROJECTION THEORY
How to present a three dimension
object on a flat surface (plane, paper)?
A projection is a correct representation of an object
on a two dimensional plane OR The projection
theory is used to graphically represent 3-D objects
on 2-D media (paper, computer screen).
Four elements of projection:
• The plane of projection
• The line of sight (projecting line)
• The point of sight
• The object
Line of sight is an imaginary ray of light between an
observer’s eye and an object.
There are 2 types of LOS : parallel and converge
Parallel projection Perspective projection
Line of sight
Line of sight
Plane of projection is an imaginary flat plane which
the image is created.
The image is produced by connecting the points where
the LOS pierce the projection plane.
Parallel projection Perspective projection
Plane of projection Object Plane of projection
Point of sight
PROJECTION METHOD
Perspective Parallel
One Two Three Oblique Orthographic
point point point
cabinet Cavalier Others
Axonometric Multiview
Kinds of projections (the kinds of
projections are connected with the
relationship between the four
elements of projection):
Perspective Projections.
• perspective projection – the lines of sight converge to a point
which is at finite distance from the plane of projection.
• Defined by projection plane and centre of projection.
• Visual effect is termed perspective foreshortening.
– The size of the projection of an object varies inversely with
distance from the centre of projection.
– Similar to a camera - Looks realistic !
• Not useful for metric information
– Parallel lines do not in general project as parallel.
– Angles only preserved on faces parallel to the projection plane.
– Distances not preserved
Perspective:
The line of sight is cone-shaped - which makes objects far
away appear smaller to our view. Objects are not “true
shape and size”.
The first ever painting
(Trinity with the Virgin, St.
John and Donors) done in
perspective by Masaccio, in
1427.
Perspective Projections
• A set of lines not parallel
to the projection plane
converge at a vanishing
point.
– Can be thought of in 3D
as the projection of a
point at infinity.
– Homogeneous
coordinate is 0 (x,y,0)
Perspective Projections
• Lines parallel to a principal axis converge at an axis
vanishing point.
– Categorized according to the number of such points
– Corresponds to the number of axes cut by the
projection plane. y
y
x
z x
z Projection plane
1-Point Projection
Projection plane cuts 1
axis only.
• One principle axis cut by
projection plane
• One axis vanishing point
1-Point Perspective
A painting (The
Piazza of St. Mark,
Venice) done by
Canaletto in 1735-
45 in one-point
perspective
2-Point Perspective
z x
Projection plane
• Two principle axes cut by projection plane
• Two axis vanishing points
2-Point Perspective
Painting in two point
perspective by
Edward Hopper
The Mansard Roof
1923 (240 Kb);
Watercolor on paper,
13 3/4 x 19 inches;
The Brooklyn
Museum, New York
3-Point Perspective
Generally held to add little beyond 2-point
perspective.
• Three principle axes cut by
projection plane
• Three axis vanishing points
A painting (City Night,
1926) by Georgia
O'Keefe, that is
approximately in three-
point perspective. y
z x
Projection plane
Disadvantage of Perspective Projection
Perspective projection is not used by
engineer for manufacturing of parts,
because
1) It is difficult to create.
2) It does not reveal exact
shape and size.
Width is distorted
Parallel Projections
• Specified by a direction to the centre of projection,
rather than a point.
– Centre of projection at infinity.
• Orthographic-the lines of sight are parallel to each
other and perpendicular to the plane of projection.
• Oblique-the lines of sight are parallel to each other
but are oblique to the plane of projection.
Parallel:
The line of sight is always parallel regardless of how far
away the object is from our view. This allows surfaces to
be drawn “true shape and size”.
Orthographic Projection Oblique projection
MEANING
Orthographic projection is a parallel projection technique
in which the parallel lines of sight are perpendicular to the
projection plane
Object views from top
1
2
1 5 2 3 4
5
3
Projection plane
ORTHOGRAPHIC VIEW
Orthographic view depends on relative position of the object
to the line of sight.
Rotate
Two dimensions of an
object is shown. Tilt
More than one view is needed
to represent the object.
Multiview drawing
Three dimensions of an object is shown.
Axonometric drawing
ORTHOGRAPHIC VIEW
NOTES
Orthographic projection technique can produce either
1. Multiview drawing
that each view show an object in two dimensions.
2. Axonometric drawing
that show all three dimensions of an object in one view.
Both drawing types are used in technical drawing for
communication.
Axonometric (Isometric) Drawing
Advantage Easy to understand
Disadvantage Shape and angle distortion
Example Distortions of shape and size in isometric drawing
Circular hole
becomes ellipse.
Right angle becomes obtuse angle.
Multiview Drawing
Advantage It represents accurate shape and size.
Disadvantage Require practice in writing and reading.
Example Multiviews drawing (2-view drawing)
