1. Projection
By
Altaf Ahmed
By Altaf Ahmed, email:
the.nothingness@hotmail.co
m

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OVERVIEW
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Definition
Taxonomy
Terms used
Parallel Projection
Perspective Projection

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Projection
• Theoretically projection can b defined as”The
mapping of a 3-D object having points P(x,y,z)
onto its image P’(x’,y’,z’) in the projection plane
or view plane, which constitutes the display
surface”.

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TAXONOMY
Projection
Perspective
Projection
Parallel Projection
Oblique
Orthographic
Axonometric
Multi-view
One Point
General
Two
Points
Isometric
Di-metric
Trimetric
Cabinet
Cavalier
Three
Points

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TERMS USED
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View Plane
Point of View
Projector
Centre of Projection
Direction of Projection

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Methods of Projection
• Two methods are used to solve the basic
problems of pictorial representation;
1. Parallel Projection
2. Perspective Projection

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PARALLAL PROJECTION
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In parallel projection
Direction of Projection is same for all points
All projectors are parallel to each others
Used by Drafter and Engineers to create working
drawings of an object which preserves its scale
and shape.

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• Types of Parallel Projection
1. Orthographic Projection
2. Oblique Projection

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Orthographic Projection
• When the Direction of Projection is
perpendicular ( at 90◦) to the view plane, then
the projection is Orthographic Projection.

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Types of Orthographic Projections
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Multi-View Orthographic Projection
Axonometric orthographic projections

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Multi-View Orthographic Projections
• Orthographic projections that show only one
side of an object are called multiview orthographic projections
• When direction of projection is parallel to any
principal axis, this produces front, top and side
view of an object

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Axonometric Projection
• Orthographic projections that show more than 1
side of an object are
called axonometric orthographic projections
• In axonometric orthographic projections, the
direction of projection is not parallel to any of
the principal axis.

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Continued…..
• Sub categories of Axonometric orthographic
Projections are;
1. Isometric
2. Di-metric
3. Trimetric

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Continued…..
• Isometric Projection: The direction of projection
makes equal angles with all of the principal axis.

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Continued…..
• Di-metric Projection: The direction of projection
makes equal angles with exactly two of the
principal axis.

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Continued…..
• Trimetric Projection: The direction of Projection
makes unequal angles with the principal axis.

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Oblique Projection
• Parallel projections that does not intersect the
view plane perpendicularly
• Direction of Projection is perpendicular to view
plane

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Continued…..
• Special Cases of Oblique Projection
1. Cavaliar
2. Cabinet

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Continued…..
• Cavalier: the direction of projection is chosen so
that there is no fore-shortening of lines
perpendicular to the xy-lane
• It is achived by projecting the projectors at an
angle of 45◦

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Continued…..
• Cabinet: the direction of projection is chosen so
that the line perpendicular to the xy-plane are
fore-shortening by half of their length.
• For cabinet projection the angle is kept 63.40◦

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PERSPECTIVE PROJECTION
• Projectors are not projected perpendicular to the
view plane
• Objects closer to view looks larger
• Parallel lines appear to converge at a single point

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Subtypes
One-point
Two-points
Three-points

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• One point : This perspective projection occurs
when the projection plane is perpendicular to
one of the principle axis
• Two points: this perspective projection occurs
when the projection plane intersects exactly two
of the principal axis.
• Three points: this perspective projection occurs
when the projection plane intersect all the three
principal axes, x,y and z axes.

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