Transform 3-D objects on to a 2-D plane using
projections
2 types of projections
Perspective
Parallel
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PROJECTIONS
PARALLEL
(parallel projectors) PERSPECTIVE
(converging projectors)
One point
(one principal
vanishing point)
Two point
(Two principal
vanishing point)
Three point
(Three principal
vanishing point)
Orthographic
(projectors perpendicular
to view plane)
Oblique
(projectors not perpendicular to
view plane)
General
Cavalier
Cabinet
Multiview
(view plane parallel
to principal planes)
Axonometric
(view plane not parallel to
principal planes)
Isometric Dimetric Trimetric
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Parallel Projection
Discards z-coordinate and parallel
lines from each vertex
Specify a direction of projection
instead of center of projection
Project points on the object
surface along parallel lines onto
the display plane.
Parallel lines are still parallel after
projection
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1. Orthographic projection :
If the direction of projection
is perpendicular to the
projection plane then it is an
orthographic projection.
Parallel Projection: Types
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2. Oblique projection : If the
direction of projection is not
perpendicular to the projection
plane then it is an oblique
projection.
Parallel Projection: Types
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Cavalier
The Cavalier projection
makes 45° angle with the
projection plane.
The projection of a line
perpendicular to the view
plane has the same length as
the line itself in Cavalier
projection.
Oblique Projection: Types
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Cabinet
The Cabinet projection makes
63.4° angle with the
projection plane.
In Cabinet projection, lines
perpendicular to the viewing
surface are projected at ½
their actual length.
Oblique Projection: Types
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Perspective Projection
Project points to the display plane along converging
paths.
This is the way that our eyes and a camera lens form
images and so the displays are more realistic.
Parallel lines appear to converge to a distant point in
the background.
Distant objects appear smaller than objects closer to
the viewing position.
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Types of Perspective Projection
One point perspective projection is simple to draw.
Two point perspective projection gives better
impression of depth.
Three point perspective projection is most difficult
to draw.
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Types of Perspective Projection
Perspective Projection
When we do 3-D graphics, we think of the
screen as a 2-D window onto the 3-D world:
How tall should
this bunny be?
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Perspective Projection
The geometry of the situation is that of similar
triangles. View from above:
d
X P (x, y, z)
Z
View
plane
(0,0,0) x’ = ?
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Perspective vs. Parallel
Projection
Perspective projection
Size varies inversely with distance - looks realistic
Distance and angles are not (in general) preserved
Parallel lines do not (in general) remain parallel
Parallel projection
Good for exact measurements
Parallel lines remain parallel
Angles are not (in general) preserved
Less realistic looking
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Depth Cueing