Projections
Since our viewing surface is 2D, we must have some way of projecting
3D object onto 2D screen.
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Conceptual Model of the 3D viewing process
3D PROJECTIONS
(Rays converge on eye position)
Perspective
(Rays parallel to view plane)
Parallel
Orthographic
Elevations
Axonometric
Isometric
Oblique
Cavalier
Cabinet
PARALLEL PROJECTION
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All projection lines are parallel to each other and intersects
view plane
z- coordinate is discarded.
Point of intersection is projection of vertex.
preserve relative proportions
Does not produce realistic views.
Connect projected vertices which correspond to connections on
the original object.
PARALLEL PROJECTION(EG)
View
Plane
DOP
PARALLEL PROJECTIONS
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2 principle types:
 orthographic and oblique.
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Orthographic :
 direction of projection = normal (means perpendicular)
to the projection plane or view plane.
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Oblique :
 direction of projection != normal to the projection
plane or view plane. (means not perpendicular)
PARALLEL PROJECTIONS: ORTHOGRAPHIC
AND OBLIQUE
View plane
Orthographic
Oblique
PARALLEL PROJECTIONS
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Orthographic (or orthogonal) projections:
 front elevation, top-elevation and side-elevation.
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In all these projection plane or view plane is normal to
principal axes.
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Useful because angle and distance measurements can be
made...
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However, As only one face of an object is shown, it can be
hard to create a mental image of the object, even when
several view are available.
Parallel Projections
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Orthogonal projections:
AXONOMETRIC PROJECTION
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The front , side and top view of an object resting in its
simple position gives an incomplete idea of the shape
of the object.
In Axonometric projections, view planes are not parallel to
principal axis.
Parallelism of lines is preserved but angles are not.
Isometric Projection
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“ Iso” means “equal” and “metric projection ” means “a
projection to reduced measure”.
An isometric projection is one type of pictorial projection in
which the dimensions of a solid are not only shown in one
view but also their dimensions can be scaled from this
drawing.
OBLIQUE
PROJECTIONS
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It is parallel projection.
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Projection lines are parallel but not normal to the projection
plane.
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Oblique means slanting.
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Projection lines are at an angle to the view plane.
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Let the angle be an angle the projection line makes with the view
plane
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Notice that the view plane normal and direction of projection are
not same.
Cavalier projections
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The direction of projection makes 45° angle with view plane.
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The projection of a line perpendicular to the view plane has the
same length as the line itself.
1
a
1
1
1
Cabinet projections
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The direction of projection makes angle of arc tan 63.4° angle with
view plane.
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For this angle, line perpendicular to the viewing surface are
projected at one – half their actual length.
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Cabinet projections appears more realistic than cavalier projection
bcoz of this reduction in the length of perpendiculars
2
a
1
1/2
PERSPECTIVE PROJECTION
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Projection lines are intersecting the view plane and
converge at a single point called centre of projection or
projection reference point.
Projection lines are not parallel
Perspective projection produces realistic views
Does not preserves relative proportions.
The object positions are transformed to the view plane along
these converged projection lines and projected view of an
object is determined by calculating the intersection of
converged projection lines with view plane.
PERSPECTIVE PROJECTION
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Vanishing Point : the perspective projection of any set of
parallel lines that are not parallel to the projection plane
converge to a vanishing point.
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The vanishing point for any set of lines that are parallel to
one of three principal axes of an object is referred to as a
principal vanishing point or axis vanishing point
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Category of perspective projection
1 point perspective projection
2 point perspective projection
3 point perspective projection
1.
2.
3.
ONE POINT PERSPECTIVE PROJECTION
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Based on single vanishing point.
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Object is placed so that one of surfaces is parallel to the plane of
projection.
TWO POINT PERSPECTIVE PROJECTION
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Based on two vanishing points.
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This is achieved by rotating object along y-axis so that lines along
that axis remain parallel to viewing plane, but those along the two
other axes have vanishing points
THREE POINT PERSPECTIVE PROJECTION
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Based on three vanishing points.
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This achieved by positioning abject so that none of its axes are
parallel to plane of projection
PERSPECTIVE
VS.
PARALLEL
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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
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Parallel projection
+ Good for exact measurements
+ Parallel lines remain parallel
– Angles are not (in general) preserved
– Less realistic looking
VIEWING
PARAMETERS
VIEWING
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PARAMETERS
We can view the object from the top, or the side or from
the behind. Therefore , it is necessary to choose a
particular view for a picture by defining view plane.
View plane : it is film in the camera ..on which we want
to take photograph.
View reference point: this point is the center of our
viewing coordinate system.
View plane normal vector: this normal vector is the
direction perpendicular to the view plane.
View distance: distance between the view plane and the
view reference point.
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It is possible to obtain the different views by rotating the
camera about the view plane normal vector and keeping
view reference point and direction of N vector fixed.
view-up vector V :Rotation of camera or view plane is
specified by view-up vector V
3D Clipping ( clipping against volume) Cube
Cohen – Sutherland clipping algo readily extend to 3D.
 Cohen- Sutherland algo uses two extra bit in out code for
incorporating z<zmin and z > zmax regions.
 We to use outcode of 6 –bit instead of 4 – bit
Bit 1 = if end point is to the left of the volume.
Bit 2 = if end point is to the right of the volume.
Bit 3 = if end point is to the bellow of the volume.
Bit 4 = if end point is to the above of the volume.
Bit 5 = if end point is to the front of the volume.
Bit 6 = if end point is to the back of the volume.
Otherwise bit is set to zero
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