Projection

ProjectionByAltaf Ahmed

By Altaf Ahmed, email: the.nothingness@hotmail

.com

By Altaf Ahmed, email: [email protected]

OVERVIEW

•Definition•Taxonomy•Terms used•Parallel Projection•Perspective Projection


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”.


TAXONOMY Projection

Cavalier

One Point

Two Points

Isometric Three

Points

ObliqueOrthographic

Perspective ProjectionParallel Projection

Di-metric Cabinet

Trimetric

General Axonometric Multi-view


TERMS USED

•View Plane•Point of View•Projector •Centre of Projection•Direction of Projection


Methods of Projection

•Two methods are used to solve the basic problems of pictorial representation;

1. Parallel Projection2. Perspective Projection


PARALLAL PROJECTION •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.




•Types of Parallel Projection

1. Orthographic Projection2. Oblique Projection


Orthographic Projection

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



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


Multi-View Orthographic Projections

•Orthographic projections that show only one side of an object are called multi-view orthographic projections

•When direction of projection is parallel to any principal axis, this produces front, top and side view of an object



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.


•Sub categories of Axonometric orthographic Projections are;

1. Isometric2. Di-metric3. Trimetric

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


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


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


Oblique Projection

•Parallel projections that does not intersect the view plane perpendicularly

•Direction of Projection is perpendicular to view plane


•Special Cases of Oblique Projection1. Cavaliar2. Cabinet

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•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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•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



•Subtypes•One-point•Two-points•Three-points


•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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Projection