Parallel Projection

Parallel Projection

• Basic Principles: –

The parallel projection used  by drafters and engineers to create working  drawings of an object which preserves its scale and shape. The complete representation  of these details often requires two or more  views (projections) of the object onto  different view planes.

• In parallel projection, image points are found as the  intersection of the  view plane with a  projector drawn from  the object point and  having a fixed  direction.
• 
• A Parallel projection is determined by prescribing a direction of projection vector V  and a view plane. The view  plane is  determined by its view reference point Ro and view plane normal N.
• The object point P is located in world co-ordinates at (x,y,z). The problem is to determine the image point co-  ordinates P’(x’,y’,z’).

Types of Parallel Projection

1. Orthographic Projection
2. Oblique Projection

“Projections are characterized by the fact that the direction of projection is perpendicular to the viewing plane. They are used to produce the  front, side and top views of an object.”

• • Example: – Engineering & architectural drawings employ it.
  • Multiview Projections: –  When the direction of  projection is parallel to any of the principal  axis, this produces front, top and side views  of an object
  • Multiview Projections: –
    • Example: -mechanical drawings employ it.

Axonometric Projections: –

These projections are those in which  the direciton of projection is not parallel to any of the three principal axis.

Some common sub-categories of Axonometric  Projections are: –

• Isometric
• Di-metric
• Tri-metric 

1. Isometric Projection: -The direction of projection makes equal angles with all the three principal axes.
2. Di-Metric Projection: – The direction of projection  makes equal angles with exactly two of the  principal axes.
3. Tri-Metric: – The direction of projection makes  unequal angles with the three principal axes.

Oblique Projection

“Projection obtained by projecting points along  parallel lines that are not perpendicular to  viewing plane i.e. at any angle of consideration  is called oblique parallel projections.”

OR

“Non-orthographic parallel projections are  Called oblique parallel projections.”

Sub-categories of axonometric  projections

Cavalier: – The direction of projections is chosen so  that there is no fore-shortening of lines  perpendicular to xy-plane.

Cabinet: -The direction of projections is chosen so  that lines perpendicular to xy-plane are fore-  shortening by half their lengths.

Cavalier Projection

• DOP is at 45 degree angle to VPN
• Lines parallel to any axis are foreshortened equally. Lines parallel to the z axis appear at an angle a, which is dependent upon the direction of projection.

Cabinet projection

• Projection plane normal is at an arctan(2) = 63.4° degree angle to the projection plane. (typically projecting onto the x,y plane)
• Lines parallel to the axis defining the projection plane are foreshortened equally. Lines parallel to the projection plane normal are halved!