Projection

Consider an arrangement for a simple phenomenon of shadow formation. When an object is placed between a light source and a screen, the light rays coming from the source are obstructed by the object. As a result, a shadow is formed on the screen behind the object.

This occurs because light travels in straight lines, and any object that blocks the light prevents it from reaching the screen in the region directly behind the object.

In this setup, the shadow formed is larger than the actual size of the object.

If the light source is moved farther away from the object, the size of the shadow decreases. This happens because the rays from the source become less divergent, resulting in a smaller projection of the object on the screen.

When the light source is placed at an infinite distance, the light rays that reach the object are almost parallel to each other. In such a case, the shadow formed on the screen is nearly equal in size to the actual object.

Projection is a technique used in engineering drawing to show the size, shape, and features of an object by projecting its edges and surfaces onto a reference plane using straight lines.

· The lines of sight are popularly called projectors.

· The planes on which the drawings are made are called planes of projection.

Types of Planes of Projection

1. Horizontal Plane (HP)

2. Vertical Plane (VP)

When these planes intersecting each other at right angle, divide the space into four dihedral angles or quadrants. The line of intersection between these planes is called a reference line. Any position in space with reference to the principal planes can be defined as in figure below:

Classification Of Projections

Pictorial View: A pictorial view is a 3D representation of an object drawn on a 2D plane.

Parallel vs. Perspective Projection

Both are methods used in technical drawing to convert 3D objects into 2D images on a screen. The key difference is how they handle depth and distance.

Parallel Projection

In parallel projection, all the projection lines (imaginary lines from the object to the viewing plane) are parallel to each other. There is no single point where they converge.

Key characteristics:

Objects keep their actual size and shape, no matter how far they are from the viewer
Parallel lines in the object remain parallel in the image
No sense of depth (things far away look the same size as things close up)
Distances and angles are preserved — good for measurement
The "camera" is imagined to be at an infinite distance from the object

Types:

Orthographic — projection lines are perpendicular to the viewing plane (e.g., front view, top view, side view — used in engineering drawings)
Oblique — projection lines are at an angle to the viewing plane (e.g., Cavalier, Cabinet projections)

Used in: CAD software, architectural drawings, engineering blueprints

Perspective Projection

In perspective projection, all the projection lines converge to a single point called the center of projection (like a camera lens or the human eye).

Key characteristics:

Objects appear smaller as they get farther away (just like real life)
Parallel lines appear to converge toward a vanishing point (think of railway tracks meeting in the distance)
Creates a realistic sense of depth
Distances and angles are not preserved — not good for exact measurement
The camera is at a finite distance from the object

Used in: Realistic simulations, photography, 3D rendering.

Simple Table Comparison

Feature	Parallel Projection	Perspective Projection
Projection lines	Parallel to each other	Converge at a single point
Object size with distance	Stays the same	Gets smaller with distance
Realism	Less realistic	More realistic (like human eye)
Measurement accuracy	Accurate (true size/shape)	Distorted
Camera distance	Infinite	Finite
Common use	Engineering, CAD	Real-world simulation

Oblique Projection

Oblique projection is a method of pictorial projection in which the projectors are parallel to each other but inclined at an angle other than 90° to the plane of projection.

In an oblique projection, the front face of the object is usually kept parallel to the plane of projection, so its shape and dimensions can be shown directly. The depth of the object is represented by inclined lines.

Main characteristics

Projectors are parallel to one another.
Projectors are inclined to the projection plane.
The front surface can be shown in its true shape and size.
Depth is represented by inclined receding lines.
It is commonly used for engineering drawings and pictorial representations.

Terminology

1. Receding axis — In oblique projection, two of the three axes always lie in the front face, at right angles to each other, and are drawn true to scale. The third axis, representing an edge perpendicular to the plane of projection, may be inclined at any convenient angle; this inclined line is called the receding axis.

2. Receding angle — The angle formed between the receding axis and the horizontal is termed the receding angle. Conventionally, this is set to 30°, 45°, or 60°, since these angles can be constructed easily using set-squares. The most suitable receding angle depends on the shape of the object and which feature needs emphasis — a larger angle gives a better view of a recess on the top of the object, while a smaller angle favors a recess on the side.

3. Receding edge — The projected image of an edge that lies perpendicular to the plane of projection, drawn parallel to the receding axis, is called a receding edge.

4. Receding plane — The projected image of a surface that lies perpendicular to the plane of projection (and either parallel or perpendicular to the ground) is called a receding plane.

Types of Oblique Projection

Cavalier Projection

Definition: Cavalier projection occurs when the projectors make an angle of 45° with the plane of projection.
True Length: Lines perpendicular to the plane of projection are projected at their true length, just like lines lying within the plane.
Defining Feature: All three principal axes are represented at the same true scale, so a single scale can be used for construction.
Receding Axis: The receding axis may be drawn at a convenient angle such as 30°, 45°, or 60° to the horizontal.
Advantage: Uniform scaling makes dimensioning and construction relatively simple.
Visual Effect: The object may appear unnaturally stretched or exaggerated in depth because there is no foreshortening along the receding axis.
Preferred Angle: Among common receding-axis angles, 30° generally provides the most visually acceptable appearance.

Cabinet Projection

Definition: Cabinet projection occurs when the projectors make an angle of 63°26′ with the plane of projection, for which tan θ = 2. [which means that a line perpendicular to the vertical plane is just twice as long as its projectors. In other words, the line perpendicular to the vertical plane will have its projection length one-half of the actual line length.]
Foreshortening: Lines perpendicular to the plane of projection appear at half their true length in the projection.
Receding Edges: The depth or receding edges are therefore drawn at one-half scale, while lines lying within the plane of projection remain at their true length.
Receding Axis: The angle of the receding axis is independent of the 63°26′ projector angle and may be selected conveniently.
Preferred Receding Angle: A receding-axis angle of 45° generally provides the best visual proportion and is commonly preferred.
Visual Effect: The half-scale foreshortening reduces the depth distortion associated with cavalier projection.
Appearance: It produces a more realistic and natural-looking pictorial representation.
Name: The term cabinet projection comes from its historical use in furniture and cabinet-making drawings.

General Oblique Projection

Definition: General oblique projection occurs when the projectors make an angle other than 45° or 63°26′ with the plane of projection.
Projected Length: Lines perpendicular to the plane of projection are represented at a reduced length.
Foreshortening: The projected length commonly ranges between 0.5 and 0.75 of the true length, depending on the angle selected.
Receding Axis: The angle of the receding axis can be selected according to the drawing requirements and desired visual appearance.
Purpose: It provides flexibility in choosing the degree of foreshortening and visual representation.
Appearance: Compared with cavalier projection, it generally produces a more realistic appearance because the depth is reduced.

Fig: General projection of a cube having its projection length is 0.75 of the actual line length, and receding axis inclined at different angles with the horizontal.

Orthographic Projection

The term orthographic comes from the Greek word orthos, meaning perpendicular. In orthographic projection, the observer is assumed to view the object from an infinite distance, ensuring that the rays of sight (projectors) are:

Parallel to each other
Perpendicular to the plane of projection

Orthographic projection can produce:

1. Single pictorial views – showing all three dimensions in one view.

2. Multi-view drawings – each view shows only two dimensions, such as:

o Front view (height and width)

o Top view (width and depth)

o Side view (height and depth)

Multi-View Drawing

Multi-view drawing requires two or more orthographic projections to accurately define the shape of a three-dimensional object. Each orthographic view is a two-dimensional representation, showing only two of the three dimensions—typically height, width, or depth.

Since no single view can provide complete information about the object, multiple views are required. These views must be correlated and interpreted together to understand the full shape and structure of the object.

Because of this, the arrangement and relationship among the views are interdependent. Over time, standardized conventions and rules have been established to ensure consistency and clarity in technical drawings.

Orthographic Projection Planes

Orthographic projections are primarily drawn on two principal planes, also referred to as reference planes:

Vertical Plane (VP) – usually used for the front view
Horizontal Plane (HP) – typically used for the top view

These two planes are perpendicular to each other, and they divide the 3D space into four quadrants, commonly referred to as angles:

1. First Angle

2. Second Angle

3. Third Angle

4. Fourth Angle

Depending on the position of the object, the orthographic projection can be classified as follows:

1. First angle projection:

The object lies in the first angle, i.e., above H.P. and in front of V.P.

2. Second angle projection:

The object lies in the second angle, i.e., above H.P. and behind V.P.

3. Third angle projection:

The object lies in the third angle, i.e., below H.P. and behind V.P.

4. Fourth angle projection:

The object lies in the fourth angle, i.e., below H.P. and in front of V.P.

The following terms are frequently used in multi-view drawings:

Vertical plane: Vertical plane, also known as front reference plane, is assumed to be placed vertically and is denoted by V.P.

Horizontal plane: Horizontal plane, also known as horizontal reference plane, is assumed to be placed horizontally and is denoted by H.P. It is perpendicular to V.P.

Profile plane: A plane perpendicular to both the above planes is known as a profile plane. The plane on the right end of the planes is known is right profile plane while the plane on the left end is known as left profile plane.

Reference plane: All the above mentioned mutually perpendicular planes are called reference planes.

Principal plane: It is an alternative name of the reference plane.

Reference line: The line of intersection between the principal planes is known as a reference line. It is also popularly called xy line.

Front view: The view of an object by observing it from the front and drawn on the V.P. is called front view (F.V.) or elevation.

Top view: The view of an object by observing it from the top and drawn on the H.P. is called top view (T.V.) or plan.

Side view: The view of an object by observing it from the left-hand side or right-hand side and drawn on a profile plane is called side view or end view.

Features of First Angle Projection

1. Object Position:

The object is located in the first quadrant, i.e., in front of the Vertical Plane (V.P.) and above the Horizontal Plane (H.P.).

2. Observer's Position:

The object is placed between the observer and the plane of projection.

3. Top View Placement:

The top view (plan) is drawn below the front view.

4. Left-Hand Side View Placement:

The left-side view is drawn on the right side of the front view.

5. Right-Hand Side View Placement:

The right-side view is drawn on the left side of the front view.

Fig: (a) Front view on V.P. (b) Top view on H.P. (c) Left-hand side view on P.P.

Features of Third Angle Projection

1. Object Position:

The object is located in the third quadrant, i.e., behind the Vertical Plane (V.P.) and below the Horizontal Plane (H.P.).

2. Observer's Position:

The plane of projection lies between the observer and the object.

3. Top View Placement:

The top view (plan) is drawn above the front view.

4. Left-Hand Side View Placement:

The left-side view is drawn on the left side of the front view.

5. Right-Hand Side View Placement:

The right-side view is drawn on the right side of the front view.

Fig. (a) Front view on V.P. (b) Top view on H.P. (c) Left-hand side view on P.P

Conversion of Pictorial View into Orthographic Multi-Views

Problem 1: Pictorial view of an object is shown in Fig. Using first angle projection, draw its (a) front view from the X-direction, (b) top view and (c) left-hand side view.

Fig. (a) Pictorial view (b) Orthographic views

Problem 2: Pictorial view of an object is shown in Fig. below. Using first angle projection, draw its (a) front view, (b) top view and (c) right-hand side view.

Fig. (a) Pictorial view (b) Orthographic views

Problem 3: Pictorial view of an object is shown in Fig. below. Using first angle projection, draw its (a) front view, (b) top view and (c) right-hand side view.

Fig. (a) Pictorial view (b) Orthographic views

Problem 4: Pictorial view of an object is shown in Fig. below. Using first angle projection, draw its (a) front view, (b) top view and (c) side view.