Design, Drawing & Importance of Safety: Projection of Points & Lines

By Vijay Pratap Singh|Updated : May 21st, 2021

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Introduction:

1. Principle of Projection

If straight lines are drawn from various points on the contour of an object & by joining these lines, an image is obtained of which is known as projection of the object.

The object through which lines are drawn is said to be projected object.

The lines from the object to the plane are called projectors.

2. Methods of Projection

There are four methods of projection which are commonly used

(i) Orthographic projection

(ii) Isometric projection

(iii) Oblique projection

(iv) Perspective projection.

3. Orthographic Projection:

When the projectors are parallel to each other and also perpendicular to the plane, the projection is called orthographic projection.

The projection on the V.P. is called the front view or the elevation of the object.

The projection on the H.P. is called the top view or the plan.

(i) First-Angle Projection:

When the object is situated in the first quadrant and projected in vertical plane and horizontal plane then This method of projection is known as first-angle projection method.

In this type of projection, the object is placed in front of the V.P. and above the H.P.

(ii) Third-angle projection method:

In this type of projection, object is placed in third quadrant i.e. the object is placed in behind the V.P. and below the H.P.

4. Isometric Projection - Isometric projection is a type of pictorial projection in which the three dimensions of a solid are shown in one view & their actual dimension can be measured directly from it.

5. Oblique Projection- An oblique projection also a pictorial projection.

The oblique projection represents three dimensional object on the projection plane by one view only.

6. Perspective projection- Perspective projection is the representation of an object on a plane surface, called the picture plane, as it appears to the human eye, when viewed from a fixed position.

Projection of point:

(i) A Point is Situated in First Quadrant:

(ii) A point is situated in the second quadrant:

(iii) A point is situated in the third quadrant:

(iv) A point is situated in the fourth quadrant:

(v) A Point Lying on one of the planes or both the plane:

Projections of a lines:

A straight line is the shortest distance between two points.

Hence, the projections of a straight line may be drawn by joining the respective projections of its ends which are points.

(i)Line Contained by one or both the Planes:

(ii) Line parallel to one or both the Planes:

(iii) Line perpendicular to one of The Planes:

(iv) Line inclined to HP & Parallel to VP:

(v) Line inclined to VP & Parallel to HP:

Thus, the inclination of a line with the H.P. is seen in the front view i.e. in VP & that with the V.P. is seen in the top view i.e. in HP.

(vi) Line Inclined to both the Planes:

(vii) Line Contained By a plane perpendicular to Both the reference planes:

Traces of a line:

When a line is inclined to a plane, it will meet that plane, produced if necessary.

The point in which the line or line-produced meets the plane is called its trace.

The point of intersection of the line with the H.P. is called the horizontal trace, usually denoted as H.T. and that with the V.P. is called the vertical trace or V.T.