Unit No:03Projections of Points & Lines

Yash B. ParikhM.Tech. (CIM)

Assistant ProfessorDepartment of Mechanical Engineering

Symbiosis Institute of Technology

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What is a point????

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What is a point????

A French word meaning "dot, point, period (the punctuation mark)”

When you puncture something, you use a sharp object to make a tiny hole in it.

That tiny hole, especially from a distance, looks like a dot, so a point is a dot.

In mathematics a point is assumed to be dimensionless, but of course any physical representation of a point must be of some size.

A point is often represented in textbooks by the smallest of all printing symbols, the period.

In fact printers' type sizes are measured in units called points.

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Introduction

Point, together with line, is a basic concept of elementary geometry.

You can't get too wrong if you say that point is a mere location, location without width, breadth or length.

It makes no point to give a definition without a purpose.

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Introduction

It is practically impossible to define point without mentioning the joints that may go between the points.

And this is how we come around to talking about points and - simultaneously - lines.

”It takes line to know point -- and vice versa.”

The common practice is to leave the terms point and line undefined but just start using them in the first principles:

1. There is a single line through two points.

2. There is a single point at the intersection of two lines.

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Principal Planes of Projections

The principal planes of projections are:

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Positions of a Point

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Notations of a Point

Following Notations should be followed while naming different views in orthographic projections.

IT’S FRONT VIEW a’ a’ b’

OBJECT POINT A LINE AB

IT’S TOP VIEW a a b

IT’S SIDE VIEW a” a” b”

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Positions of a Point

1. Point is above H.P. & in front of V.P.

2. Point is above H.P. & behind V.P.

3. Point is below H.P. & behind V.P..

4. Point is below H.P. & in front of V.P.

5. Point is in H.P. & in front of V.P.

6. Point is in H.P. & behind V.P.

7. Point is above H.P. & in V.P.

8. Point is below H.P. & in V.P.

9. Point is in both H.P. & V.P.

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HP

VPa’

a

A

POINT A IN1ST QUADRANT

OBSERVER

VP

HP

POINT A IN2ND QUADRANT

OBSERVER

a’

a

A

OBSERVER

a

a’

POINT A IN3RD QUADRANT

HP

VP

A

OBSERVER

a

a’POINT A IN4TH QUADRANT

HP

VP

A

Point A is Placed In different quadrantsand it’s Fv & Tv are brought in same plane for Observer to see clearly. Fv is visible asit is a view on VP. But as Tv is a view on Hp, it is rotateddownward 900, In clockwise Direction (in 1st quadrant).The In front part of Hp comes below xy line.

The HP behind the Vp is also rotated clockwise, and thereforecomes above the xy line.

Observe and note the process. Convention: Horizontal plane is always rotated clockwise

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PROJECTIONS OF A POINT IN THE 4 QUADRANTS

HP

VP

POINT IN 2nd QUADRANT

VP

HP

PT

PF

HP

VP

POINT IN 3rd QUADRANT

HP

VP

POINT IN 4th QUADRANT

VP

VP

HP

HP

PT: TOP VIEW

PF: FRONT VIEW

PF

PT

PF

HP

VP

POINT IN 1st QUADRANT

VP

HP

PT

PF

PT

P

PP

P

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How you will draw on the sheet

POINT IN 2nd QUADRANT

PT

PF

POINT IN 3rd QUADRANT

POINT IN 4th QUADRANT

PT: TOP VIEW

PF: FRONT VIEW

PF

PT

PF

POINT IN 1st QUADRANT

PT

PF

PT

y

yy

y

xx

xx

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A

a

a’A

a

a’

Aa

a’

X

Y

X

Y

X

YFor Fv

For Tv

For Fv

For Tv

For Tv

For Fv

POINT A ABOVE HP& INFRONT OF VP

POINT A IN HP& INFRONT OF VP

POINT A ABOVE HP& IN VP

PROJECTIONS OF A POINT IN FIRST QUADRANT.

ORTHOGRAPHIC PRESENTATIONS OF ALL ABOVE CASES.

X Y

a

a’

VP

HP

X Y

a’

VP

HP

a X Y

a

VP

HP

a’

Fv above xy,Tv below xy.

Fv above xy,Tv on xy.

Fv on xy,Tv below xy.

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Problem on Projections of Point

Question: 01

Draw the projections of the following points on a common XY line. Keep the distance between two consecutive projectors as 20 mm;

# A, 30 mm above the HP and 40 mm in front of VP.

# B, 80 mm above the HP and 40 mm behind the VP.

# C, 30 mm below the HP and 40 mm behind the VP.

# D, 30 mm below the HP and 40 mm in front of the VP.

# E, in the HP and 40 mm behind the VP.

# F, in the VP and 40 mm below the HP.

# G, in both the HP and VP.

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Thank You