Lecture 1: Monge’s projection “The point”

Gaspard Monge 1746-1818

Monge’s projection

1 -Frames of reference.

2 -Principles of Monge’s projection.

3 -Representation of a point.

4 -Examples

x

y

z

1

2

3

Frames of reference

O

Horizontal plane

vertical plane

Side or profile plane

x+

+z

2

Frames of reference

1

O

3

1

Y+

+y

3

+y

z+

z -

x+ x-

y- y+

y-

y+

2

Frames of reference

1

x+

+z

O

3

1

Y+

3

+y

A

A2

A3

A1

Projecting lines

A1

A3

+y

Z+

Z -

x+ X- xA

A1

A2

A3

yA

yA

zA

y- y+

y-

y+

O

d( A1 or A2, z-axis)=xA

d(A1,x-axis) = yA

d(A2,x-axis) = zA

d(A3,z-axis) = yA

Z+ , y-

Z - , y+

x+ , y-X- , y+

3

A1

A2A3

5

5 2

Projecting lineLocus of A1 , A2

Represent the projections of the point A (3,5,2)

Projecting lineLocus of A2 , A3

Z+ , y-

Z - , y+

x+ , y-X- , y+

2B2

B1

B3

1

-3

-3

Projecting lineLocus of B1 , B2

Represent the projections of the point B (2,-3,1)

Projecting lineLocus of B2 , B3

Z+ , y-

Z - , y+

x+ , y-X- , y+

G2

G3

G1

-5

-2

Projecting lineLocus of G2 , G3

Represent the projections of the point G(-5,-2,-3)

Projecting lineLocus of G1 , G2

-3

-2

Z+ , y-

Z - , y+

x+ , y-X- , y+

A1

A2

A3

yA

Find the missing projections of the given points

Projecting lineLocus of A2 , A3

yA

Z+ , y-

Z - , y+

x+ , y-X- , y+

D1

D2D3

yD

Find the missing projections of the given points

Projecting lineLocus of D2 , D3

yD

Z+ , y-

Z - , y+

x+ , y-X- , y+

A1=A2

A3

yA

Find the missing projections of the given points

Projecting lineLocus of A2 , A3

yA

Z+

Z -

x+ X- xA

A1

A2

A3

yA

yA

zA

y- y+

y-

y+

O

d(A ,z-axis)

d(A, y

-axis

) d(A

,x-axis)

The distance between the point A and the coor. axes

d(A ,z-axis) = OA1 =

d(A, y-axis) = OA2 =

d(A ,x-axis) = OA3 =

Z+

Z -

x+ X- xA

A1

A2

A3

yA

zA

y- y+

y-

y+

O

d( A, origin)=

d(A ,z)

d(A, y

) d(A ,x)

The distance between the point A and the coor. axes

d( A, O)

zA

Z+ , y-

Z - , y+

x+ , y-X- , y+

A3

A1=A2

Represent a point A Given that yA= -zA ,d(A,O)=8, A is above 1 and A is on the left hand of 3 at a distance

=6

L: A1 , A2

zA=yA

xA =-6

8

zA=yA

L:A3

zA is +ve

xA =-6

Represent the three projections of regular tetragonal 5,2,?),C(4,5,?))prism ABCDA\B\C\D\ if its base 1,A and its height = 6 units

Z+ , y-

Z - , y+

x+ , y-x- , y+

A1=A\1

A2C3C2

C1=C\1

A3

B1=B\1

D1=D\1

L :B2L:D2

B2D2

6 unit

D\2

C\2 A\

2 B\2

B3 D3

C\3 B\

3D\

3 A\3

1

DC

B

A\

A

D\C\

B\