1. Lecture 1: Monge’s projection “The point”
Gaspard Monge

2. Monge’s projection 1- Frames of reference.
2- Principles of Monge’s projection.
3- Representation of a point.
4- Examples

3. Frames of reference Side or profile plane vertical planez
Side or profile
plane 2
vertical plane 3 O x
Horizontal plane 1 y

4. Frames of reference
+ z +y 3 3 2
+ y x+ O 1 1 Y+

6. y- z+ x- x+ y+ y- y+
z -

7. Frames of reference 3 2 1 Projecting lines x+ + z O +y 3 A3 A2 A3

8. d(A1,x-axis) = yA d(A2,x-axis) = zA d(A3,z-axis) = yAO y+ y- yA
d(A1,x-axis) = yA A1
d(A2,x-axis) = zA y+
Z -
d(A3,z-axis) = yA
d( A1 or A2, z-axis)=xA

9. Represent the projections of the point A (3,5,2)
Z+ , y-
Projecting line
Locus of A1 , A2
Projecting line
Locus of A2 , A3 A3 A2 5 2
X- , y+ 3
x+ , y- 5 A1
Z - , y+

10. Represent the projections of the point B (2,-3,1)
Z+ , y-
Projecting line
Locus of B1 , B2 B1
Projecting line
Locus of B2 , B3 -3 -3 B3 B2
X- , y+ 2
x+ , y- 1
Z - , y+

11. Represent the projections of the point G(-5,-2,-3)
Z+ , y-
Projecting line
Locus of G1 , G2 G1 -2
X- , y+
x+ , y- -5 -3 G3
Projecting line
Locus of G2 , G3 G2 -2
Z - , y+

12. Find the missing projections of the given points
Z+ , y-
Projecting line
Locus of A2 , A3 yA A2 A3
X- , y+
x+ , y- yA A1
Z - , y+

13. Find the missing projections of the given points
Z+ , y- D1 yD
X- , y+
x+ , y- yD D2
Projecting line
Locus of D2 , D3 D3
Z - , y+

14. Find the missing projections of the given points
Z+ , y-
X- , y+
x+ , y- yA yA
Projecting line
Locus of A2 , A3
A1=A2 A3
Z - , y+

15. The distance between the point A and the coor. axesyA y- Z+ A3 A2
d(A, y-axis) zA
d(A ,x-axis) xA X- x+ O y+ y-
d(A ,z-axis) = OA1 = yA
d(A ,z-axis)
d(A, y-axis) = OA2 = A1 y+
Z -
d(A ,x-axis) = OA3 =

16. The distance between the point A and the coor. axes
d( A, origin)= y- Z+ A3 A2
d(A, y) zA
d(A ,x) xA X- x+ O y+ y- yA
d(A ,z)
d( A, O) A1 y+
Z - zA

17. 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
Z+ , y-
L: A1 , A2 A3
L:A3
A1=A2
zA=yA
X- , y+
x+ , y-
xA =-6 8
zA is +ve
xA =-6
zA=yA
Z - , y+

18. Represent the three projections of regular tetragonal 5,2,. ),C(4,5,
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
L:D2
L :B2
Z+ , y-
D\3
C\2
A\2
C\3
B\3
A\3
D\2
B\2
6 unit
x- , y+ C2 A2
x+ , y- C3 B3 D3 A3 D2 B2
A1=A\1 C\ D\ A\ B\
D1=D\1
B1=B\1 C D 1 B A
Z - , y+
C1=C\1