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

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

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

y- z+ x- x+ y+ y- y+ z -

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

d(A1,x-axis) = yA d(A2,x-axis) = zA d(A3,z-axis) = yA O 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

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+

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+

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+

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+

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+

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+

The distance between the point A and the coor. axes yA 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 =

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

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+

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