Revision By Dr Samah Mohamed Mabrouk www smmabrouk

Revision By Dr. Samah Mohamed Mabrouk www. smmabrouk. faculty. zu. edu. eg

1 - The point

Represent the projections of the point A (3, 5, 2) Z+ , y Projecting line Locus of A 2 , A 3 X- , y+ Projecting line Locus of A 1 , A 2 A 3 A 2 5 2 3 x+ , y - 5 Z - , y+ A 1 Revision. S. M. Mabrourk

2 - The straight line Straight line is defined by. 2 - A point and direction 1 - Two points. m B C m d A Revision. S. M. Mabrourk

m{A(2, 2, 5) and B(6, 5, 1)} A 3 Z+ , y - A 2 m 3 B 2 x- , y+ x+ , y - m 1 is the horizontal projction A 1 m 2 is the vertical projction m 1 m 3 is the profile(side) projction ﻣﺴﺎﻗﻂ ﺍﻟﻨﻘﻄﻪ ﺗﻘﻊ ﻋﻠﻰ ﻣﺴﺎﻗﻂ ﺍﻟﺨﻂ Z - , y+ B 1 Revision. S. M. Mabrourk

Triangles of solution T. L z. AB . of T. L AB y. AB A 1 T. L A 3 . of AB A 2 B 1 x. AB . of B 2 ( m, 1) ( m, 2) ( m, 3) AB B 3 Revision. S. M. Mabrourk

Traces of a str. line S 2 S 3 V 2 Z+ , y - m 3 x- , y+ H 3 m 2 S 1 x+ , y - V 1 1 - H is the horizontal trace H 2 m 1 2 - V is the vertical trace 3 - S is the side or profile trace Z - , y+ H 1 Revision. S. M. Mabrourk

3 - The plane

The Plane is defined by 1 -Tow intersecting lines n 2 -Tow parallel lines n m m 3 -Three non-linear points A B 4 -line and a point not on it A C m Revision. S. M. Mabrourk

Represent the plane (5, 3, 4) z+ , y-- x-- s v 4 , y+ x+ , y-- 5 3 h z-- , y+ Revision. S. M. Mabrourk

Represent the plane (-3, 30 , 60 ) z+ , y-- v 60 X+ , y-- 3 X-- , y+ 30 h Z-- , y+ Revision. S. M. Mabrourk

Given a plane {a, M, M a} V 2 b 2 v a 2 M 2 H 2 X 12 H 2 V 1 b 1 H 1 a 1 M 1 H 1 h Revision. S. M. Mabrourk

The special str. line in the plane frontal line v v f 2 horizontal line h 2 =T . L H 2 v 2 X 12 v 1 f 1 H 1 h h 1 . L T = h ﺍﺛﺮ ﺍﻟﻤﺴﺘﻮﻯ // ﺍﻟﻄﻮﻝ ﺍﻟﺤﻘﻴﻘﻲ Revision. S. M. Mabrourk

4 - The Auxiliary projection

1 - Auxiliary projection in a plane 3 1. A 2 z. A x 12 A 1 z. A x 1 3 A 3 x 35 A 5 Revision. S. M. Mabrourk

2 - Auxiliary projection in a plane 4 2. x 46 A 6 y. A A 2 A 4 x 2 4 x 12 y. A A 1 Revision. S. M. Mabrourk

Problem (1): The true length of a straight line in space. B 2 A 2 x 12 B 1 A 1 B 3 T. L. x 13 A 3 Revision. S. M. Mabrourk

Problem (1): The true length of a straight line in space. B 4 T. L. A 4 B 2 x 2 4 A 2 x 12 B 1 A 1 Revision. S. M. Mabrourk

Problem (2): Convert a straight line into a point. B 2 A 2 x 12 B 1 A 1 x 13 B 3 T. L. A 3 A 5=B 5 x 35 Revision. S. M. Mabrourk

The auxiliary projection of a plane. Problem (3): Convert a plane into a line v A 2 x 12 A 1 h 1 3 x 1 3 A 3 Revision. S. M. Mabrourk

Example : Given the two projections of Parallelogram and the vertical projection of the point M. find the horizontal projection of point M if d(M, ABCD)=3 cm also, find the true shape of the Parallelograms ABCD. B 2 M 2 K 2 A 2 z. M C 2 x 12 D 2 L: M 3 3 B 1 z. M x 1 A 1 M 2 K 1 D 1 L: M 3 3 cm C 1 D 3 C 3 A 3 B 3

C 2 x 12 D 2 3 B 1 x 1 A 1 M 1 K 1 D 1 C 1 x 35 D 3 C 5 B 3 A 3 D 5 T. S. B 5 A 5