1. Lecture 3: Revision By Dr. Samah Mohamed Mabrouk www.smmabrouk.faculty.zu.edu.eg By Dr. Samah Mohamed Mabrouk www.smmabrouk.faculty.zu.edu.eg

2. Z +, y - Z -, y + x +, y - X-, y + 3 A1A1 A2A2 A3A3 5 5 2 Projecting line Locus of A 1, A 2 Represent the projections of the point A (3,5,2) Projecting line Locus of A 2, A 3

3. X +,y -- X --,y+ z +,y -- Z -,y + A1A1 A2A2 A3A3 Find the missing projections L: A 3 YAYA YAYA

4. X +,y - - X --,y+ z +,y -- Z --,y + B 2 = B 3 B1B1 YBYB YBYB L:B 1

5. X +,y - - X --,y+ z +,y -- Z --,y + C 2 = C 1 C3C3 YCYC YCYC L:C 3

6. X +,y - - X --,y+ z +,y -- Z --,y + D3D3 D1D1 YDYD L:D 1 D2D2 YDYD

7. 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 + A 1 =A \ 1 A2A2 C3C3 C2C2 C 1 =C \ 1 A3A3 B 1 =B \ 1 D 1 =D \ 1 L :B 2 L:D 2 B2B2 D2D2 6 unit D\2D\2 C\2C\2 A\2A\2 B\2B\2 B3B3 D3D3 C\3C\3 B\3B\3 D\3D\3 A\3A\3 11 D C B A\A\ A D\D\ C\C\ B\B\

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

9. m{A(2,2,5) and B(6,5,1)} Z +, y - Z -, y + x +, y - x-, y + B1B1 A1A1 B2B2 A2A2 m3m3 B3B3 A3A3 m2m2 m1m1 m 1 is the horizontal projction m 2 is the vertical projction m 3 is the profile(side) projction مساقط النقطه تقع على مساقط الخط

10. Special positions of a str. line m //  1 (Horizontal line) الخط الموازى للمستوى مسقطه على هذا المستوى = طوله الحقيقى (True length) الخط العمودى على مستوى مسقطه على هذا المستوى = نقطة وعلى باقى المستويات = طول حقيقى m //  2 frontal linem //  3 profile line m   1 m   2 m   3  m 2 = T.L m1m1 m3m3 m 1 = T.L m3m3  m2m2 m2m2   m1m1 m 3 = T.L m 2 = T.Lm 3 = T.L m1m1 m 1 = T.L m2m2 m 3 = T.L m3m3 m 2 = T.L m 1 = T.L

11. B1B1  T.L. of m A1A1  z AB B2B2  T.L. of m A2A2  y AB B3B3  T.L. of m A3A3  x AB Triangles of solution   ( m,  1 )   ( m,  2 )   ( m,  3 )

12. Z +, y - Z -, y + x +, y - x-, y + H1H1 V1V1 V2V2 H2H2 m3m3 H3H3 V3V3 m2m2 m1m1 Traces of a str. line S1S1 S2S2 S3S3 1- H is the horizontal trace 3- S is the side or profile trace 2- V is the vertical trace

13. Example(2): Given A 2 B 2 the vertical projection of a segment AB and the horizontal projection A 1 of the point A and <(AB,  3 )=45 ,find the remaining projections of AB Z +, y - Z -, y + x +, y - x-, y + B1B1 A1A1 B2B2 A2A2  x AB yAyA A3A3 B3B3 T.L. of AB A3A3 B\3B\3 B3B3 yAyA L :B 3 L :A 3 L :B 1 45 

14. Example(3): Given the straight line m in general position and a point A lying on m required, find a point M on m at a distance 4cm from A x +, y - x-, y + B1B1 A1A1 B2B2 A2A2  z AB m2m2 [M] m1m1 4  z AB M1M1 T.L. m M2M2

15. Example(4): Represent the two projections of an equilateral triangle ABC if its side AB is given and C(?, 1, ?) x +, y - B1B1 A1A1 B2B2 A2A2  y AB C1C1  y BC L :C 1 1  z AB  y AC  z AB T.L. of AB = AC T.L. of AB = AC = BC C2C2  T.L. of AB =AC A2A2  y AC C2C2 T.L. of AB =AC B2B2  y BC L :C 2 C2C2

16. X 12 Example (5): A cube ABCDA \ B \ C \ D \ is given by it’s vertex A \, it’s base ABCD   1 and it’s vertex C =(?, 5, ?), represent the cube by it’s two projections A2\A2\ A 1 \ =A 1 L: A 2, B 2, C 2, D 2 A2A2 T.L of square T.L of AC L: C 1 B2B2 D2D2 C2C2 B2\B2\ D2\D2\ C2\C2\ C 1 \ =C 1 D 1 \ =D 1 B 1 \ =B 1 B\B\ C\C\ C A\A\ A D\D\ D B 11 A 1 B 1 C 1 D 1 T.S A 2 B 2 C 2 D 2  x- axis

17. 1- A point A(0,2,3)  …….. (π 1, π 2, π 3 ) 3- For a point 'A' with three projections (A 1,A 2,A 3 ) the length ………………= d(A, z-axis) (OA 1,OA 2,OA 3 ) 2- The point 'A' with x A = z A =0  ……. (π 1,y- axis, x- axis) 4- The str. Line with vertical projection = T.L…………… (  π 2, //π 2,  π 3 )

18. 5- If the str. Line m  π 1,then ……projection is a point (horizontal, vertical, frontal) 6- The point of intersection of m with π 3 is called………… Side trace