1. Technical Drawing in Photonics
Lesson 8
Point on a line. Point on a plane. Line on a plane. Intersection of a line and a plane. Intersection of two planes.
Dr. Zsolt István Benkő
TAMOP C-12/1/KONV project
„Preparation of the concerned sectors for educational and R&D activities related to the Hungarian ELI project”

2. e” x1,2 e’ Lesson 8 Technical drawing in Photonics
If a point is needed to be fit to a line then both of the views should be placed onto the views of the line.
Technical drawing in Photonics

3. e” P” x1,2 P’ e’ Lesson 8 Technical drawing in Photonics
The proper view of the point should be placed onto the proper view of the line. Point P is fitted to the line e. e’
Technical drawing in Photonics

4. e” Q’ x1,2 Q” e’ Lesson 8 Technical drawing in Photonics
Point Q looks like being on line e, but it is not: the line is in the 1st quadrant and point Q is in the 3rd quadrant. e’
Technical drawing in Photonics

5. g” f” x1,2 P’ f’ g’ Lesson 8 Technical drawing in Photonics
A point should be fitted to the (f,g) plane. The 1st view is given.
Technical drawing in Photonics

6. g” f” x1,2 P’ f’ g’ Lesson 8 Technical drawing in Photonics
A supporting line is needed (red). This line passes through P and intersects with f and g.
Technical drawing in Photonics

7. g” f” x1,2 P’ f’ g’ Lesson 8 Technical drawing in Photonics
The 2nd view of the supporting line is found by organizers.
Technical drawing in Photonics

8. g” f” x1,2 P’ f’ g’ Lesson 8 Technical drawing in Photonics
The 2nd view of the supporting line is drawn (upper red line).
Technical drawing in Photonics

9. g” f” P” x1,2 P’ f’ g’ Lesson 8 Technical drawing in Photonics
By the organizer the 2nd view of point P is found.
Technical drawing in Photonics

10. Lesson 8
Technical drawing in Photonics

11. t2 x1,2 P’ t1 Lesson 8 Technical drawing in Photonics
Point P should be fitted onto the (t1,t2) plane. P’ is given.
Technical drawing in Photonics

12. t2 x1,2 P’ t1 Lesson 8 Technical drawing in Photonics
A main line should be used. One view of the main line is parallel to the trace line of the plane, the other view is parallel to the axis. Draw a line through P’ parallel to t1.
Technical drawing in Photonics

13. t2 x1,2 P’ t1 Lesson 8 Technical drawing in Photonics
Where the main line intersects the axis an organizer should be drawn to the other trace line.
Technical drawing in Photonics

14. t2 x1,2 P’ t1 Lesson 8 Technical drawing in Photonics
From the intersection of t2 and the organizer the 2nd view of the main line can be drawn parallel to the axis.
Technical drawing in Photonics

15. t2 P” x1,2 P’ t1 Lesson 8 Technical drawing in Photonics
By drawing the organizer from P’ the other view can be achieved on the main line. Now P is on the (t1,t2) plane.
Technical drawing in Photonics

16. Lesson 8
Technical drawing in Photonics

17. e” x1,2 e’ A’ Lesson 8 Technical drawing in Photonics
A is a projecting plane: it consists of rays. A projecting plane is perpendicular to one of the projection planes. A is a 1st projecting plane because it is perpendicular to the 1st projection plane and because of it its 1st view is a single line. It is usually drawn till the axis. The intersection of line e and plane A is to be determined. The 1st view is the intersection of e’ and A’.
Technical drawing in Photonics

18. e” I” x1,2 I’ e’ A’ Lesson 8 Technical drawing in Photonics
For the 2nd view the organizer should be drawn.
Technical drawing in Photonics

19. g” f” x1,2 g’ f’ Lesson 8 Technical drawing in Photonics
An (f,g) plane is given.
Technical drawing in Photonics

20. g” f” e” x1,2 e’ g’ f’ Lesson 8 Technical drawing in Photonics
The intersection of line e and the (f,g) plane should be determined. g’ f’
Technical drawing in Photonics

21. g” f” e” x1,2 A’=e’ g’ f’ Lesson 8 Technical drawing in Photonics
The first step is a logical step only: a projecting plane should be fitted to line e. g’ f’
Technical drawing in Photonics

22. g” f” e” F’ F” G’ G” x1,2 A’=e’ g’ f’ Lesson 8
The intersections of line f and g with plane A should be found (F and G). g’ f’
Technical drawing in Photonics

23. g” f” e” F’ F” G’ G” I” x1,2 A’=e’ g’ f’ Lesson 8
F and G are on plane A and naturally on the (f,g) plane. Therefore the yellow line is the 2nd view of the intersection line between the (f,g) plane and plane A. The 1st view equals to e’. The yellow line is on plane A and line e is on plane A, too. Their intersection is a real intersection (I”). It is the point where line e meets the (f,g) plane. g’ f’
Technical drawing in Photonics

24. g” f” e” F’ F” G’ G” I” I’ A’=e’ g’ f’ Lesson 8
By drawing the organizer I’ could be achieved. g’ f’
Technical drawing in Photonics

25. Lesson 8
Technical drawing in Photonics

26. t2 x1,2 t1 Lesson 8 Technical drawing in Photonics
(t1,t2) plane is given.
Technical drawing in Photonics

27. t2 e” x1,2 t1 e’ Lesson 8 Technical drawing in Photonics
The intersection with line e is to be found.
Technical drawing in Photonics

28. t2 e” x1,2 t1 A’=e’ Lesson 8 Technical drawing in Photonics
The first step is to fit a projecting plane to line e. Now the intersection line between the two planes need to be found. Two points are needed to draw this line.
Technical drawing in Photonics

29. t2 e” x1,2 t1 A’=e’ Lesson 8 Technical drawing in Photonics
One point is obvious: the point where plane A intersects the trace line.
Technical drawing in Photonics

30. t2 e” x1,2 t1 A’=e’ Lesson 8 Technical drawing in Photonics
An arbitrary point could be drawn by a main line.
Technical drawing in Photonics

31. t2 e” I” x1,2 t1 A’=e’ Lesson 8 Technical drawing in Photonics
By connecting these points the intersection line between the two planes are drawn (yellow line). Where it intersects e” is a real intersection.
Technical drawing in Photonics

32. t2 e” I” x1,2 I’ t1 A’=e’ Lesson 8 Technical drawing in Photonics
With the help of the organizer I’ could be drawn.
Technical drawing in Photonics

33. Lesson 8
Technical drawing in Photonics

34. f” g” g’ f’ Lesson 8 Technical drawing in Photonics
Now the intersection of two planes is investigated. The result is an intersection line. One plane is the (f,g) plane.
Technical drawing in Photonics

35. f” g” b” a” a’ b’ g’ f’ Lesson 8 Technical drawing in Photonics
The second plane is the (a,b) plane. g’ f’
Technical drawing in Photonics

36. f” g” b” a” a’ b’ g’ f’ Lesson 8 Technical drawing in Photonics
The intersection of line a and plane (f,g) should be found. g’ f’
Technical drawing in Photonics

37. f” g” b” a” a’ b’ g’ f’ Lesson 8 Technical drawing in Photonics
The intersection of line b and plane (f,g) should be found, too. g’ f’
Technical drawing in Photonics

38. f” g” b” a” i’ i” a’ b’ g’ f’ Lesson 8 Technical drawing in Photonics
These two points are on the (f,g) plane and they are also on line a or line b. They denote the intersection line i between the planes (f,g) and (a,b). g’ f’
Technical drawing in Photonics

39. Technical drawing in Photonics
Lesson 8
All the necessary lines are shown.
Technical drawing in Photonics

40. Lesson 8
Technical drawing in Photonics

41. t2 t1 Lesson 8 Technical drawing in Photonics
The (t1,t2) plane is given.
Technical drawing in Photonics

42. t2 u2 t1 u1 Lesson 8 Technical drawing in Photonics
The (u1,u2) plane is also given.
Technical drawing in Photonics

43. t2 u2 t1 u1 Lesson 8 Technical drawing in Photonics
There are obvious intersection points: where the trace lines are intersect each other. This is one point.
Technical drawing in Photonics

44. t2 u2 t1 u1 Lesson 8 Technical drawing in Photonics
This is the other point.
Technical drawing in Photonics

45. t2 u2 i” t1 u1 i’ Lesson 8 Technical drawing in Photonics
By connecting these points the intersection line i of the two planes could be drawn.
Technical drawing in Photonics

46. Lesson 8
Technical drawing in Photonics
Technical drawing in Photonics

47. Lesson 8
References
Ocskó Gy., Seres F.: Gépipari szakrajz, Skandi-Wald Könyvkiadó, Budapest, 2004
Lőrincz P., Petrich G.: Ábrázoló geometria, Nemzeti Tankönyvkiadó Rt., Budapest, 1998
Pintér M.: AutoCAD tankönyv és példatár, ComputerBooks, Budapest, 2006
Technical drawing in Photonics
Technical drawing in Photonics