1. TA 111/D : Engineering
Graphics
2024-25 II Semester
Dr. Arnab Samanta
Department of Aerospace Engineering
Indian Institute of Technology Kanpur
Office : A-02 Low Speed Laboratory
Phone : 2182
Email : asamanta@iitk.ac.in
3. F
H
bH
bF
aH
aF
TL
H
aA1
bA1
A
1
A2
A1
aA2, bA2
PV of AB
dA
dB
d
A
d
B
d
1
A
d
1
B
d1A
=d1B
Find TL and PV of line AB
Review: Concept of Auxiliary Plane
3
Notice the direction of Projectors
Notice the distance
measurements along Projectors
4. A
B
C
A B C
A
B
C
A
B
C
A B C
A B
C
A
B
C
A
B
C
A
B
C
EV
EV
TS
TS
EV
EV
TS
EV
EV
Note: TS of plane is visible if LOS is perpendicular to EV
Review: True Shape of Planes
4
5. Review: EV, TS of a Plane
TL
H
F
E
V
H
A1
PV
A1 A2
TRUE
SHAPE
Recall:
TS of a plane is available if Line of
Sight is perpendicular to EV
Find EV & TS
of plane ABC
5
View a line contained in the plane in TL
Find PV of the line in TL
6. Review: EV, TS of a Plane
TL
H
F
E
V
H A1
PV (AD)
TS
Find EV & TS of plane
ABC by Rotation
7. Lines that have common ‘space direction’ (i.e. slope
and bearing) are parallel lines
Lines may appear to be parallel in one or even two
views but may not be parallel
Parallel lines will remain parallel in ALL the views
H
F
Are the two lines parallel?
Yes !
Oblique lines are parallel if they
appear parallel in any two
principal orthographic views
P
Review: Parallel Lines
7
9. Given: AB in H and F views; BC only in F view. Complete
line BC in H view such that AB and BC are perpendicular
to each other
F
H
bH
bF
aH
aF
d
TL
aA1
bA1
A1
cF
cA1
cH
If the lines are making a 90o
angle in an auxiliary view where one of
the lines in TL, the lines are perpendicular to each other
Review: Perpendicular Lines
9
H
10. O
F
H
A B
P
Is OP perpendicular to AB?
Yes!
Is the TL of OP seen in F
view?
No, it needs to be found
out in an auxiliary view
Review : Shortest Dist from Point to Line
10
Given: AB in TL and O and AB are in same vertical plane
TL
12. 6. O is not fixed in space,
somewhere in line AB
7. Project OP back in A1, H,
and F views (from A2)
9. How do you locate
point O in A1?
8. Notice that P is in CD
and O is in AB
5. CD is NOT in TL in A2. OP is the
required TL of the shortest distance
between AB and CD (in A2)
AH
BH
CH
DH
OH
PH
AF
CF
DF
BF
OF
PF
BA1
AA1
DA1
PA1
OA1
F
H
H
A1
A
1
A
2
CA2
PV of AB (OA2)
DA2
PA2
900
1. Get TL of AB and project CD in A1
2. Get PV of AB and project CD in A2
4. In A2, which line is in TL? CD or OP?
10. OP is parallel to hinge-
line A1-A2. Why?
TL
Review: Shortest Distance between Two Lines
TL
12
3. Drop perpendicular from PV of
AB to CD in A2
Find shortest distance
between AB and CD
CA1
13. 13
Story so far…
Till now, we learnt the basics…
Point view (PV) of a line
True length (TL) of a line
Edge view (EV) of a plane
True shape (TS) of a plane
We also learnt…
If any line on a plane is in PV, the plane will be in EV
TS of a plane is available when LoS is normal to EV
Correct slope of a line is visible when it is in TL
Conditions of parallelism and perpendicularity of lines
Shortest distance from: point to a line; line to a line
14. 14
A Line in a Plane
How will you determine this?
Get EV of the plane and project the line in
same view. If no part of the line is outside
of EV, then the line is in the plane
There is another easier way…
Check for the ‘common point of
intersection’ between plane and line
If the intersection of AB with lines 1-2 and
3-4 stay aligned in both H and F view,
then AB is in the plane
Let’s check this…
AH
BH
BF
AF
2H
3H
2F
3F
1H
4H
4F
F
H
1F
Line AB is in Plane 1234
Is line AB in plane 1234?
15. A Line in a Plane
AH BH
CH
AF
BF
CF
DH
DF
PH
QH
PF
QF
AA1
BA1
CA1 DA1
PA1
QA1
H
A1
F
H
A plane may be extended to check this
Notice that AC is in TL in H view
Here, the line PQ is indeed contained in the plane that contains the given plane ABC
TL
Get EV of plane, if line is in plane, line will completely lie within the EV
Is there another way to check this?? YES!
Once the plane is extended, check whether common points of intersection
(between line & plane) are aligned (if yes, then line is in the plane)
Is line PQ in plane ABC?
16. 16
AH
BH
CF
AF
DF
DH
1H
2H
1F
BF
CH
F
H
2F
A line is parallel to a plane if
the line remains parallel to a
line in the plane in all views
Line 12 is parallel to plane ABC
A Line Parallel to a Plane
Is line 12 parallel to plane ABC?
17. 17
𝐴𝑉
𝐶𝑉
𝐴𝐻
𝐵𝐻
𝐶𝐻
𝐷𝐻
TL
H
F
F A1
𝐷𝑉
𝐵𝐴1
𝐶𝐴1
𝑃 𝐻
𝑃𝑉
EV
,
𝑃 𝐴1
T
L
𝑄𝐴1
𝑄𝑉
𝑄𝐻
A line is perpendicular to a plane when the
line in TL is at 90o
with the EV of the plane
A Line Perpendicular to a Plane
Find a line perpendicular to plane ABC from point P
900
18. 18
A Line Perpendicular to a Plane
𝐴𝑉
𝐵𝑉
𝐶𝑉
𝐴𝐻
𝐵𝐻
𝐶𝐻
𝐷𝐻
TL
H
F
𝐷𝑉
𝐵𝐴1
𝐶𝐴1
𝑃𝑉
,
T
L
𝑄𝐴1
𝑄𝑉
𝑄𝐻
𝐵𝐴 2
𝐴𝐴2
𝐶𝐴 2
TS
A
1
A
2
,
𝑃 𝐻
F A1
EV
Verify via PV of PQ
PV of PQ
19. 19
Intersections
Intersection occurs very frequently in design world
For example: Joining of ducts in heating and ventilation
work, hookup of pipes in various installations,
placement of braces within structures
Here, we will learn intersection between
lines
line with plane
plane with plane
Later, we will learn intersection between
line with solid
plane with solid
solid with solid
20. 20
Intersection between Lines
Case A: intersecting lines, Case B: non-intersecting lines
The point of intersection of two lines must stay aligned in all views
To establish if two oblique lines intersect or not, two principal
orthographic views are sufficient
21. 21
Do lines AB and
CD intersect?
A
B
A
B
H
F P
A
B
C
D
C D C, D
Two non-oblique lines
NO!
To establish if two non-oblique lines intersect or not, all three
principal orthographic views are needed
The point of intersection will be aligned in all three views
Intersection between Lines
22. 22
Intersection of a Line and a Plane
I. Edge View Method
1A
4A
2A , XA
5A
3A EV123
A H
3H
XH
2H
1H 5H
4H
H
F
2F
3F
XF
1F
5F
4F
MH
MF
No need to get TL of the line
to find intersection point,
an EV of the plane is
sufficient
MA
TL
Does plane 1-2-3 intersect line 4-5?
23. 23
II. Cutting Plane Method
4H
1H
2H
3H
5H
YH
XH
1F
2F
3F
4F
5F
XF
YF
H
F
MH
MF
If line 4-5 intersects plane 1-2-3 in H
view, the point of intersection must lie
on the projection of 4-5 on 1-2-3 in F
view
Lines XH-YH and 4-5 lie on top of each
other in H view
Project line XH-YH in F view and the point
of intersection between XF-YF and 4F-5F
can be projected back to other view
Cutting Plane: Imaginary vertical plane
that contains the given line 4-5, whose
trace XF-YF on the given plane 1-2-3
contains the intersection point M
Intersection of a Line and a Plane
Does plane 1-2-3 intersect line 4-5?
24. 24
Visibility of intersection
M between plane 1-2-3
and line 4-5
Visibility of Intersection
3A
2H
1H 5H
4H
H
F
2F
3F
1F
5F
4F
MH
MF
Line 4-5 must be below
plane 1-2-3 in H view at A
(4-5 is hidden from A to MH)
Line 4-5 must be in-front of plane
1-2-3 in F view at B
(4-5 is visible from B to MF)
A
B
Line 1-2 is seen first
and line 4-5 is seen
second in F view
Line 4-5 is seen first and line
2-3 is seen second in H view
Note: Visibility always reverses at the
intersection point / piercing point
Projection Method
i. Select an apparent point
of intersection between
two lines (say 4-5 and 1-2)
ii. Project it to an adjacent
view
iii. Check which of the two
lines is seen first along the
projector in the adjacent
view
iv. The line seen first will be
visible and the other line
will be hidden in the
original view
25. 25
Visibility of intersection
M between plane 1-2-3
and line 4-5
Visibility in Edge View
1A
4A
2A
5A
3A EV
A H
3A
XH
2H
1H 5H
4H
H
F
2F
3F
XF
1F
5F
4F
MH
MF
Notice the EV and find
which part of line 4-5 is
hidden in H view
MA
Similarly, find which
part is hidden in F view
TL
26. 26
Intersection of two Planes
I. Edge View Method
2H
3H
4H’
1H
4H
5H
7H
6H
TL
H
F 1F
7F
4F
3F
2F
4F’
6F
5F
H A
6A
3A
1A
7A
5A
2A
4A
QH
PH
QF
PF
EV(1234)
QA
PA
PQ is the desired Line of Intersection
Line of intersection between
planes 1-2-3-4 and 5-6-7
27. 27
Intersection of two Planes
1H
XH
CH
6H
4H
3H
2H
7H
5H
QH
PH
1F
6F
2F
5F
7F
4F
CF
3F
PF
XF
H
F
DH
DF YF
YH
PQ is the desired Line of Intersection
II. Cutting Plane Method Line of intersection between
planes 1-2-3-4 and 5-6-7
QF
30. 30
Angle between two Planes
The angle would be available in the auxiliary
plane showing the two planes in EV
Step 1: Draw a common line in TL
Step 2: Draw PV of this common line
– The same auxiliary view would give the angle
between two planes
33. 33
H
F
1H
2H
4H
3H
5H
6H
TL
1F 2F
3F 4F
5F 6F
E
V
EV
TRUE
ANGLE
If the planes are in their EVs, the angle
between EVs is the true angle between planes
TL Available in one of the
principal orthographic planes;
No auxiliary view needed
Angle between Two Planes
Special Case
34. 34
DF
E
V
The line must be in TL and plane in EV
First get the plane in EV & project the line
in A1
F
H AH
BH
CH
DH
T
L
H
A1
BF
BA1
AF
EH
EF
EA1
AA1
A
1
A
2
CA2
AA2
DA3
BA2
EA2
TS
CA1
DA1
CF A2
A3
T
L
T
R
U
E
A
N
G
L
E
AA3
BA3
CA3
EA3
DA2
True angle between an oblique line
and an oblique plane?
Now get the plane in true
shape and project line in A2
Take an auxiliary plane such that line is in TL and plane in EV
Now what?
Angle between a Line and a Plane
EV
