This document discusses the projection of points and lines in space. It begins by introducing the topic and presenters. It then covers the following: 1. The orientation and projection of points in different quadrants and planes. Various examples are shown with diagrams. 2. The definition and notation used for projecting straight lines, including their true length, front and top views, and inclinations. 3. The different positions of lines in relation to the horizontal and vertical planes, including perpendicular, parallel, and oblique lines. Several examples are shown diagrammatically.

1. PROJECTION OF POINTS
AND LINES
PREPARED BY : - B.E.(IT)
EN NO NAME
16BEITV120 DHRUNAIVI
16BEITV121 PRITEN
16BEITV122 ANKUR
16BEITV123 DHRUMIL
16BEIV124
16BEIV125
DARSHAN
NIKUNJ
Guided By : -
PROF. ROMA PATEL
INFORMATION TECHNOLOGY

2. PROJECTION OF
POINTS

3. (d) Projections of Right & Regular Solids like;
(Prisms, Pyramids, Cylinder and Cone)
SOLID GEOMETRYSOLID GEOMETRY
Following topics will be covered in Solid
Geometry ;
(a) Projections of Points in space
(b) Projections of Lines
(Without H.T. & V.T.)
(c) Projections of Planes

4. (1)In quadrant I (Above H.P & In
Front of V.P.)
(2) In quadrant II (Above H.P & Behind
V.P.)
(3) In quadrant III (Below H.P &
Behind V.P.)
(4) In quadrant IV (Below H.P & In
Front of V.P.)
Orientation of Point in SpaceOrientation of Point in Space

5. (5) In Plane (Above H.P. & In V.P.)
(6) In Plane (Below H.P. & In V.P.)
(7) In Plane ( In H.P. & In front of V.P.)
(8) In Plane ( In H.P. & Behind V.P.)
(9) In Plane ( In H.P. & V.P.)
Orientation of Point in SpaceOrientation of Point in Space

6. ..
..
..
..
..
XX
YY
aa11’’
AA11
aa11
aa11’’
aa11
YYXX
XX
YY
POSITION: 1 (I Qua.)POSITION: 1 (I Qua.)
POINTPOINT Above H.P.Above H.P.
In Front Of V.P.In Front Of V.P.
AA11- Point- Point
aa11’- F.V.’- F.V.
aa11 - T.V.- T.V.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D In 2DIn 2D
Point, AbovePoint, Above
H.P.H.P.
Point, In- FrontPoint, In- Front
Of V.P.Of V.P.
T.V.T.V.
Below XYBelow XY
F.V.F.V.
Above XYAbove XY
(3D)(3D)
(2D)(2D)

7. ..
..
..
..
..
POINTPOINT
Above H.P.Above H.P.
Behind V.P.Behind V.P.
(3D)(3D)
(2D)(2D)
XX
YY
XX YY
AA22
aa22
aa22’’
aa22
aa22’’
AA22- Point- Point
XX
aa22’- F.V.’- F.V.
YY aa22 - T.V.- T.V.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D
Point, AbovePoint, Above
H.P.H.P.
Point, BehindPoint, Behind
V.P.V.P.
T.V.T.V.
Above XYAbove XY
F.V.F.V.
Above XYAbove XY
In 2DIn 2D
POSITION:2 (II Qua.)POSITION:2 (II Qua.)

8. aa33
AA33
POINTPOINT Below H.P.Below H.P.
Behind V.P.Behind V.P.
aa33’’
XX
YY
..
..aa33
aa33’’
XX
YY
XX YY
(2D)(2D)
(3D)(3D)
AA33- Point- Point
aa33’- F.V.’- F.V.
aa33- T.V.- T.V.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D
Point, BelowPoint, Below
H.P.H.P.
Point BehindPoint Behind
V.P.V.P.
T.V.T.V.
Above XYAbove XY
F.V.F.V.
Below XYBelow XY
In 2DIn 2D
..
..
..
POSITION: 3 (III Qua.)POSITION: 3 (III Qua.)

9. AA44
aa44
..
aa44’’
..
aa44’’
XX
YY
XX
YY
XX YY
..
(2D)(2D)
(3D)(3D)
POINTPOINT Below H.P.Below H.P.
In Front of V.P.In Front of V.P.
AA44- Point- Point
aa44’- F.V.’- F.V.
aa44- T.V.- T.V.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D
Point, BelowPoint, Below
H.P.H.P.
Point, InPoint, In
Front Of V.P.Front Of V.P.
T.V.T.V.
Below XYBelow XY
F.V.F.V.
Below XYBelow XY
In 2DIn 2D
..
..aa44
POSITION: 4 (IV Qua.)POSITION: 4 (IV Qua.)

10. H.P.
H.P.
H.P.
H.P. V.P.
V.P.
..
..
..
..
POINTPOINT Above H.P.Above H.P.
In V.P.In V.P.
In 3DIn 3D In 2DIn 2D
Point, AbovePoint, Above
H.P.H.P.
Point,Point,
In V.P.In V.P.
T.V.T.V.
On XYOn XY
F.V.F.V.
Above XYAbove XY
YY
XX
aa55’’AA55
aa55
aa55’’
aa55
XX YY
AA55
XX
YY
(3D)(3D)
(2D)(2D)
AA55- Point- Point
aa55’- F.V.’- F.V.
aa55 - T.V.- T.V.
CONCLUSIONS:CONCLUSIONS:
POSITION: 5POSITION: 5

11. ..POINTPOINT Below H.P.Below H.P.
In V.P.In V.P.
XX
YY
XX
YY
AA66
aa66
aa66’’
aa66’’..
XX YY
(2D)(2D)
aa66
..
AA66
(3D)(3D)
..
AA66- Point- Point
aa66’- F.V.’- F.V.
aa66- T.V.- T.V.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D
Point, BelowPoint, Below
H.P.H.P.
Point In V.P.Point In V.P. T.V.T.V.
On XYOn XY
F.V.F.V.
Below XYBelow XY
In 2DIn 2D
POSITION: 6POSITION: 6

12. AA77
..
..
POINTPOINT
In Front of V.P.In Front of V.P.
In H.P.In H.P.
AA77
aa77
aa77’’
XX
YY
YY
XX
(3D)(3D)
(2D)(2D)
YYXX
AA77 PointPoint
..
..
aa77’- F.V.’- F.V.
aa77’’
aa77
T.V.T.V.
Below XYBelow XY
Point, In-Point, In-
Front Of V.P.Front Of V.P.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D In 2DIn 2D
Point In H.P.Point In H.P. F.V.F.V.
On XYOn XY
aa77 - T.V.- T.V.
POSITION: 7POSITION: 7

13. AA88
..
..
POINTPOINT
In H.P.In H.P.
Behind V.P.Behind V.P.
YY
XX
YY
XX
AA88
aa88
aa88’’
XX YY
(3D)(3D)
(2D)(2D)
aa88
..
..aa88’’
AA88- Point- Point
aa88’- F.V.’- F.V.
aa88 - T.V.- T.V.
F.V.F.V.
On XYOn XY
Point, InPoint, In
H.P.H.P.
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D
Point, BehindPoint, Behind
V.P.V.P.
T.V.T.V.
Above XYAbove XY
In 2DIn 2D
POSITION: 8POSITION: 8

14. POINTPOINT
In VIn V.P..P.
In H.PIn H.P
H.P.
H.P.
(3D)(3D)
(2D)(2D)
XX
YY
YYXX
..AA99
AA99- Point- Point
XX
aa99’’
aa99’- F.V.’- F.V.
..aa99’’
aa99
aa99
AA99
CONCLUSIONS:CONCLUSIONS:
In 3DIn 3D In 2DIn 2D
Point, InPoint, In
H.P.H.P.
F.V.F.V.
On XYOn XY
T.V.T.V.
On XYOn XY
Point,Point,
In V.P.In V.P.
aa99 - T.V.- T.V.
POSITION: 9POSITION: 9

15. PROJECTION OF
STRAIT LINE

16. Definition of Straight lineDefinition of Straight line
A straight line is the shortest distance between two
points.
- Top views of two end points of a straight line,
when joined, give the top view of the straight
line.
- Front views of the two end points of a straight
line, when joined, give the front view of the
straight line.
- Both the above projections are straight lines.

17. Orientation of Straight Line in SpaceOrientation of Straight Line in Space
- A line in space may be parallel, perpendicular
or inclined to either the H.P. or V.P. or both.
- It may be in one or both the reference Planes.
- Line ends may be in different Quadrants.
- Position of Straight Line in space can be fixed
by various combinations of data like distance
of its end points from reference planes,
inclinations of the line with the reference
planes, distance between end projectors of the
line etc.

18. Notations used for Straight LineNotations used for Straight Line
True length of the lineTrue length of the line:
Denoted by Capital letters. e.g. AB=100 mm, means
that true length of the line is 100 mm.
Front View LengthFront View Length:
Denoted by small letters. e.g. a’b’=70 mm, means
that Front View Length is 70 mm.
Top View LengthTop View Length:
Denoted by small letters. e.g. ab=80 mm, means
that Top View Length is 80 mm.
Inclination of True Length of Line with H.P.Inclination of True Length of Line with H.P.:
It is denoted by θ. e.g. Inclination of the line with
H.P. (or Ground) is given as 30º means that θ =
30º.

19. Inclination of Front View Length with XYInclination of Front View Length with XY :
It is denoted by α. e.g. Inclination of the
Front View of the line with XY is given as 50º
means that α = 50º.
Inclination of Top View Length with XYInclination of Top View Length with XY :
It is denoted by β. e.g. Inclination of the Top
View of the line with XY is given as 30º means
that β = 30º.
End Projector DistanceEnd Projector Distance:
It is the distance between two projectors
passing through end points of F.V. & T.V.
measured parallel to XY line.
Inclination of True Length of Line with V.P.Inclination of True Length of Line with V.P.:
It is denoted by Φ. e.g. Inclination of the line
with V.P. is given as 40º means that Φ = 40º.

20. Line in Different Positions with respectLine in Different Positions with respect
to H.P. & V.P.to H.P. & V.P.
CLASS A: Line perpendicular to (or in) oneCLASS A: Line perpendicular to (or in) one
reference plane & hence parallel toreference plane & hence parallel to
both the other planesboth the other planes
(1)(1) Line perpendicular to P.P. & (hence) parallelLine perpendicular to P.P. & (hence) parallel
to both H.P. & V.P.to both H.P. & V.P.
(2) Line perpendicular to V.P. & (hence) parallel(2) Line perpendicular to V.P. & (hence) parallel
to both H.P. & P.P.to both H.P. & P.P.
(3) Line perpendicular to H.P. & (hence) parallel(3) Line perpendicular to H.P. & (hence) parallel
to both V.P. & P.P.to both V.P. & P.P.

21. Line in Different Positions with respectLine in Different Positions with respect
to H.P. & V.P.to H.P. & V.P.
CLASS B: Line parallel to (or in) oneCLASS B: Line parallel to (or in) one
reference plane & inclined to otherreference plane & inclined to other twotwo
planesplanes
(1)(1) Line parallel to ( or in) V.P. & inclined to H.P.Line parallel to ( or in) V.P. & inclined to H.P.
byby ..
(2) Line parallel to ( or in) H.P. & inclined to V.P.(2) Line parallel to ( or in) H.P. & inclined to V.P.
byby ..
(3) Line parallel to ( or in) P.P. & inclined to H.P.(3) Line parallel to ( or in) P.P. & inclined to H.P.
byby  & V.P. by& V.P. by ..

22. Line in Different Positions with respectLine in Different Positions with respect
to H.P. & V.P.to H.P. & V.P.
CLASS C: Line inclined to all three referenceCLASS C: Line inclined to all three reference
planes ( Oblique lines )planes ( Oblique lines )
Line inclined to H.P. byLine inclined to H.P. by , to V.P. by, to V.P. by  and also inclinedand also inclined
to profile plane.to profile plane.

23. P.P.
.
H.P.
V.P.
Y
X
B
A
a’
b
’
b
a
b”
a”
z
x
Y
Class A(1) : Line perpendicular to P.P. & henceClass A(1) : Line perpendicular to P.P. & hence
parallel to both the other planesparallel to both the other planes

24. XX
YY
a’a’
b’b’
H.P.
H.P.
V.P.
V.P.
aa
bb
Line perpendicular to P.P. & hence parallel to bothLine perpendicular to P.P. & hence parallel to both
the other planesthe other planes

25. P.P.
P.P.
a”, b”a”, b”
YY11
..
H.P.
H.P.
V.P.
V.P.
a’a’
b’b’
aa
bb
XX
YY
Line perpendicular to P.P. & hence parallel to bothLine perpendicular to P.P. & hence parallel to both
the other planesthe other planes

26. V.P.
V.P.
H.P.
H.P.
YY
XX
AA
BB
bb
aa
a’, b’a’, b’..
XX
Class A(2):Line perpendicular to V.P. & (hence)Class A(2):Line perpendicular to V.P. & (hence)
parallel to both the other Planesparallel to both the other Planes
(i.e. H.P. & P.P.)(i.e. H.P. & P.P.)

27. a’, b’a’, b’
XX
YY
V.P.
V.P.
H.P.
H.P.
aa
bb
..
Line perpendicular to V.P. & (hence) parallel to bothLine perpendicular to V.P. & (hence) parallel to both
the other Planesthe other Planes

28. H.P.
H.P.
V.P.
V.P.
P.P.
P.P.
Class B(3): Line parallel to (or contained by) P.P., inclined toClass B(3): Line parallel to (or contained by) P.P., inclined to
H.P. byH.P. by  & to V.P. by& to V.P. by 
YY
XX
AA
BB
a”a”
b”b”

YY
XX
ZZ
bb
aa
bb
’’
aa
’’



29. H.P.
H.P.
V.PV.P
..
XX
YY
aa bb
a’a’
b’b’


YY
XX
BB
AA
Class C : Line inclined to H.P. byClass C : Line inclined to H.P. by  & V.P. by& V.P. by  ((
i.e. Line inclined to both the planes)i.e. Line inclined to both the planes)

30. V.P.V.P.
H.PH.P
..
P.P.P.P.

Class B(3): Line parallel to (or contained by) P.P.,Class B(3): Line parallel to (or contained by) P.P.,
inclined to H.P. byinclined to H.P. by  & to V.P. by& to V.P. by 

XX
YY
a’a’
b’b’
aa
bb
bb
””
a”a”