5.projection of-points-engineering108.com

May 12, 20171 like74 views

This document discusses the projections of points in space and their orientation. It covers 9 different positions or orientations that a point can have based on its relationship to the horizontal and vertical planes. For each position, it provides an example point (A1, A2, etc.), diagrams to illustrate its location in 3D space and its projections onto the 2D planes, and conclusions about its true view (T.V.) and front view (F.V.) in both 3D and 2D. The 9 positions are: 1) above horizontal plane and in front of vertical plane, 2) above horizontal plane and behind vertical plane, 3) below horizontal plane and behind vertical plane, 4) below horizontal plane and in front of vertical

Engineering

(d) Projections of Right & Regular Solids
like;
(Prisms, Pyramids, Cylinder and Cone)
SOLID 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

5.projection of-points-engineering108.com

(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 Space

(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 Space

.
.
.
.
.
X
Y
a1’
A1
a1
a1’
a1
YX
X
Y
POSITION: 1 (I Qua.)
POINT
A1
Above H.P.
In Front Of V.P.
A1- Point
a1’- F.V.
a1 - T.V.
CONCLUSIONS:
In 3D In 2D
Point, Above
H.P.
Point, In-
Front Of V.P.
T.V.
Below XY
F.V.
Above XY
(3D)
(2D)

.
.
.
.
.
POINT
A2
Above H.P.
Behind V.P.
(3D)
(2D)
X
Y
X Y
A2
a2
a2’
a2
a2’
A2- Point
X
a2’- F.V.
Y a2 - T.V.
CONCLUSIONS:
In 3D
Point, Above
H.P.
Point,
Behind V.P.
T.V.
Above XY
F.V.
Above XY
In 2D
POSITION:2 (II Qua.)

a3
A3
POINT
A3
Below H.P.
Behind V.P.
a3’
X
Y
.
.a3
a3’
X
Y
X Y
(2D)
(3D)
A3- Point
a3’- F.V.
a3- T.V.
CONCLUSIONS:
In 3D
Point, Below
H.P.
Point Behind
V.P.
T.V.
Above XY
F.V.
Below XY
In 2D
.
.
.
POSITION: 3 (III Qua.)

A4
a4
.
a4’
.
a4’
X
Y
X
Y
X Y
.
(2D)
(3D)
POINT
A4
Below H.P.
In Front of V.P.
A4- Point
a4’- F.V.
a4- T.V.
CONCLUSIONS:
In 3D
Point, Below
H.P.
Point, In
Front Of V.P.
T.V.
Below XY
F.V.
Below XY
In 2D
.
.a4
POSITION: 4 (IV Qua.)

.
.
.
.
POINT
A5
Above H.P.
In V.P.
In 3D In 2D
Point, Above
H.P.
Point,
In V.P.
T.V.
On XY
F.V.
Above XY
Y
X
a5’
A5
a5
a5’
a5
X Y
A5 X
Y
(3D)
(2D)
A5- Point
a5’- F.V.
a5 - T.V.
CONCLUSIONS:
POSITION: 5

.POINT
A6
Below H.P.
In V.P.
X
Y
X
Y
A6
a6
a6’
a6’.
X Y
(2D)
a6
.
A6
(3D)
.
A6- Point
a6’- F.V.
a6- T.V.
CONCLUSIONS:
In 3D
Point, Below
H.P.
Point In V.P.
T.V.
On XY
F.V.
Below XY
In 2D
POSITION: 6

A7
.
.
POINT
A7
In Front of V.P.
In H.P.
A7
a7
a7’
X
Y
Y
X
(3D)
(2D)
YX
A7 Point
.
.
a7’- F.V.
a7’
a7
T.V.
Below XY
Point, In-
Front Of V.P.
CONCLUSIONS:
In 3D In 2D
Point In H.P. F.V.
On XY
a7 - T.V.
POSITION: 7

A8
.
.
POINT
A8
In H.P.
Behind V.P.
Y
X
Y
X
A8
a8
a8’
X Y
(3D)
(2D)
a8
.
.a8’
A8- Point
a8’- F.V.
a8 - T.V.
F.V.
On XY
Point, In
H.P.
CONCLUSIONS:
In 3D
Point,
Behind V.P.
T.V.
Above XY
In 2D
POSITION: 8

POINT
A9
In V.P.
In H.P
(3D)
(2D)
X
Y
YX
.A9
A9- Point
X
a9’
a9’- F.V.
.a9’
a9
a9
A9
CONCLUSIONS:
In 3D In 2D
Point, In
H.P.
F.V.
On XY
T.V.
On XY
Point,
In V.P.
a9 - T.V.
POSITION: 9

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1. SOLID GEOMETRY

2. (d) Projections of Right & Regular Solids like; (Prisms, Pyramids, Cylinder and Cone) SOLID 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 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 Space

6. . . . . . X Y a1’ A1 a1 a1’ a1 YX X Y POSITION: 1 (I Qua.) POINT A1 Above H.P. In Front Of V.P. A1- Point a1’- F.V. a1 - T.V. CONCLUSIONS: In 3D In 2D Point, Above H.P. Point, In- Front Of V.P. T.V. Below XY F.V. Above XY (3D) (2D)

7. . . . . . POINT A2 Above H.P. Behind V.P. (3D) (2D) X Y X Y A2 a2 a2’ a2 a2’ A2- Point X a2’- F.V. Y a2 - T.V. CONCLUSIONS: In 3D Point, Above H.P. Point, Behind V.P. T.V. Above XY F.V. Above XY In 2D POSITION:2 (II Qua.)

8. a3 A3 POINT A3 Below H.P. Behind V.P. a3’ X Y . .a3 a3’ X Y X Y (2D) (3D) A3- Point a3’- F.V. a3- T.V. CONCLUSIONS: In 3D Point, Below H.P. Point Behind V.P. T.V. Above XY F.V. Below XY In 2D . . . POSITION: 3 (III Qua.)

9. A4 a4 . a4’ . a4’ X Y X Y X Y . (2D) (3D) POINT A4 Below H.P. In Front of V.P. A4- Point a4’- F.V. a4- T.V. CONCLUSIONS: In 3D Point, Below H.P. Point, In Front Of V.P. T.V. Below XY F.V. Below XY In 2D . .a4 POSITION: 4 (IV Qua.)

10. . . . . POINT A5 Above H.P. In V.P. In 3D In 2D Point, Above H.P. Point, In V.P. T.V. On XY F.V. Above XY Y X a5’ A5 a5 a5’ a5 X Y A5 X Y (3D) (2D) A5- Point a5’- F.V. a5 - T.V. CONCLUSIONS: POSITION: 5

11. .POINT A6 Below H.P. In V.P. X Y X Y A6 a6 a6’ a6’. X Y (2D) a6 . A6 (3D) . A6- Point a6’- F.V. a6- T.V. CONCLUSIONS: In 3D Point, Below H.P. Point In V.P. T.V. On XY F.V. Below XY In 2D POSITION: 6

12. A7 . . POINT A7 In Front of V.P. In H.P. A7 a7 a7’ X Y Y X (3D) (2D) YX A7 Point . . a7’- F.V. a7’ a7 T.V. Below XY Point, In- Front Of V.P. CONCLUSIONS: In 3D In 2D Point In H.P. F.V. On XY a7 - T.V. POSITION: 7

13. A8 . . POINT A8 In H.P. Behind V.P. Y X Y X A8 a8 a8’ X Y (3D) (2D) a8 . .a8’ A8- Point a8’- F.V. a8 - T.V. F.V. On XY Point, In H.P. CONCLUSIONS: In 3D Point, Behind V.P. T.V. Above XY In 2D POSITION: 8

14. POINT A9 In V.P. In H.P (3D) (2D) X Y YX .A9 A9- Point X a9’ a9’- F.V. .a9’ a9 a9 A9 CONCLUSIONS: In 3D In 2D Point, In H.P. F.V. On XY T.V. On XY Point, In V.P. a9 - T.V. POSITION: 9

15. PROJECTIONS OF POINTS

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