Transcript Projection of Points

SOLID GEOMETRY
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
(d) Projections of Right & Regular Solids
like;
(Prisms, Pyramids, Cylinder and Cone)
Orientation of Point in Space
(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.)
POSITION: 1 (I Qua.)
POINT Above H.P.
A1
In Front Of V.P.
X
CONCLUSIONS:
In 2D
In 3D
Point, Above
F.V.
H.P.
Above XY
T.V.
X
Point, InFront Of V.P. Below XY
.a1’
Y
A1- Point
a1’- F.V.
a1 - T.V.
.A1 Y
(3D)
.a1
.a1’
X
Y
. a1
(2D)
A2- Point
a2’- F.V.
a2 - T.V.
POSITION:2 (II Qua.)
POINT
A2
Above H.P.
Y
Behind V.P.
CONCLUSIONS:
In 2D
In 3D
Point, Above
F.V.
H.P.
Above XY
T.V.
Point,
Behind V.P. Above XY
A2
.
a2’
.
a2.
Y
(3D)
X
X
.a2
. a 2’
X
(2D)
Y
A3- Point
a
’F.V.
3
Y
a3- T.V.
(3D)
a.3
Y
POSITION: 3 (III Qua.)
POINT
A3
Below H.P.
Behind V.P.
CONCLUSIONS:
In 2D
In 3D
Point, Below
F.V.
H.P.
Below XY
Point Behind
T.V.
V.P.
Above XY
X
.
A3
.a3
X
.a3’
.a3’
X
Y
(2D)
A4- Point
a4’- F.V.
Y
Y a4- T.V.
POSITION: 4 (IV Qua.)
POINT
A4
Below H.P.
X
a. 4
In Front of V.P.
.
CONCLUSIONS:
In 2D
In 3D
Point, Below
F.V.
H.P.
Below XY
T.V.
Point, In
Front Of V.P. Below XY
a4’
.
A4
X
. a 4’
. a4
(3D)
X
Y
(2D)
POSITION: 5
A5- Point
a5’- F.V.
a5 - T.V.
Y
POINT
A5
A5
Above H.P.
.a ’
5
In V.P.
CONCLUSIONS:
In 2D
Point, Above
F.V.
H.P.
Above XY
T.V.
Point,
On XY
In V.P.
In 3D
Y (3D)
.a
X
5
A5
.a5’
X
a
.5
X
(2D)
Y
A6- Point
a6’- F.V.
a6- T.V.
Y
POSITION: 6
Y
POINT
A6
Below H.P.
X
In V.P.
CONCLUSIONS:
In 2D
In 3D
Point, Below
F.V.
H.P.
Below XY X
T.V.
Point In V.P.
On XY
.a
6
A6.a6’
X (3D)
.
a6
A6.a6’
Y
(2D)
A7 Point
POSITION: 7
a7’- F.V.
a7 - T.V.
Y
POINT
A7
In H.P.
a7’
.
In Front of V.P.
X
CONCLUSIONS:
In 2D
In 3D
T.V.
Point, InFront Of V.P. Below XY
Point In H.P.
F.V.
On XY
Y
(3D)
a7
.
A
7
X
X
a
’
7
.
Y
A7 . a 7
(2D)
A8- Point
a8’- F.V.
a8 - T.V.
POSITION: 8
Y
POINT
A8
In H.P.
Behind V.P.
CONCLUSIONS:
In 2D
In 3D
T.V.
Point,
Behind V.P. Above XY
Point, In
H.P.
F.V.
On XY
a8
.
A8
a8’
.
X
A8.a8
X
Y
a
’
8
.
X
(3D)
(2D)
Y
POSITION: 9
POINT
A9
A9- Point
a9’- F.V.
a9 - T.V.
In H.P
In V.P.
CONCLUSIONS:
In 3D
Point, In
H.P.
Point,
In V.P.
In 2D
F.V.
On XY
T.V.
On XY
X
a 9’
.
A9 a 9
Y
(3D)
X
X A9.a9’
a9
Y
(2D)
PROJECTIONS OF
POINTS