Computer Graphics Unit-3 3D Projection contain Parallel and Perspective Projection and its type

1. 3D Projection
By:
Arvind Kumar
Assistant Professor
(Vidya College of Engineering)

2. Projection
Mapping of 3D viewing coordinates to 2D screen
coordinates
cgvr.korea.ac.kr
- By Arvind Kumar

3. Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Projection
Parallel Perspective
Orthographic Oblique
Top
Front
Side
Axonometric Cabinet
Cavalier
Other
One-point
Two-point
Three-point

4. Parallel & Perspective
cgvr.korea.ac.kr
- By Arvind Kumar
Parallel Projection:
Perspective Projection:

5. Parallel Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Parallel Projection :
Center of projection is at infinity.
-Direction of projection (DOP) same for all points
View Plane
DOP

6. Orthographic Parallel Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Orthographic Parallel Projection :
The projection is perpendicular to the view
plane

7. Orthographic Parallel Projection
cgvr.korea.ac.kr
- By Arvind Kumar
The projection is perpendicular to the view plane
Front
Top Side

8. Orthographic Parallel Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Axonometric Projection: It uses projection planes
that are not normal to a principle axis.
Type of Axonometric:
Isometric : All three principle axis are foreshortened equally.
Dimetric: Two Principle axis are foreshortened equally.
Trimetric: All three principle axis are foreshortened unequally.

9. Oblique Parallel Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Oblique Parallel Projection :
– The projectors are inclined with respect to the
view plane.

10. Oblique Parallel Projection
cgvr.korea.ac.kr
- By Arvind Kumar
DOP not perpendicular to view plane
Cavalier- DOP at 45ᵒ
Cabinet- DOP at 63.4ᵒ
Cavalier
(DOP at 45 )
Cabinet
(DOP at 63.4 )

11. Parallel Projection Matrix
cgvr.korea.ac.kr
- By Arvind Kumar
Parallel Projection transformation
)sin(
)cos(
tan
,tan
sin,cos
1
1
1





Lzyy
Lzxx
zL
z
L
L
z
LyyLxx
p
p
pp




Where L1 is the inverse of tan α , which is also the value of
L when z=1

12. Parallel Projection Matrix
cgvr.korea.ac.kr
- By Arvind Kumar







































11000
0000
0sin10
0cos01
1
1
z
y
x
L
L
w
z
y
x
p
p
p
p















1000
0000
0sin10
0cos01
1
1


L
L
parallelM

13. Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Projection
Parallel
Orthographic Oblique
Top
Front
Side
Axonometric Cabinet
Cavalier
Other
One-point
Two-point
Three-point
Perspective

14. Perspective Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Perspective Projection :
The line of projection are not parallel. They all
converge at a single point called the “Center of
Projection.”

15. Perspective Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Perspective Projection :







































10100
0100
0010
0001
z
y
x
Dw
z
y
x
p
p
p
p













0100
0100
0010
0001
D
Mpersp

16. Perspective Projection
cgvr.korea.ac.kr
- By Arvind Kumar
Perspective projection of any set of parallel
lines that are not parallel to the projection
plane converge to a “Vanishing Point”.
Type of Perspective Projection :
One-Point Perspective
Two-Point Perspective
Three-Point Perspective

17. One-Point Perspective
cgvr.korea.ac.kr
- By Arvind Kumar
It is based on single vanishing point. Hence , object
is placed so that one of its surfaces is parallel to the
plane of projection.
One-point perspective
(Single vanishing Point)

18. Two-Point Perspective
cgvr.korea.ac.kr
- By Arvind Kumar
In this two surfaces of the object have vanishing
point.
Two-point perspective
(Two vanishing Point)

19. Three-Point Perspective
cgvr.korea.ac.kr
- By Arvind Kumar
None of the axes are parallel to the plane of
projection
Three-point perspective
(Three vanishing Point)