The document discusses different types of 3D projections including parallel, perspective, and their variations. Parallel projection projects points onto the view plane using parallel lines while perspective projection uses lines that converge at a single center point. Specific types covered include orthographic, oblique, axonometric, one-point, two-point and three-point perspective projections. Parallel projection can be represented by a transformation matrix while perspective uses matrices with divisions by z to simulate depth.

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)