Three dimensional rotation in Computer graphics

2. CONTENTS
C
O
N
T
E
N
T
S
What is 3 D rotation?
1
X axis rotation
2
Y axis rotation
3
Z axis rotation
4

3. In Computer graphics, 3D Rotation is
a process of rotating an object with
respect to an angle in a three
dimensional plane. Consider a point
object O has to be rotated from one
angle to another in a 3D plane. Let -
Initial coordinates of the object O =
(Xold, Yold, Zold)
What is 3 D
rotation?

4. Fo r X - A x i s Ro tat i o n
In this kind of rotation, the object is
rotated parallel to the x-axis (principal
axis), where the x coordinate remains
unchanged and the rest of the two
coordinates y and z only change.
Consider a point with initial coordinate
P(x,y,z) in 3D space is made to rotate
parallel to the principal axis(x-axis).
The coordinate position would change
to P'(x,y,z).

5. A r o t a t i o n t r a n s f o r m a t i o n m a t r i x i s
u s e d t o c a l c u l a t e t h e n e w p o s i t i o n
c o o r d i n a t e P ’ .

6. F o r Y a x i s r o t a t i o n
In this kind of rotation, the object is
rotated parallel to the y-axis
(principal axis), where the y
coordinate remains unchanged and
the rest of the two coordinates x and
z only change.

7. C o n s i d e r a p o i n t w i t h i n i t i a l
c o o r d i n a t e P ( x , y , z ) i n 3 D s p a c e i s
m a d e t o r o t a t e p a r a l l e l t o t h e
p r i n c i p a l a x i s ( y - a x i s ) . T h e
c o o r d i n a t e p o s i t i o n w o u l d c h a n g e
t o P ' ( x , y , z ) .

8. For Z axis rotation
In this kind of rotation, the object is rotated
parallel to the z-axis (principal axis),
where the z coordinate remains
unchanged and the rest of the two
coordinates x and y only change.

9. C o n s i d e r a p o i n t w i t h i n i t i a l
c o o r d i n a t e P ( x , y , z ) i n 3 D s p a c e i s
m a d e t o r o t a t e p a r a l l e l t o t h e
p r i n c i p a l a x i s ( y - a x i s ) . T h e c o o r d i n a t e
p o s i t i o n w o u l d c h a n g e t o P ' ( x , y , z ) .

10. THANK YOU