Lecture Computer graphics: Lecture 16 - Fasih ur Rehman

This chapter discuss the purpose of the components required for successful communications; describe these uses of computer communications: wireless messaging services, wireless Internet access points, cybercafés, global positioning systems, collaboration, groupware, voice mail, and Web services;

Computer Graphics

Lecture 16 Fasih ur Rehman

Last Class

• Homogeneous transformations

• Types of Transformations

– Linear Transformations

– Affine Transformations

– Projective Transformations

• Combining Homogeneous transformations

Today’s Agenda

• 3D Transforms

• Inverse Rotation

• Clipping

3D Transforms

• The idea of 3D transforms is the same as that of 2D

– A 3D point is represented by (x, y, z)

– Homogeneous Coordinates are defined as

• A 4th Coordinate is added to every 3D point

• (x, y, z, t) represents (x/t, y/t, z/t)

• (x, y, z, 0) represents infinity

• (0, 0, 0, 0) is not allowed

General 3D Homogeneous

Transform

w z y x

p o

n m

l k

j i

h g

f e

d c

b a

w z y x

' ' ' '

• Scaling matrix

w z y

x c

b a

w z y x

1 0 0 0

0 0

0

0 0 0

0 0 0 '

' '

• Translation matrix

w z y

x c

b a

w z y x

1 0

0 0

1 0

0

0 1

0

0 0

1 '

' '

• Reflection Matrix about yz – plane

• What are other reflection matrices

w z y x

w z y x

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1 '

' '

Other Reflection Matrices

• Rotation about Z – axis

w z y x

w z y x

1 0

0 0

0 1

0 0

0 0

cos sin

0 0

sin cos

' ' '

• Rotation about Y – axis

w z y x

w z y x

1 0

0 0

0 cos

0 sin

0 0

1 0

0 sin

0 cos

' ' '

• Rotation about X – axis

w z y x

w z y x

1 0

0 0

0 cos

sin 0

0 sin

cos 0

0 0

0 1

' ' '

Inverse Rotation

• 3D Transforms

• Inverse Rotation

• Clipping

• Fundamentals of Computer Graphics Third Edition by Peter Shirley and Steve

Marschner

• Interactive Computer Graphics, A

Top-down Approach with OpenGL (Sixth

Edition) by Edward Angel