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Kumar Vishal, Lovely Professional University Unit 6: 2-D Transformation

Unit 6: 2-D Transformation

CONTENTS
Objectives
Introduction
6.1 Transformation Matrix
6.1.1 Translation Transformation
6.1.2 Scaling Transformation
6.1.3 Reflection Transformation
6.1.4 Rotation Transformation

6.1.5 Shear Transformation
6.2 Homogeneous Coordinate System
6.3 Composite and Inverse Transformations
6.4 Affine Transformation
6.5 Summary
6.6 Keywords

6.7 Self Assessment
6.8 Review Questions
6.9 Further Readings

Objectives
After studying this unit, you will be able to:

• Define transformation matrix
• Explain homogeneous co-ordinate system
• Discuss composing and inverting of 2-D transformation
• Explain affine transformation
Introduction

Any object or image represented in a graph with only X and Y axis is called two-dimension or 2-D
object or image. The graph with X and Y axis is called 2-D space. Any object represented in this space
can be mapped or transformed. Mapping or transformation means changing or modifying the various
parameters of an object used to define the object such as length, angle, area, position, and so on.
Transformations that cause such modifications are called linear transformations.

Matrix is the mathematical tool used to carry out linear transformation. This provides easy and accurate
transformation values of the object before and after transformation. In computer graphics, a graphic
designer can write programs to represent an object in the matrix form and apply transformations on the
object. Thus, the use of matrix to transform a 2-D object not only helps the programmer to define the
object but also to have a good control over the object that is being transformed.

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