Page 149 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Unit 9: Translation
Kumar Vishal, Lovely Professional University

Unit 9: Translation Notes

CONTENTS

Objectives
Introduction
9.1 2–Dimensional Translation in C program
9.2 3–Dimensional Translation in C program
9.3 Translating with Matrices

9.4 Translating Addresses
9.5 The Inverse of a Translation
9.6 Summary
9.7 Keywords

9.8 Review Questions
9.9 Further Readings

Objectives

After studying this unit, you will be able to:
• Explain the 2-dimensional translation in c program

• Describe translating with matrices
• Explain the 3-dimensional translation in c program
• Describe translating addresses

• What is the inverse of a translation?

Introduction

Translation is one of the easiest transformations. A translation goes all points of an object
a fixed distance in a particular direction. It can also be stated in words of two frames by
expressing the coordinate system of object in terms of translated frames. We can develop the
matrix involved in a straightforward manner by considering the translation of a single frame.
 
If we are given a frame, F = (, , wo a translated frame would be one that is given by
uv
, )
 
, )
F = (, ,uv wo that is, the origin is moved, and the vectors stay the same. If we write O in
terms of the previous frame by
If we write O in terms of the previous frame by
  
O = au + bv + cw + O
then we can write the frame F in terms of the frame F by
 
u
È 1 000˘ È ˘ u È ˘

Í 01 00 ˙ Í ˙ v  Í Í ˙
v
Í
Í ˙ Í ˙ =  ˙

Í 00 10˙ Í ˙ Í w ˙
w
Í ˙ Í ˙ Í ˙
O
Î ab c 1 ˚ Î ˚ Î O ¢ ˚
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