This book introduces fundamental concepts and principles of 2D and 3D graphics and is written for undergraduate and postgraduate students of computer science, graphics, multimedia, and data science. It demonstrates the use of MATLAB(R) programming for solving problems related to graphics and discusses a variety of visualization tools to generate graphs and plots. The book covers important concepts like transformation, projection, surface generation, parametric representation, curve fitting, interpolation, vector representation, and texture mapping, all of which can be used in a wide variety of educational and research fields. Theoretical concepts are illustrated using a large number of practical examples and programming codes, which can be used to visualize and verify the results.

** **Key Features

Covers fundamental concepts and principles of 2D and 3D graphics

Demonstrates the use of MATLAB(R) programming for solving problems on graphics

Provides MATLAB(R) codes as answers to specific numerical problems

Provides codes in a simple copy and execute format for the novice learner

Focuses on learning through visual representation with extensive use of graphs and plots

Helps the reader gain in-depth knowledge about the subject matter through practical examples

Contains review questions and practice problems with answers for self-evaluation

**Author(s):** Ranjan Parkeh

**Publisher:** CRC Press

**Year:** 2020

**Language:** English

**Pages:** xvi+410

Cover

Half Title

Title Page

Copyright Page

Contents

Preface

Author

CHAPTER 1 Interpolating Splines

1.1 INTRODUCTION

1.2 LINEAR SPLINE (STANDARD FORMS)

1.3 LINEAR SPLINE (PARAMETRIC FORM)

1.4 QUADRATIC SPLINE (STANDARD FORM)

1.5 QUADRATIC SPLINE (PARAMETRIC FORM)

1.6 CUBIC SPLINE (STANDARD FORM)

1.7 CUBIC SPLINE (PARAMETRIC FORM)

1.8 PIECEWISE SPLINES (STANDARD FORM)

1.9 PIECEWISE SPLINES (PARAMETRIC FORM)

1.10 CHAPTER SUMMARY

1.11 REVIEW QUESTIONS

1.12 PRACTICE PROBLEMS

CHAPTER 2 Blending Functions and Hybrid Splines

2.1 INTRODUCTION

2.2 BLENDING FUNCTIONS

2.3 BLENDING FUNCTIONS OF INTERPOLATING SPLINES

2.4 HERMITE SPLINE

2.5 CARDINAL SPLINE

2.6 CATMULL–ROM SPLINE

2.7 BEZIER SPLINE

2.8 SPLINE CONVERSIONS

2.9 CHAPTER SUMMARY

2.10 REVIEW QUESTIONS

2.11 PRACTICE PROBLEMS

CHAPTER 3 Approximating Splines

3.1 INTRODUCTION

3.2 LINEAR UNIFORM B-SPLINE

3.3 CHANGING NUMBER OF CONTROL POINTS

3.4 QUADRATIC UNIFORM B-SPLINE

3.5 JUSTIFICATION FOR KNOT-VECTOR VALUES

3.6 QUADRATIC OPEN-UNIFORM B-SPLINE

3.7 QUADRATIC NON-UNIFORM B-SPLINE

3.8 CUBIC UNIFORM B-SPLINE

3.9 CHAPTER SUMMARY

3.10 REVIEW QUESTIONS

3.11 PRACTICE PROBLEMS

CHAPTER 4 2D Transformations

4.1 INTRODUCTION

4.2 HOMOGENEOUS COORDINATES

4.3 TRANSLATION

4.4 SCALING

4.5 ROTATION

4.6 FIXED-POINT SCALING

4.7 FIXED-POINT ROTATION

4.8 REFLECTION

4.9 FIXED-LINE REFLECTION

4.10 SHEAR

4.11 AFFINE TRANSFORMATIONS

4.12 PERSPECTIVE TRANSFORMATIONS

4.13 VIEWING TRANSFORMATIONS

4.14 COORDINATE SYSTEM TRANSFORMATIONS

4.15 CHAPTER SUMMARY

4.16 REVIEW QUESTIONS

4.17 PRACTICE PROBLEMS

CHAPTER 5 Spline Properties

5.1 INTRODUCTION

5.2 CRITICAL POINTS

5.3 TANGENT AND NORMAL

5.4 LENGTH OF A CURVE

5.5 AREA UNDER A CURVE

5.6 CENTROID

5.7 INTERPOLATION AND CURVE FITTING

5.8 NOTES ON 2D PLOTTING FUNCTIONS

5.9 CHAPTER SUMMARY

5.10 REVIEW QUESTIONS

5.11 PRACTICE PROBLEMS

CHAPTER 6 Vectors

6.1 INTRODUCTION

6.2 UNIT VECTOR

6.3 DIRECTION COSINES

6.4 DOT PRODUCT

6.5 CROSS PRODUCT

6.6 VECTOR EQUATION OF A LINE

6.7 VECTOR EQUATION OF PLANE

6.8 VECTOR ALIGNMENT (2D)

6.9 VECTOR EQUATIONS IN HOMOGENEOUS COORDINATES (2D)

6.10 VECTOR EQUATIONS IN HOMOGENEOUS COORDINATES (3D)

6.11 NORMAL VECTOR AND TANGENT VECTOR

6.12 CHAPTER SUMMARY

6.13 REVIEW QUESTIONS

6.14 PRACTICE PROBLEMS

CHAPTER 7 3D Transformations

7.1 INTRODUCTION

7.2 TRANSLATION

7.3 SCALING

7.4 ROTATION

7.5 FIXED-POINT SCALING

7.6 FIXED-POINT ROTATION

7.7 ROTATION PARALLEL TO PRIMARY AXES

7.8 VECTOR ALIGNMENT (3D)

7.9 ROTATION AROUND A VECTOR

7.10 ROTATION AROUND AN ARBITRARY LINE

7.11 REFLECTION

7.12 SHEAR

7.13 CHAPTER SUMMARY

7.14 REVIEW QUESTIONS

7.15 PRACTICE PROBLEMS

CHAPTER 8 Surfaces

8.1 INTRODUCTION

8.2 PARAMETRIC SURFACES

8.3 BEZIER SURFACES

8.4 IMPLICIT SURFACES

8.5 EXTRUDED SURFACES

8.6 SURFACES OF REVOLUTION

8.7 NORMAL VECTOR AND TANGENT PLANE

8.8 AREA AND VOLUME OF SURFACE OF REVOLUTION

8.9 TEXTURE MAPPING

8.10 SURFACE ILLUMINATION

8.11 NOTES ON 3D PLOTTING FUNCTIONS

8.12 CHAPTER SUMMARY

8.13 REVIEW QUESTIONS

8.14 PRACTICE PROBLEMS

CHAPTER 9 Projection

9.1 INTRODUCTION

9.2 2D PROJECTION

9.3 3D PROJECTION

9.4 MULTI-VIEW PROJECTION

9.5 AXONOMETRIC PROJECTION

9.6 FORESHORTENING FACTORS

9.7 ISOMETRIC, DIMETRIC, AND TRIMETRIC

9.8 OBLIQUE PROJECTION

9.9 PERSPECTIVE PROJECTION

9.10 CHAPTER SUMMARY

9.11 REVIEW QUESTIONS

9.12 PRACTICE PROBLEMS

APPENDIX I: MATLAB® FUNCTION SUMMARY

APPENDIX II: ANSWERS TO PRACTICE PROBLEMS

REFERENCES

INDEX