Contents. Recommended for publishing as a study aid

E.S. Cherdyntsev

COMPUTER GRAPHICS

Recommended for publishing as a study aid

by Editorial Board of Tomsk Polytechnic University

TPU Publishing House

UDC 681.327.1 (0.75.8)

BBC 32.973.202 Я73

CH 459

Cherdyntsev E.S.

CH 459 Computer Graphics: Textbook / E.S. Cherdyntsev;

Tomsk Polytechnic University. – Tomsk: TPU Publishing House, 2012. – 96 pp.

The textbook is intended for studying basics of Computer Graphics, including necessary matrix operations as mathematical basis of Computer Graphics (2D and 3D transformations, use of homogeneous coordinate system), and basic Computer Graphics algorithms.

The study aid has been developed in the framework of the TPU Bachelor Degree Program “Applied Informatics” at the Control System Optimization Department of TPU.

UDC 681.327.1 (0.75.8)

BBC 32.973.202 Я73

Reviewers

Doctor of Engineering, Professor of the Tomsk Polytechnic University

O.G. Berestneva

Doctor of Engineering, Chief of the Information Technology Department of Tomsk Oil and Gas Research and Design Institute

A.A. Naprushkin

© STE HPT TPU, 2012

© Cherdyntsev E.S., 2012

© Design. Tomsk Polytechnic University Publishing House, 2012

Contents

Preface. 6

Introduction to Computer Graphics. 7

Chapter 1. Two-Dimensional Transformations. 12

1.1. Point Transformations. 12

1.2. Parallel Lines Transformation. 14

1.3. Intersecting Lines Transformation. 15

1.4. Rotation. 16

1.5. Reflection. 18

1.6. Scaling. 19

1.7. Composite Transformations. 20

1.8. Unit Square Transformation. 21

1.9. Homogeneous Coordinates. 23

1.10. Rotation around an Arbitrary Point 24

1.11. Reflection about an Arbitrary Line. 24

1.12. Geometric Interpretation of Homogeneous Coordinates. 25

1.13. The Point at Infinity. 26

Self-Study Questions. 29

Chapter 2. 3D Transformations and Projections. 31

2.1. Introduction. 31

2.2. 3D Scaling. 32

2.3. 3D Shearing. 32

2.4. 3D Rotation. 33

2.5. 3D Reflection. 34

2.6. 3D Translation. 34

2.7. 3D Rotation around an Arbitrary Axis. 35

2.8. Affinity and Perspective Geometry. 37

2.9. Orthographic Projections. 38

2.10. Axonometric Projections. 39

2.11. Perspective Transformations. 44

2.12. Vanishing Points. 48

2.13. Plane Equations. 50

Self-Study Questions. 52

Chapter 3. Curves. 53

3.1. Non-Parametric Curves. 53

3.2. Parametric Curves. 53

3.3. General Equations for Conic Sections. 55

3.4. Representation of Spatial Curves. 56

3.5. Cubic Splines. 57

3.6. Parabolic Interpolation. 58

3.7. Bezier Curves. 58

Self-Study Questions. 59

Chapter 4. Raster Graphics. 60

4.1. Line Drawing Algorithms. 60

4.2. Simplest Line Drawing Algorithm.. 61

4.3. Bresenham's Line Algorithm.. 61

4.4. Bresenham's Circle Algorithm.. 64

4.5. Area Filling on Raster Systems. 68

4.5.1. Scan-Line Polygon Fill Algorithm.. 68

4.5.2. Boundary-Fill Algorithm.. 72

4.5.3. Flood-Fill Algorithm.. 75

Self-Study Questions. 76

Chapter 5. Clipping. 77

5.1. Line Clipping Algorithms. 78

5.1.1. Cohen–Sutherland Algorithm.. 78

5.1.2. Liang–Barsky Algorithm.. 79

5.1.3. Cyrus–Beck Algorithm.. 80

5.1.4. Nicholl-Lee-Nicholl Algorithm.. 81

5.2. Polygon Clipping Algorithms. 81

5.2.1. Sutherland–Hodgman Algorithm.. 81

5.2.2. Weiler–Atherton Clipping Algorithm.. 82

5.2.3. Vatti Clipping Algorithm.. 84

Self-Study Questions. 84

Chapter 6. Visible-Surface Detection Algorithms. 85

6.1. Classification of Visible-Surface Detection Algorithms. 85

6.2. Back-Face Detection. 86

6.3. Depth-Buffer Method. 87

6.4. A-Buffer Method. 88

6.5. Scan-Line Method. 89

6.6. Depth-Sorting Method. 90

6.7. Wireframe Methods. 91

Self-Study Questions. 93

Summary. 94

References. 95

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