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Chapter 10 Projections

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Mathematics for Computer Graphics and Game Programming
This chapter is in the book Mathematics for Computer Graphics and Game Programming
10ChapterProjections10.1 INTRODUCTION 3D viewing operations are more complex than 2D viewing, not only because of the additional dimensions, but also because of limited display surface. In 2D, simple mapping produces an image; in 3D, there are many options depending on how the model is to be viewed—front, side, top, back. There is also a mismatch between the 3D model and the 2D image. To overcome all these differences, projection must be used to map the 2D projection plane; various types of projection are used in order to generate multiple views of a model. Therefore, projection is an important concept of the 3D viewing process. 10.2 PROJECTIONS The problem of projecting a n-dimensional object into a 2D surface has been studied by engineers, architects, and artists for many years. In general, projections transform points in a coordinate system of n-dimensions into points in a coordinate system of a dimension less than n.
© 2019 Walter de Gruyter GmbH, Berlin/Boston

10ChapterProjections10.1 INTRODUCTION 3D viewing operations are more complex than 2D viewing, not only because of the additional dimensions, but also because of limited display surface. In 2D, simple mapping produces an image; in 3D, there are many options depending on how the model is to be viewed—front, side, top, back. There is also a mismatch between the 3D model and the 2D image. To overcome all these differences, projection must be used to map the 2D projection plane; various types of projection are used in order to generate multiple views of a model. Therefore, projection is an important concept of the 3D viewing process. 10.2 PROJECTIONS The problem of projecting a n-dimensional object into a 2D surface has been studied by engineers, architects, and artists for many years. In general, projections transform points in a coordinate system of n-dimensions into points in a coordinate system of a dimension less than n.
© 2019 Walter de Gruyter GmbH, Berlin/Boston

Chapters in this book

  1. Frontmatter i
  2. Contents v
  3. Preface xi
  4. Chapter 1 Introduction to Computer Graphics 1
  5. Chapter 2 Vector Representation of Geometric Entities 29
  6. Chapter 3 Two-Dimensional Transformation 83
  7. Chapter 4 Three-Dimensional Transformation 135
  8. Chapter 5 Parametric Representation of Planar Curves 169
  9. Chapter 6 Parametric Representation of Space Curves 191
  10. Chapter 7 Parametric Representation of Surfaces 215
  11. Chapter 8 Windowing and Clipping 229
  12. Chapter 9 Generation of a 3D Model 249
  13. Chapter 10 Projections 269
  14. Chapter 11 Graphics Programs in C Language 291
  15. Chapter 12 OpenGL with Computer Graphics 311
  16. Chapter 13 Programming Graphics Using OpenGL 323
  17. Index 395
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https://doi.org/10.1515/9781683923572-011

Chapters in this book

  1. Frontmatter i
  2. Contents v
  3. Preface xi
  4. Chapter 1 Introduction to Computer Graphics 1
  5. Chapter 2 Vector Representation of Geometric Entities 29
  6. Chapter 3 Two-Dimensional Transformation 83
  7. Chapter 4 Three-Dimensional Transformation 135
  8. Chapter 5 Parametric Representation of Planar Curves 169
  9. Chapter 6 Parametric Representation of Space Curves 191
  10. Chapter 7 Parametric Representation of Surfaces 215
  11. Chapter 8 Windowing and Clipping 229
  12. Chapter 9 Generation of a 3D Model 249
  13. Chapter 10 Projections 269
  14. Chapter 11 Graphics Programs in C Language 291
  15. Chapter 12 OpenGL with Computer Graphics 311
  16. Chapter 13 Programming Graphics Using OpenGL 323
  17. Index 395
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