• 1. Computer Graphics
  • 1.1. Screen
  • 1.2. Colours
  • 1.3. Rasterisation
  • 1.4. Anti-Aliasing
  • 1.5. Geometric Transformations
    • 1.5.1. Geometric Transformations
    • 1.5.2. Homogeneous Coordinates
    • 1.5.3. Exemplary Computation
    • 1.5.4. Unit-Summary
  • 1.6. Curves
  • 1.7. Paths
  • 1.8. Self Assessment
  • 1.9. Summary
  • 1.10. Recommended Reading
  • 1.11. Glossary
  • 1.12. Bibliography
  • 1.13. Metadata

1.5. Geometric Transformations

Learning Objectives

• You will be able to list the three transformation types.
• You will be able to distinguish the transformation types by their formulas.
• You will be able to list the main characteristics of homogeneous coordinates.

Introduction

You are certainly already familiar with the three geometric transformation types: translation, scaling and rotation. In this chapter we repeat their characteristics and their formula.

You will see that translation, addition and multiplication expressed in the usual matrix form cannot be combined that easily. Whereas the use of homogeneous coordinates allows to treat all three transformations as multiplications and alleviates their combination. That's why we introduce homogeneous coordinates and their principles in this chapter.

We will concentrate on tranformations in the 2D-Space.

Update: 26.1.2012 (eLML) - Contact - Print (PDF) - © CartouCHe 2004-2007 (Creative Commons) - layout based on YAML