• 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

1.5.4. Unit-Summary

There are three different types of transformations:

• Translation
• Scaling
• Rotation

To combine these transformations easily, we use homogeneous coordinates. In homogeneous coordinates we add a third coordinate (W) to a point (x, y). By dividing the x- and y-coordinate by W, we receive coordinates of the form (x/W, y/W, 1). By doing so, the translation can be expressed as a multiplication. Therefore we are able to combine the three transformations by only calculating matrix products.

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