• 1. Computer Graphics
  • 1.1. Screen
  • 1.2. Colours
  • 1.3. Rasterisation
  • 1.4. Anti-Aliasing
  • 1.5. Geometric Transformations
  • 1.6. Curves
    • 1.6.1. Bézier Curve
    • 1.6.2. Quadratic and Cubic Bézier Curves
    • 1.6.3. De Casteljau Algorithm
    • 1.6.4. Unit-Summary
  • 1.7. Paths
  • 1.8. Self Assessment
  • 1.9. Summary
  • 1.10. Recommended Reading
  • 1.11. Glossary
  • 1.12. Bibliography
  • 1.13. Metadata

1.6.4. Unit-Summary

Bézier curves are used to model objects with smooth contours such as a ball, a teacup etc. Bézier curves are composed of Bernstein basis polynomials of degree n and points P_i called control points. By connecting all control points with lines, we receive the control polygon. The Bézier curve is completely contained in the hull built from the control polygon.

A Bézier curve of degree 2 is called quadratic Bézier curve and a curve of degree 3 is called cubic Bézier curve.

The "De Casteljau Algorithm" is used to construct a Bézier curve or to find a particular point on the curve.

In the following interaction part you find again the different steps of the construction of a Bézier curve using the De Casteljau algorithm.

Be aware that not all applications are able to visualise Bézier curves e.g. some GIS applications. In this case the Bézier curves have to be converted into paths. The higher the number of vertices of the new path the better it equals a Bézier curves. Take into account that such a path needs much more storage space than an original Bézier curves, because of the many vertices.

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