• 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. Curves

Learning Objectives

• You will be able to distiguish between cubic and quadratic Bézier curves.
• You will be able to draw a Bézier curve using the "De Casteljau Algorithm".
• You will be able to list at least three main characteristics of Bèzier curves.

Introduction

The majority of the objects of the real-world can not be modelled by approximated straight lines, because the objects have smooth contours. To model objects such as e.g. rivers in a map, we have to introduce smooth curves. A mathematical description of these objects is normally not available. Of course, one can use the coordinates of the infinitely many points of the object as a model, but this is not feasible for a computer with finite storage.

Normally the form of the objects is approximated with pieces of planes, spheres, or other shapes that are easy to describe mathematically. In computer graphics, particularly Bézier curves are used to model smooth objects. That's why the definition and characteristics of Bézier curves are explained in the next few paragraphs.

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