Some of theses properties may sound somewhere obvious, but they are presented here because they are still valid for Bézier curves of higher degree
The degree of the polynomial is always one less than the number of control points. In computer graphics, we generally use degree 3. Quadratic curves are not flexible enough and going above degree 3 gives rises to complications and so the choice of cubics is the best compromise for most computer graphics applications.
Moving any control point affects all of the curve to a greater or lesser extent. All the basis functions are everywhere non-zero except at the point u = 0 and u = 1
This is the basis of the intuitive 'feel' of a Bézier curve interface.
The curve does not oscillate about any straight line more often than the control point polygon
The curve is transformed by applying any affine transformation (that is, any combination of linear transformations) to its control point representation. The curve is invariant (does not change shape) under such a transformation.
As soon as you move one control point, you affect the entire curve
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Pascal Vuylsteker / eScience / Computer Science / ANU
|Last modified: 20/4/2004
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