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Erschienen in:
2019 | OriginalPaper | Buchkapitel
3. General Properties of Splines
verfasst von : Alvin Penner
Erschienen in: Fitting Splines to a Parametric Function
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Abstract
Basic properties of Bézier curves and B-splines are summarized. These are piecewise continuous functions of a given degree, except where they meet at breakpoints. The individual segments are defined in terms of the basis functions which operate on each interval. The level of continuity at breakpoints is determined by a knot vector. The individual segments can be adjusted using control points. Relationships between different representations of a B-spline can be obtained using knot insertion. These relationships can be used to either initialize a complex spline using a simpler type, or to decompose a B-spline into a sequence of Bézier curves which may be more easily drawn on a computer.