B-spline
Sign in to saveIn numerical analysis, a B-spline (short for basis spline) is a type of spline function designed to have minimal support (overlap) for a given degree, smoothness, and set of breakpoints (knots that partition its domain), making it a fundamental building block for all spline functions of that degree. A B-spline is defined as a piecewise polynomial of order n, meaning a degree of n - 1. It is built from sections that meet at these knots, where the continuity of the function and its derivatives depends on how often each knot repeats (its multiplicity). Any spline function of a specific degree can
Article
17 sectionsContents
- Definition
- Properties
- Cardinal B-spline
- P-spline
- Derivative expressions
- Moments of univariate B-splines
- Relationship to piecewise/composite Bézier
- Curve fitting
- Computer-aided design and computer graphics
- Cubic B-Splines
- Clamped B-Splines
- NURBS
- See also
- Notes
- References
- Further reading
- External links
In numerical analysis, a B-spline (short for basis spline) is a type of spline function designed to have minimal support (overlap) for a given degree, smoothness, and set of breakpoints (knots that partition its domain), making it a fundamental building block for all spline functions of that degree. A B-spline is defined as a piecewise polynomial of order n, meaning a degree of n - 1. It is built from sections that meet at these knots, where the continuity of the function and its derivatives depends on how often each knot repeats (its multiplicity). Any spline function of a specific degree can be uniquely expressed as a linear combination of B-splines of that degree over the same knots, a property that makes them versatile in mathematical modeling. A special subtype, cardinal B-splines, uses equidistant knots.
The concept of B-splines traces back to the 19th century, when Nikolai Lobachevsky explored similar ideas at Kazan University in Russia, though the term "B-spline" was coined by Isaac Jacob Schoenberg in 1967, reflecting their role as basis functions.