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In numerical analysis, a B-spline is a type of spline function designed to have minimal support (overlap) for a given degree, smoothness, and set of breakpoints, making it a fundamental building block for all spline functions of that degree. A B-spline is defined as a piecewise polynomial of order , meaning a degree of . 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. 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.
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