B-Spline Basis Functions
a high degree is required in order to satisfy a large number of constraints; e.g., (n − 1)-degree is needed to pass a polynomial Bézier curve through n data points. However, high degree curves are inefficient to process and are numerically unstable;
a high degree is required to accurately fit some complex shapes;
single-segment curves (surfaces) are not well-suited to interactive shape design; although Bézier curves can be shaped by means of their control points (and weights), the control is not sufficiently local.
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