B-spline

A B-spline curve is a piecewise polynomial curve defined by the degree of the polynomial, control points, and optional knots and weights. B-splines provide smooth curve continuity and local control, allowing adjustments to individual control points without affecting the entire curve.

The number of weights is the same as the number of control points. The number of knots is the number of control points + degree + 1.

Weights determine how much each corresponding control point influences the curve.

Knots determine the intervals of the polynomials which define the B-spline.

B-splines without knots are also known as Bézier curves. B-splines with knots and weights are also known as NURBS curves.