These objects are called "natural" if their curvature equals zero at their boundaries, and their third order, or "cubic" variant is used in constructing Bézier curves.
When knots are inserted into a curve or a tensor product surface, the Oslo algorithm modifies these functions to keep the model up-to-date. A method for evaluating these kinds of functions at a given point is given by De Boor's algorithm. The Kochanek-Bartels type of these expressions feature bias and continuity parameters so that tangents can be altered; by setting all of those parameters to zero, those expressions become the simpler Catmull-Rom type of these functions. A set of control points and a knot vector are used to define the non-uniform type of these basis functionsthat type of them is often called a NURBS and is used in computer assisted design. These objects are called "natural" if their curvature equals zero at their boundaries, and their third order, or "cubic" variant is used in constructing Bézier curves. A piece of metal used by drafters gives its name to, for 10 points, what piecewise-defined polynomials often used in interpolation?
When knots are inserted into a curve or a tensor product surface, the Oslo algorithm modifies these functions to keep the model up-to-date.
splines [or basis splines; or b-splines; prompt on "NURBS"]