B-spline

There are two types of B-spline - uniform and non-uniform.

When the knots are equidistant the B-spline is said to be uniform, otherwise non-uniform.

When the B-spline is uniform, the basis B-splines for a given degree n are just shifted copies of each other.

The constant B-spline is the simplest spline.

Cubic B-splines with uniform knot-vector is the most commonly used form of B-spline.

For examples which go near key points see nonuniform rational B-spline, or Bézier curve.

B-spline and thin plate spline models are commonly used for parameterized transformation fields.

Catmull-Clark (1978) generalized bi-cubic uniform B-spline to produce their subdivision scheme.

This conceptually simple algorithm fit cubic polynomial B-spline curves to the peptide planes.

The class covered Bezier curves, Bezier to B-spline and surfaces.

The term P-spline stands for "penalized B-spline".

The linear B-spline is defined on two consecutive knot spans and is continuous on the knots, but not differentiable.

In particular, the B-Spline basis function coincides with the n-th degree univariate Bernstein polynomial.

The term "B-spline" was coined by Isaac Jacob Schoenberg and is short for basis spline.

It supports subdivision surfaces, b-spline, NURBS and boolean operations.

In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.

Rhino specializes in free-form non-uniform rational B-spline (NURBS) modeling.

NURBS (Non-uniform rational B-spline)

The most commonly used splines are cubic spline, i.e., of order 3-in particular, cubic B-spline and cubic Bézier spline.

A non-uniform B-spline is a curve where the intervals between successive control points are not necessarily equal (the knot vector of interior knot spans are not equal).

A B-spline is simply a generalisation of a Bézier curve, and it can avoid the Runge phenomenon without increasing the degree of the B-spline.

PHIGS+ also introduced more advanced graphics primitives, such as Nonuniform Rational B-spline (NURBS) surfaces.

The main reference for Bézier, B-Spline and NURBS; chapters on mathematical representation and construction of curves and surfaces, interpolation, shape modification, programming concepts.

Most systems today use nonuniform rational B-spline (NURBS) mathematics to describe the surface forms; however, there are other methods such as Gorden surfaces or Coons surfaces .

Each pair was used to fit a cubic spline function, f ( ), where f was a spline function generator that fits the parameters of a natural cubic spline (B-spline).