Given a set of points

,

, this Demonstration interpolates between these points using a degree

nonrational B-spline curve. Assigning a parameter value

to each

and selecting an appropriate knot vector

leads to the

system of linear equations

. (1)

The control points

are the

unknowns. Let

be the number of coordinates in the

(typically 2, 3, or 4). Equation (1) has one coefficient matrix with

elements in the right-hand column and, correspondingly,

solution sets for the

coordinates of the

.

The problem of choosing the

and

remains; their choice affects the shape and parametrization of the curve. Assume that the parameter lies in the range

. Three common methods of choosing the

are, with (

):

let

, then

let

, then

Lastly, the following method was used to generate the knots (

):

Here is an example of an application of this algorithm:

Let

, and assume the interpolation is a cubic curve. Use equations (3) and (5) to compute the

and

, and then set up the system of linear equations, equation (1). The separate chord lengths are given by

,

,

,

and the total chord length is

. Thus

So

.

Thus

The system of linear equations is then represented by

[1] L. Piegl and W. Tiller,

*The NURBS Book*, 2nd ed., Berlin: Springer–Verlag, 1997.