B-spline of order one are step functions defined by

Building a

B-Spline Surface from Elevation Data in OpenGL

In order to keep the splines zero-mean, instead of the original exponential

B-spline [beta](t), we shall use a real-valued function

In this section the

B-spline concept will be extended to two dimensions in order to fit two dimensional scattered data by a surface function.

Here we have introduced two extra cubic

B-splines, [B.

In above equations, Pi's are the n+1 defining polygon vertices, k is the order of the

B-spline and [N.

Ristic, "Efficient fitting of Non-Uniform Rational

B-Spline surfaces using non-organized 3D data," SPIE'S.

Hence a second time domain representation of the complex

B-spline is given by

Least-Squares Fitting of Data with

B-Spline Surfaces.

Some topics covered include:

B-spline surfaces, Box-spline surfaces, convergence and smoothness, evaluation and estimation of surfaces, and shape control.

We used a cubic

B-spline at the center of our domain of interest as the right hand side.

In order to reduce the amount of data, the polygonal lines are compressed with

B-spline curves.

We estimate the tensor-product

B-spline coefficients from values of |B| computed on a grid by a numerical code that numerically solves the Biot-Savart law numerically corresponding to the geometry of the solenoid and current bars that produce the magnetic field.

In the 1990s, CAD/CAM's mathematics advanced to surfaces, utilizing nonuniform rational

B-spline (NURBS) technology, which provided support for significantly more complex shapes.

These features include a

B-Spline tool, updated artistic media, scalable arrowheads, enhanced Connector and Dimension tools, and the new Segment Dimension tool.