This program interactively demonstrates a non-uniform rational B-spline curve (NURBS) and the N_i,m blending functions. This page accompanies the planned second edition of 3D Computer Graphics: A mathematical approach with OpenGL, by Sam Buss, Cambridge University Press, 2003. See that book for the mathematical background. The latest draft of the second edition is available online from the web page for the second edition.

Instructions:

• First select the degree k or the order m, and the number of knot positions. The degree can be no larger than 3; the order can be no larger than 4.
• Optionally set the minimum and maximum values for the knots.
• In the first graph, click and drag the knot positions to change their values. Do this, by clicking on the small red circles on the number line Repeated knot positions stack up vertically.
• Click an "N_i,m" button to highlight a single knot position and blending function, and the corresponding control point.
• In the lower graph, move a control point by clicking and dragging to the desired position.

Parameter settings:

Degree (k):	Number of knots:
Order (m):	Number of control points:

Reset Knots, equally spaced     Reset Knots, with end multiplicities

Knot Positions and Blending Functions

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Control Points and the NURBS Curve

Reset Control Points              Show Labels          Show Control Polygon

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