NURBS Curve Plotting

NURBS (Non-Uniform Rational B-Spline) curves are mathematical tools widely used in computer graphics and CAD modeling, capable of flexibly controlling curve shapes by adjusting control vertices and weight parameters. Implementing NURBS curve plotting in MATLAB primarily relies on basis function computation and parametric processing.

The program's core lies in the basis function subroutines, which calculate B-spline basis function values for different degrees. Through recursive or iterative approaches, these functions efficiently compute basis function values for each parameter point, determining the curve's position at that point. The implementation typically involves algorithms like de Boor's recursion for basis function evaluation. Control vertices directly influence the curve's shape, while weight parameters further adjust convexity or concavity in specific intervals.

Users can observe real-time curve modifications by adjusting control vertex coordinates and weight values. For example, increasing a control vertex's weight pulls the curve closer to that vertex, while repositioning vertices alters the overall curve trajectory. This flexibility makes NURBS curves essential for industrial design and animation production. The MATLAB code structure typically includes functions for knot vector generation, basis function calculation using algorithms like Cox-de Boor recursion, and weighted control point summation.

This program was developed in MATLAB 2008a and suits academic research or engineering practice. Through simple parameter adjustments, users can intuitively understand NURBS curves' mathematical properties and rapidly verify how different control point configurations affect curve shapes. Key implementation functions may include nrbasis() for basis function computation and nrbmak() for constructing NURBS curves from control points and knots.