Creating NURBS Curves with MATLAB: A Practical Implementation Guide

To create a NURBS curve using MATLAB, you can follow these structured implementation steps: First, ensure MATLAB is properly installed on your system with the Curve Fitting Toolbox or Spline Toolbox, which provides essential NURBS manipulation functions. Open MATLAB and create a new script file (.m file) where you'll implement the NURBS algorithm. The core implementation involves three key components: control points, knot vector, and weights. Define the control points matrix specifying the curve's spatial coordinates. For 2D curves, use a 2×n matrix; for 3D curves, use a 3×n matrix where n represents the number of control points. Simultaneously, define the weights vector corresponding to each control point, which determines the curve's rational behavior. Construct the knot vector using the nrbmak function, which takes control points and knot sequence as inputs. The knot vector determines the parameterization and continuity of the curve. For open curves, use clamped knot vectors where the first and last knots have multiplicity equal to the curve order. Utilize MATLAB's NURBS evaluation functions like nrbeval to compute curve points at specified parameter values. This function implements the de Boor algorithm for efficient B-spline basis function calculation and combines it with rational weighting. Visualize the curve using plot for 2D or plot3 for 3D representations. For enhanced visualization, include control polygon display using line function and mark control points with scatter plots. The complete implementation typically involves 10-15 lines of MATLAB code, leveraging functions from the Spline Toolbox for robust NURBS manipulation. This approach enables precise curve generation for applications in computer-aided design, automotive styling, and aerospace engineering where complex curvature control is required.