Drawing Uniform Cubic B-Spline Curves with MATLAB

The process of drawing uniform cubic B-spline curves using MATLAB can be described through the following key steps: 1. Data Import: First, import the required data into MATLAB, which typically includes x and y coordinate values or other relevant control point data. In MATLAB implementation, this is commonly done using array variables or loading data from external files. 2. Knot Vector Calculation: Next, calculate the knot vector - a vector containing knot values. For uniform cubic B-splines, the knot vector is generated with uniform spacing between knots. The calculation considers the degree of the B-spline curve (3 for cubic) and the number of control points, typically using algorithms that ensure proper parameterization. 3. Basis Function Computation: Calculating basis functions is a crucial step in B-spline curve generation. These functions, determined by the knot vector, degree, and control point count, are computed recursively using the Cox-de Boor algorithm. MATLAB implementations often utilize built-in functions or custom recursive code to evaluate these basis functions efficiently. 4. Coordinate Point Calculation: Finally, multiply the computed basis functions with the control point values and sum the results to obtain coordinate points along the B-spline curve. This involves matrix operations where basis function values are weighted by control point coordinates to generate the final curve points. This methodology is not limited to uniform cubic B-splines but can be extended to other B-spline curve types with appropriate modifications to the knot vector generation and basis function calculations. Therefore, the MATLAB-based approach for drawing B-spline curves offers broad applicability and significant reference value for various computational geometry applications.