MATLAB Code Implementation for B-Spline Curve Generation

B-spline curves are mathematical curve representations widely used in computer graphics and CAD modeling. Compared to Bézier curves, B-splines offer local control properties and greater flexibility, enabling adjustments to local curve segments without altering the overall shape. Implementing B-spline curve generation in MATLAB typically involves these core steps: First, define control points that determine the approximate shape of the curve. Second, establish a knot vector that influences the curve's parameterization method. Finally, calculate points on the curve based on B-spline basis functions. For open curves, uniform knot vectors are commonly used, while closed curves require special periodic treatment. In code implementation, the `spcol` function can be utilized to generate B-spline basis functions, while `fnplt` provides direct curve plotting capabilities. The Rilling version implementation may include support for HHT (Hilbert-Huang Transform) plugins, an advanced tool for non-stationary signal analysis. This version might be optimized for specific application scenarios, such as improving computational efficiency or enhancing curve smoothness control through algorithmic improvements like adaptive knot vector generation. Developers should pay attention to several key parameters: curve degree (determining smoothness), control point weights (affecting curve shape), and knot vector distribution strategies. Higher-degree B-splines produce smoother curves but require more computational resources, necessitating a balance between real-time performance and precision requirements. Code implementation often involves using `spapi` for spline approximation or `bspline` functions with carefully tuned tolerance parameters. This implementation serves as a practical case study for learning B-spline theory. By adjusting parameters and observing curve variations, users can intuitively understand how control points and knot vectors influence curve characteristics, which holds significant importance for applications like 3D modeling and motion trajectory planning. The code typically includes visualization components using `plot` functions with customizable line properties for clear demonstration of parameter effects.