How do B-Spline curves and surfaces work in 3D modeling? What are their advantages compared to other curve and surface approximation methods?
B-Spline curves and surfaces are mathematical representations used in 3D modeling to create smooth, flexible shapes. They are defined by control points and basis functions, which determine the curve’s shape and continuity. B-Splines offer local control, meaning that modifying a single control point only affects the nearby region of the curve or surface.
Compared to other methods like Bezier curves, B-Spline curves have several advantages. First, they provide better approximation capabilities due to their higher degree of flexibility. Second, they maintain a more uniform parameterization, resulting in evenly distributed control points and avoiding clustering. Third, B-Splines can represent complex shapes with fewer control points, reducing computational complexity and memory requirements.
