What is the Difference Between Bezier Curve and B-Spline Curve?

The main difference between Bezier curves and B-spline curves lies in the control points and the way they are used to define the shape of the curve. Here are the key differences:

Control Points: In a Bezier curve, all control points are on the curve itself, and there are handlebars for adjustments. In contrast, B-spline curves have control points off the curve, creating a cage-like system for control.
Local Control: B-spline curves allow for local control over the curve surface, meaning that changing any control point only affects a specific segment of the curve. In Bezier curves, changing any control point affects the entire curve.
Flexibility: B-spline curves are specified by Bernstein basis functions, which have limited flexibility. Bezier curves, on the other hand, can be specified with boundary conditions, a characterizing matrix, or blending function.
Degree: The degree of a Bezier curve is determined by the number of control points used to approximate the curve segment. B-spline curves allow the order of the basis function to change, hence the degree of the resulting curve can vary.
Smoothness: B-spline curves possess a high degree of smoothness at the places where the polynomial pieces connect. Bezier curves may not have the same level of smoothness.

In summary, Bezier curves use control points on the curve itself, while B-spline curves use control points off the curve. B-spline curves allow for local control and have limited flexibility, whereas Bezier curves offer more flexibility but affect the entire curve when a control point is changed. B-spline curves also provide a higher degree of smoothness compared to Bezier curves.