BezierCurve[{pt_1, pt_2, ...}] is a graphics primitive that represents a Bézier curve with control points pt_i.
BSplineCurve[{pt_1, pt_2, ...}] is a graphics primitive that represents a non-uniform rational B-spline curve with control points pt_i.
Mathematica has over 3000 built-in functions and other objects, all based on a single unified framework, and all carefully designed to work together, both in simple ...
Manipulate[expr, {u, u_min, u_max}] generates a version of expr with controls added to allow interactive manipulation of the value of u. Manipulate[expr, {u, u_min, u_max, ...