We are given a closed spline with n control points that has

We are given a closed spline with n control points that has the following constraints for each curve segment: P(0) = o_k P(1) = p_k=1 P\" (0) = p_k=1 - 2 p_k + p_k+1 P\" (1) = p_k - 2p_k+1 + p_k+2 If there are n control points, there are n curve segments. Why? Prove that this spline satisfies C_2 continuity between adjacent segments. Does this spline offer local control? Why? d) What would be the degree of this spline? Why?

Solution

control point isa member of set of pointused to determine the shape of a spline curve or, more generally a surface or higher dimensional for bezier curve it has become customary to to refer to the d vector pi in a parametricrepresentationof curve or surface in d spaceas control points

bezier curve is parametric curve frequently used in computer graphicsandrelated fields generlizationof bezier curves to higher dimensions arecalled curve segements