- Ryan Hirst
Some features of a function may make it unsuitable for ordinary polynomial approximation. Corners, closed curves, data errors. Consider the following Assertion: The order 3 spline offers no advantage over the order 3 polynomial. (-me) And a simple Counterexample: Circular arc: Here is a spline:
1. The ordinary 3rd degree polynomial through A, D, and sharing the tangents, is omitted. (why?) 2. The spline approximation can be made quite good. What is a practical maximum value of θ? For example, try the midpoint condition, and drag D to different positions. What is the maximum absolute error along the curve? Relative? 3. Why is the midpoint approximation better than the curvature condition?