Polynomial Interpolation
An n-th degree polynomial fits a curve to n+1 points
- Example: fit a second degree curve to three points
- x(u)= au2 + bu + c
- control points to interpolate: (u1, x1), (u2, x2), (u3, x3)
- solve for coefficients (a, b, c): 3 linear eqns, 3 unknowns
- called Lagrange Interpolation
- result is a curve that is too wiggly, change to any control point affects entire curve (nonlocal) – this method is poor
We usually want the curve to be as smooth as possible
- minimize the wiggles
- high-degree polynomials are bad
Good approach: simulate springy wire