ABSTRACT
This chapter explores methods focusing on polynomial interpolation, leading to polynomials of different degrees designed to fit the line. It looks at interpolation and extrapolation in the same way. Interpolation is finding the values of missing data in between the known values. Extrapolation extends the model outside of known data to "predict" new values for which no measure could have been taken. One of the biggest drawbacks to pure polynomial interpolation is that the values tend to diverge from true values at the endpoints, especially when dealing with higher-order polynomials. The chapter seeks piecewise approaches that use a number of different polynomials to represent the curve at different points. It considers Bezier curves provide a completely different alternative to the polynomial spline curves. Nearest neighbor may be the simplest possible option for sparse data interpolation. Interpolation is a key component of computer graphics.
