Quartic and quintic polynomial interpolation

Basis polynomials of quartic and quintic parametric interpolations are discussed to interpolate given data points. The aim is constructing a curve that exactly interpolates all data points. Besides, the shape of curve can be controlled by using parameters t and changing the magnitude of tangents, α and β. When large number of data points is given, piecewise polynomial interpolation will be used. Therefore, quartic and quintic interpolations also have been discussed to interpolate large number of data points.