# Hermite Curves

In the mathematical subfield of numerical analysis a **cubic Hermite spline**, named in honor of Charles Hermite (Hermite is pronounced *air MEET*), is a third-degree spline with each polynomial of the spline in Hermite form. The Hermite form consists of two control points and two control tangents for each polynomial.

On each subinterval, given a starting point **p**_{0} and an ending point **p**_{1} with starting tangent **m**_{0} and ending tangent **m**_{1}, the polynomial can be defined by

where t varies from 0 to 1 inclusive. The four Hermite basis functions can be defined as