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 p0 and an ending point p1 with starting tangent m0 and ending tangent m1, the polynomial can be defined by
where t varies from 0 to 1 inclusive.
The four Hermite basis functions can be defined as