Understanding cubic Hermite splines
The most common spline type used in animation for games is a cubic Hermite spline. Unlike Bézier, a Hermite spline doesn't use points in space for its control; rather, it uses the tangents of points along the spline. You still have four values, as with a Bézier spline, but they are interpreted differently.
With the Hermite spline, you don't have two points and two control points; instead, you have two points and two slopes. The slopes are also referred to as tangents—throughout the rest of this chapter, the slope and tangent terms will be used interchangeably. The point basis functions for Hermite splines look as follows:
Figure 8.7: The point basis functions of Hermite splines
When given the point basis functions, you can implement the spline evaluation function similar to how the Bézier interpolation function was implemented:
template<typename T> T Hermite(float t, T&...
