Cubic Hermite spline

A cubic Hermite spline is a fancy math tool used for drawing smooth curves on a graph. Imagine you have a car traveling along a road, and you want to show how its speed changes over time. A regular graph might just connect the dots, but a Hermite spline creates a smooth curve that hugs the points more tightly.

Here's how it works: You choose two points on the graph and the car's speed at those points (for example, you might say the car is going 50 miles per hour at point A and 30 miles per hour at point B). The spline then uses mathematical formulas to construct a curve that matches those points and speeds.

But wait, there's more! Remember that the car is traveling along a road, and its speed isn't always constant. In fact, it might speed up or slow down between point A and point B. A Hermite spline can take this into account as well, creating a curve that's even smoother and more realistic.

So in summary, a cubic Hermite spline is a tool that lets you draw smooth, realistic curves on a graph by using math formulas to match specific points and speeds (and even changing speeds in between).