Cubic interpolation

Cubic interpolation is like drawing a picture by connecting three dots, but instead of drawing a straight line like we do with two dots, we draw a smooth curve with three dots.

Let's say we have three dots on a graph, and we want to find what the value would be at a point in between those dots. To do this, we use something called interpolation.

Interpolation is like guessing what the value might be based on the values we already know. It's like if we know the height of a person when they were 5 and 7 years old, we could guess what their height would be at age 6.

In cubic interpolation, we use a special method to make our guess more accurate. We draw a smooth, curved line through the three dots we have, so we can find the value we need somewhere in between them. This curved line is called a cubic spline.

The reason we use a cubic spline is that it gives us a very smooth and accurate curve. It's like drawing a picture with lots of tiny dots instead of just three big ones. The more dots we have, the more accurate the picture will be.

So, in summary, cubic interpolation is a way to guess what a value might be between three known values on a graph by drawing a smooth curve through those points using something called a cubic spline.