What is the process called when you think through intermediate points between known points? And when you predict points in advance?

The process when you fill in the intermediate points between known points is called interpolation. For example, if you have the values of a function at two points, interpolation allows you to find the values in between.

When you predict points ahead, that is, go beyond the known data, it is called extrapolation. It is used to forecast values outside the range of the original data.

Example: interpolation is used during animation between keyframes, while extrapolation predicts the movement of an object beyond the current data.