What is Interpolation?
In many domains of [[science]], [[measurement]]s are done. If these measurements are drawn in a [[graph]], they will be shown as simple unconnected points. Such data are called data points, or [[Discrete mathematics|discrete]]. Handling and analysis of the data is easier, if it can be described using a [[continuous function]], or a line connecting the discrete data point together. In order to do this, the line between two measurements, or data points, need to be created. This process of connecting the data points together with a line called '''interpolation'''. There are different ways to invent the data, each method has its benefits and drawbacks. The simplest method is drawing a straight line between two data points, which is not very accurate. Very often, [[polynomial]]s are used to create a more accurate representation. Even if some of the data is wrong, in many cases, the results of this interpolation are usable, either as a replacement for missing data points, or as a tool to help understand more complicated data. Interpolation tries to find the values between two known points of data. It is not to be confused with [[extrapolation]], which is a similar process that tries to find data points at the edge or outside the currently defined points. ==Uses== The primary use of interpolation is to help users, be they scientists, photographers, engineers or mathematicians, determine what data might exist outside of their collected data. Outside the domain of mathematics, interpolation is frequently used to [[scaling|scale]] images and to convert the [[sampling rate]] of digital signals. In the domain of science, a scientist may need to use a computer to calculate a complicated function. However, if that function takes a very long time to compute, it may make her experiments difficult or impossible to run properly. So, she might use interpolation to create a slightly less complicated version of her function, which takes less computational time and energy to run. This interpolated function should achieve the s