Table of Contents
An Introduction
Interpolation can be described as the mathematical procedure applied in order to derive value in between two points having a prescribed value. In simple words, we can describe it as a process of approximating the value of a given function at a given set of discrete points.
Interpolation is a method of constructing new data points within the range of a given set of data points, by fitting a function to the given data points. In other words, interpolation is a method of estimating the value of a function at a point, by using the values of the function at nearby points.
Examples of Interpolation
One form of interpolation is linear interpolation, which is used to estimate a value based on two known values. The estimated value is calculated using a line that connects the two known values.
Another form of interpolation is polynomial interpolation, which is used to estimate a value based on two or more known values. The estimated value is calculated using a polynomial equation that connects the known values.
Formula of Interpolation
The interpolation formula calculates the value of a point between two known points. The interpolation formula is y = f(x) = (x – a) (b – a) y + a.
Types of Interpolation Methods
There are three types of interpolation methods:
- Linear interpolation
- Quadratic interpolation
- Cubic interpolation
Why is the concept of Interpolation Important?
Interpolation is important because it allows for the smooth transition of one value to another. This is especially important in animation and graphics where a smooth transition is needed between frames.
Drawbacks of Interpolation Method
Some of the major drawbacks of interpolation method are as follows:
- The interpolated values may not be accurate.
- The interpolated values may be sensitive to the initial conditions.
- The interpolated values may be sensitive to the step size.
