Bilinear Interpolation in Python What is Bilinear Interpolation?

Linear Interpolation in mathematics helps curve fitting by using linear polynomials that make new data points between a specific range of a discrete set of definite data points.

The term Bilinear Interpolation is an extension to linear interpolation that performs the interpolation of functions containing two variables (for example, x and y) on a rectilinear two-dimensional grid.

This tutorial will demonstrate how to perform such Bilinear Interpolation in Python.

Creating a function to perform bilinear interpolation in Python

We can implement the logic for Bilinear Interpolation in a function. This function works for a collection of 4 points. It is a very basic implementation of the mathematical formula for Bilinear Interpolation.

See the code below.

Output:

4

Using the scipy.interpolate.interp2d() function to perform bilinear interpolation in Python

The scipy library helps perform different mathematical and scientific calculations like linear algebra, integration, and many more.

The scipy.interpolate.interp2d() function performs the interpolation over a two-dimensional grid. This method can handle more complex problems. This method represents functions containing x, y, and z, array-like values that make functions like z = f(x, y). It will return the scalar value of z.

We can use it as shown below.

To use this function, we need to understand the three main parameters.

• x, y (array_like) – This parameter defines the data points of the coordinates. If the data points lie on a regular grid, then x can represent the column coordinates and y can represent the row coordinates.
• z (array_like) – This parameter defines the value of the function to interpolate at the given data points.
• kind ('linear', 'cubic', 'quintic') – This parameter informs the kind of spline interpolation to use. The default value of this parameter is linear.

Now let us see how to perform bilinear interpolation using this method.

Output: In the above code,

• The numpy.arange() function returns evenly spaced values within a given interval. This function takes the values in the form of an array.
• The numpy.meshgrid() function creates a rectangular grid with the help of one-dimensional arrays that represent cartesian indexing or matrix indexing.
• Finally, the cos() function of the numpy library helps in finding the cosine value. We use this as the main function in the above code, i.e., z.

import_contacts

You may also like: Related Posts

• 13 January

Check if variable is String in python

Table of ContentsHow to check if a given variable is of the string type in Python?Using the isinstance() function.Using the type() function.Check if function parameter is String In this post, we will see what is a string in Python and how to check whether a given variable is a string or not. There are many […]

• 13 January

Count number of characters in a string in python

Table of ContentsWays to count the number of characters in a string in PythonUsing the len() functionUsing the for loopUsing the collections.Counter classConclusion In this post, we will see how to count number of characters in a String in Python. We can think of strings as a collection of characters, with every character at a […]

• 12 January

Pandas apply function to column

Table of ContentsHow do I apply function to column in pandas?Using dataframe.apply() functionUsing lambda function along with the apply() functionUsing dataframe.transform() functionUsing map() functionUsing NumPy.square() function We make use of the Pandas dataframe to store data in an organized and tabular manner. Sometimes there, is a need to apply a function over a specific column […]

• 12 January

How to Copy File in Python?

Table of ContentsCopy file using the shutil module in PythonCopy file using the copyfileobj() function in PythonCopy file using the copyfile() function in PythonCopy file using the copy() function in PythonCopy file using the copy2() function in PythonCopy file using the operating system command in PythonCopy file using the os module in PythonCopy file using […]

• 11 January

What is % in Python?

Table of ContentsWhat is % Operator in Python?The % Operator with strings in pythonThe % Operator as a placeholder for variables  in pythonThe % Operator as format specifiers in pythonConclusion In this article, we will cover what is % in Python and what are different ways to use % in Python. In python, there are […]

• 09 January

Convert set to String in Python

Table of ContentsWays to convert set to string in PythonUsing the str() functionUsing the repr() functionUsing the join() functionUsing the map() functionConclusion Sets are an unordered collection of elements in Python. It does not contain duplicate elements and can be defined using the set() function in Python. Ways to convert set to string in Python […]

Subscribe to our newletter

Get quality tutorials to your inbox. Subscribe now.