In what fields is linear interpolation commonly used?

Linear interpolation is a simple interpolation method that estimates the value of an unknown point by drawing a straight line between two known points. This method is widely used in many fields, and the following are some common ones:

1. Computer graphics: In computer graphics, linear interpolation is commonly used in image processing and animation. For example, when changing the size of an image or rotating an image, linear interpolation can be used to smoothly change the color of the pixels. In addition, when creating animations, linear interpolation can be used to generate successive frames.

2. Data Visualization: In data visualization, linear interpolation is often used to create smooth curves or surfaces. For example, when plotting temperature maps or topographic maps, linear interpolation can be used to fill in blank areas.

3. Signal Processing: In signal processing, linear interpolation is often used to estimate the value of a discrete signal. For example, when sampling a signal, linear interpolation can be used to estimate the value of the signal between sampling intervals.

4. Numerical Analysis: In numerical analysis, linear interpolation is often used to solve differential and integral equations. For example, when solving partial differential equations using the finite difference method or the finite element method, linear interpolation can be used to estimate the value of the unknown solution.

5. Machine learning: In machine learning, linear interpolation is commonly used for preprocessing data and feature engineering. For example, when dealing with missing values or outliers, linear interpolation can be used to estimate the missing or outlier values. In addition, when creating new features, linear interpolation can be used to generate continuous features.

6. Finance: In finance, linear interpolation is often used to estimate changes in stock prices or exchange rates. For example, when calculating the average growth rate or volatility of historical data, linear interpolation can be used to estimate future trends.

7. Geographic Information Systems: In geographic information systems, linear interpolation is commonly used to estimate the height of a geographic location or terrain. For example, when extracting terrain information from aerial or satellite images, linear interpolation can be used to estimate the height of an unknown location.