# Interpolation

## Introduction
This project implements numerical interpolation methods in C. The program allows the user to enter known data points either manually or from a file and estimate unknown values using interpolation techniques.

The program supports:
- Linear interpolation
- Polynomial interpolation using the Lagrange method

The project also generates files that are ready for visualization using gnuplot.

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## Features
- Manual point input
- File-based point input
- Linear interpolation
- Lagrange interpolation
- Interpolation of a single query point
- Generation of plot-ready output files
- Automatic generation of a gnuplot script
- Handling of invalid inputs and edge cases

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## Compilation

Compile the program using:

gcc interpolation.c -o interp -lm

Explanation:
- gcc → C compiler
- -o interp → creates executable named interp
- -lm → links the math library

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## Running the Program

Run the executable:

./interp

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## How to Use the Program

### Step 1 — Choose Input Method

1. Manual input
2. File input

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### Step 2 — Enter Points

Example:

0 0
1 1
2 4

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### Step 3 — Choose Program Mode

1. Interpolate a single value
2. Generate plot files

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## Plotting with Gnuplot

Install gnuplot:

sudo apt update
sudo apt install gnuplot -y

Run the plot:

gnuplot -persistent plot.gp

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## Generated Files

### output.txt
Contains interpolation data formatted for gnuplot.

### plot.gp
Automatically generated gnuplot script.

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## Libraries Used

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

Purpose:
- stdio.h → input/output and file handling
- stdlib.h → dynamic memory management
- math.h → mathematical operations

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## Build Requirements

The project requires:
- GCC compiler
- Linux terminal
- gnuplot

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