This Java project provides a collection of algorithms and applications for various mathematical and image processing tasks.
The project encompasses the following main functionalities:
- Interpolation Methods: Implementations of various interpolation algorithms.
- Linear Algebra: Specifically, handling tridiagonal matrices and their solution.
- Fourier Transforms: Implementations of the Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT).
- Image Processing: A GUI application for image scaling using interpolation methods.
The project contains implementations of the following interpolation methods (all in src/interpolation):
- Nearest Neighbor Interpolation: (
NearestNeighbor.java) Finds the closest grid point for a given point and returns its value. - Piecewise Linear Interpolation: (
PiecewiseLinear.java) Performs linear interpolation between adjacent data points. - Cubic Spline Interpolation: (
CubicSpline.java) Uses cubic splines to interpolate a smooth function through given points. - Newton Polynomial Interpolation: (
NewtonPolynomial.java) Computes the Newton polynomial for interpolation. - 2D Interpolation: (
InterpolationMethod2D.java) Enables the application of 1D interpolation methods to 2D data, e.g., for image scaling. - Base Class: (
InterpolationMethod.java) Defines the common interface for all interpolation methods.
- Tridiagonal Matrix Solver: (
src/linalg/TridiagonalMatrix.java) Implements a solver for linear systems with tridiagonal matrices using the Thomas algorithm (Gaussian elimination without pivoting).
- Discrete Fourier Transform (DFT): (
src/fourier/DFT.java) Computes the DFT of a vector. - Fast Fourier Transform (FFT) and Inverse FFT (IFFT): (
src/fourier/IFFT.java) Implementations of the FFT and IFFT for efficient frequency analysis.< 66DE /li> - Complex Numbers: (
src/fourier/Complex.java) A utility class for representing complex numbers.
- Image Scaling: (
src/image/Picture.java,src/ui/ImageViewer.java) A GUI application that allows scaling images using various interpolation methods. The application (ImageViewer.java) provides a user interface for loading, saving, and scaling images.
- Plotter: (
src/ui/Plotter.java) A utility for visualizing data points and interpolation results.
- JUnit tests are available for some of the interpolation methods (
src/tests).
double[] x = {0, 1, 2, 3, 4};
double[] y = {1, 3, 2, 4, 1};
InterpolationMethod method = new CubicSpline();
method.init(0, 4, y);
double interpolatedValue = method.evaluate(2.5);
System.out.println("Interpolated Value: " + interpolatedValue);